From eae42ec1338de1af15a992e7d1633d78346cdc50 Mon Sep 17 00:00:00 2001
From: Caleb Brakensiek <69546117+cbrakensiek@users.noreply.github.com>
Date: Sat, 17 Apr 2021 10:46:12 -0700
Subject: [PATCH 01/33] adding remeshing functions

---
 include/geometrycentral/surface/remeshing.h |  24 ++
 src/CMakeLists.txt                          |   2 +
 src/surface/remeshing.cpp                   | 326 ++++++++++++++++++++
 3 files changed, 352 insertions(+)
 create mode 100644 include/geometrycentral/surface/remeshing.h
 create mode 100644 src/surface/remeshing.cpp

diff --git a/include/geometrycentral/surface/remeshing.h b/include/geometrycentral/surface/remeshing.h
new file mode 100644
index 00000000..ffc370f3
--- /dev/null
+++ b/include/geometrycentral/surface/remeshing.h
@@ -0,0 +1,24 @@
+#pragma once
+
+#include "geometrycentral/surface/manifold_surface_mesh.h"
+#include "geometrycentral/surface/vertex_position_geometry.h"
+
+#include <queue>
+
+namespace geometrycentral {
+namespace surface {
+
+// makes all triangles delaunay
+void fixDelaunay(SurfaceMesh& mesh, VertexPositionGeometry& geometry);
+// average positions of vertices based on surrounding vertex positions
+void smoothByLaplacian(SurfaceMesh& mesh, VertexPositionGeometry& geometry);
+// average positions of vertices based on surrounding triangle circumenters
+void smoothByCircumcenter(SurfaceMesh& mesh, VertexPositionGeometry& geometry);
+// applies splits and collapses to adjust edge lengths based on the curvature
+// flatLength: specifies how long the target edge length should be in flat regions
+// epsilon: controls how much variation in target length occurs due to curvature
+// minLength: specifies the minimum possible length an edge could become
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength, double epsilon, double minLength, bool curvatureAdaptive = true);
+
+} // namespace surface
+} // namespace geometrycentral
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index 95c0b1f7..fbf7307b 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -43,6 +43,7 @@ SET(SRCS
   surface/fast_marching_method.cpp
   surface/uniformize.cpp
   surface/parameterize.cpp
+  surface/remeshing.cpp
   surface/surgery.cpp
   surface/simple_idt.cpp
   surface/exact_polyhedral_geodesics.cpp
@@ -117,6 +118,7 @@ SET(HEADERS
   ${INCLUDE_ROOT}/surface/mesh_ray_tracer.h
   ${INCLUDE_ROOT}/surface/parameterize.h
   ${INCLUDE_ROOT}/surface/quadric_error_simplification.h
+  ${INCLUDE_ROOT}/surface/remeshing.h
   ${INCLUDE_ROOT}/surface/rich_surface_mesh_data.h
   ${INCLUDE_ROOT}/surface/rich_surface_mesh_data.ipp
   ${INCLUDE_ROOT}/surface/polygon_soup_mesh.h
diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
new file mode 100644
index 00000000..b3000f02
--- /dev/null
+++ b/src/surface/remeshing.cpp
@@ -0,0 +1,326 @@
+#include "geometrycentral/surface/remeshing.h"
+
+namespace geometrycentral {
+namespace surface {
+
+using std::queue;
+
+Vector3 vertexNormal(VertexPositionGeometry& geometry, Vertex v)
+{
+    Vector3 norm = Vector3::zero();
+    for(Corner c : v.adjacentCorners()){
+        norm += geometry.cornerAngle(c) * geometry.faceNormal(c.face());
+    }
+    return normalize(norm);
+}
+
+inline Vector3 projectToPlane(Vector3 v, Vector3 norm)
+{
+    return v - norm * dot(norm, v);
+}
+
+inline Vector3 edgeMidpoint(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e)
+{
+    Vector3 endPos1 = geometry.inputVertexPositions[e.halfedge().tailVertex()];
+    Vector3 endPos2 = geometry.inputVertexPositions[e.halfedge().tipVertex()];
+    return (endPos1+endPos2)/2;
+}
+
+Vector3 findCircumcenter(Vector3 p1, Vector3 p2, Vector3 p3)
+{
+    // barycentric coordinates of circumcenter
+    double a = (p3 - p2).norm();
+    double b = (p3 - p1).norm();
+    double c = (p2 - p1).norm();
+    double a2 = a * a;
+    double b2 = b * b;
+    double c2 = c * c;
+    Vector3 O{a2 * (b2 + c2 - a2), b2 * (c2 + a2 - b2), c2 * (a2 + b2 - c2)};
+    // normalize to sum of 1
+    O /= O[0] + O[1] + O[2];
+    // change back to space
+    return O[0] * p1 + O[1] * p2 + O[2] * p3;
+}
+
+Vector3 findCircumcenter(VertexPositionGeometry& geometry, Face f)
+{
+    // retrieve the face's vertices
+    int index = 0;
+    Vector3 p[3];
+    for (Vertex v0 : f.adjacentVertices())
+    {
+        p[index] = geometry.inputVertexPositions[v0];
+        index++;
+    }
+    return findCircumcenter(p[0], p[1], p[2]);
+}
+
+bool isDelaunay(VertexPositionGeometry& geometry, Edge e)
+{
+    float angle1 = geometry.cornerAngle(e.halfedge().next().next().corner());
+    float angle2 = geometry.cornerAngle(e.halfedge().twin().next().next().corner());
+    return angle1 + angle2 <= PI;
+}
+
+inline double diamondAngle(Vector3 a, Vector3 b, Vector3 c, Vector3 d) // dihedral angle at edge a-b
+{
+    Vector3 n1 = cross(b-a, c-a);
+    Vector3 n2 = cross(b-d, a-d);
+    return PI-angle(n1, n2);
+}
+
+inline bool checkFoldover(Vector3 a, Vector3 b, Vector3 c, Vector3 x, double angle)
+{
+    return diamondAngle(a, b, c, x) < angle;
+}
+
+bool shouldCollapse(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e)
+{
+    std::vector<Halfedge> toCheck;
+    Vertex v1 = e.halfedge().vertex();
+    Vertex v2 = e.halfedge().twin().vertex();
+    Vector3 midpoint = edgeMidpoint(mesh, geometry, e);
+    // find (halfedge) link around the edge, starting with those surrounding v1
+    Halfedge he = v1.halfedge();
+    Halfedge st = he;
+    do{
+        he = he.next();
+        if(he.vertex() != v2 && he.next().vertex() != v2){
+            toCheck.push_back(he);
+        }
+        he = he.next().twin();
+    }
+    while(he != st);
+    // link around v2
+    he = v2.halfedge();
+    st = he;
+    do{
+        he = he.next();
+        if(he.vertex() != v1 && he.next().vertex() != v1){
+            toCheck.push_back(he);
+        }
+        he = he.next().twin();
+    }
+    while(he != st);
+    
+    // see if the point that would form after a collapse would cause a major foldover with surrounding edges
+    for(Halfedge he0 : toCheck){
+        Halfedge heT = he0.twin();
+        Vertex v1 = heT.vertex();
+        Vertex v2 = heT.next().vertex();
+        Vertex v3 = heT.next().next().vertex();
+        Vector3 a = geometry.inputVertexPositions[v1];
+        Vector3 b = geometry.inputVertexPositions[v2];
+        Vector3 c = geometry.inputVertexPositions[v3];
+        if(checkFoldover(a, b, c, midpoint, 2)){
+            return false;
+        }
+    }
+    return true;
+}
+
+double getSmoothMeanCurvature(VertexPositionGeometry& geometry, Vertex v)
+{
+    double A = geometry.vertexDualArea(v);
+    double S = geometry.vertexMeanCurvature(v);
+    double K = S / A;
+    return K;
+}
+
+// flatLength: specifies how long the target edge length should be in flat regions
+// epsilon: controls how much variation in target length occurs due to curvature
+
+double findMeanTargetL(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e, double flatLength, double epsilon)
+{
+    double averageH = 0;
+    for (Vertex v : e.adjacentVertices()) {
+        averageH += getSmoothMeanCurvature(geometry, v);
+    }
+    averageH /= 2;
+    double L = flatLength * epsilon / (fabs(averageH) + epsilon);
+    return L;
+}
+
+
+
+void fixDelaunay(SurfaceMesh& mesh, VertexPositionGeometry& geometry)
+{
+    // queue of edges to check if Delaunay
+    queue<Edge> toCheck;
+    // true if edge is currently in toCheck
+    EdgeData<bool> inQueue(mesh);
+    // start with all edges
+    for (Edge e : mesh.edges())
+    {
+        toCheck.push(e);
+        inQueue[e] = true;
+    }
+    // counter and limit for number of flips
+    int flipMax = 100 * mesh.nVertices();
+    int flipCnt = 0;
+    while (!toCheck.empty() && flipCnt < flipMax)
+    {
+        Edge e = toCheck.front();
+        toCheck.pop();
+        inQueue[e] = false;
+        // if not Delaunay, flip edge and enqueue the surrounding "diamond" edges (if not already)
+        if (!e.isBoundary() && !isDelaunay(geometry, e))
+        {
+            flipCnt++;
+            Halfedge he = e.halfedge();
+            Halfedge he1 = he.next();
+            Halfedge he2 = he1.next();
+            Halfedge he3 = he.twin().next();
+            Halfedge he4 = he3.next();
+
+            if (!inQueue[he1.edge()])
+            {
+                toCheck.push(he1.edge());
+                inQueue[he1.edge()] = true;
+            }
+            if (!inQueue[he2.edge()])
+            {
+                toCheck.push(he2.edge());
+                inQueue[he2.edge()] = true;
+            }
+            if (!inQueue[he3.edge()])
+            {
+                toCheck.push(he3.edge());
+                inQueue[he3.edge()] = true;
+            }
+            if (!inQueue[he4.edge()])
+            {
+                toCheck.push(he4.edge());
+                inQueue[he4.edge()] = true;
+            }
+            mesh.flip(e);
+        }
+    }
+}
+
+void smoothByLaplacian(SurfaceMesh& mesh, VertexPositionGeometry& geometry)
+{
+    // smoothed vertex positions
+    VertexData<Vector3> newVertexPosition(mesh);
+    for (Vertex v : mesh.vertices())
+    {
+        if(v.isBoundary())
+        {
+            newVertexPosition[v] = geometry.inputVertexPositions[v];
+        }
+        else
+        {
+            // calculate average of surrounding vertices
+            newVertexPosition[v] = Vector3::zero();
+            for (Vertex j : v.adjacentVertices())
+            {
+                newVertexPosition[v] += geometry.inputVertexPositions[j];
+            }
+            newVertexPosition[v] /= v.degree();
+            // and project the average to the tangent plane
+            Vector3 updateDirection = newVertexPosition[v] - geometry.inputVertexPositions[v];
+            updateDirection = projectToPlane(updateDirection, vertexNormal(geometry, v));
+            
+            newVertexPosition[v] = geometry.inputVertexPositions[v] + 1*updateDirection;
+        }
+    }
+    // update final vertices
+    for (Vertex v : mesh.vertices())
+    {
+        geometry.inputVertexPositions[v] = newVertexPosition[v];
+    }
+}
+
+void smoothByCircumcenter(SurfaceMesh& mesh, VertexPositionGeometry& geometry)
+{
+    geometry.requireFaceAreas();
+    // smoothed vertex positions
+    VertexData<Vector3> newVertexPosition(mesh);
+    for (Vertex v : mesh.vertices())
+    {
+        newVertexPosition[v] = geometry.inputVertexPositions[v]; // default
+        if(!v.isBoundary())
+        {
+            Vector3 updateDirection = Vector3::zero();
+            for (Face f : v.adjacentFaces())
+            {
+                // add the circumcenter weighted by face area to the update direction
+                Vector3 circum = findCircumcenter(geometry, f);
+                updateDirection += geometry.faceArea(f) * (circum - geometry.inputVertexPositions[v]);
+            }
+            updateDirection /= (3 * geometry.vertexDualArea(v));
+            // project update direction to tangent plane
+            updateDirection = projectToPlane(updateDirection, vertexNormal(geometry, v));
+            Vector3 newPos = geometry.inputVertexPositions[v] + .5 * updateDirection;
+            newVertexPosition[v] = newPos;
+        }
+    }
+    // update final vertices
+    for (Vertex v : mesh.vertices())
+    {
+        geometry.inputVertexPositions[v] = newVertexPosition[v];
+    }
+}
+
+
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength, double epsilon, double minLength, bool curvatureAdaptive)
+{
+    bool didSplitOrCollapse = false;
+    // queues of edges to CHECK to change
+    std::vector<Edge> toSplit;
+    std::vector<Edge> toCollapse;
+    
+    for(Edge e : mesh.edges())
+    {
+        toSplit.push_back(e);
+    }
+    
+    // actually splitting
+    while(!toSplit.empty())
+    {
+        Edge e = toSplit.back();
+        toSplit.pop_back();
+        double length_e = geometry.edgeLength(e);
+        double threshold = (curvatureAdaptive) ? findMeanTargetL(mesh, geometry, e, flatLength, epsilon) : flatLength;
+        if(length_e > minLength && length_e > threshold * 1.5)
+        {
+            Vector3 newPos = edgeMidpoint(mesh, geometry, e);
+            Halfedge he = mesh.splitEdgeTriangular(e);
+            didSplitOrCollapse = true;
+            Vertex newV = he.vertex();
+            geometry.inputVertexPositions[newV] = newPos;
+        }
+        else
+        {
+            toCollapse.push_back(e);
+        }                
+        
+    }
+    // actually collapsing
+    while(!toCollapse.empty())
+    {
+        Edge e = toCollapse.back();
+        toCollapse.pop_back();
+        if(e.halfedge().next().getIndex() != INVALID_IND) // make sure it exists
+        {
+            double threshold = (curvatureAdaptive) ? findMeanTargetL(mesh, geometry, e, flatLength, epsilon) : flatLength;
+            if(geometry.edgeLength(e) < threshold * 0.5)
+            {
+                Vector3 newPos = edgeMidpoint(mesh, geometry, e);
+                if(shouldCollapse(mesh, geometry, e)) {
+                    Vertex v = mesh.collapseEdgeTriangular(e);
+                    didSplitOrCollapse = true;
+                    if (v != Vertex()) {
+                        if(!v.isBoundary()) {
+                            geometry.inputVertexPositions[v] = newPos;
+                        }
+                    }
+                }
+            }
+        }
+    }
+    return didSplitOrCollapse;
+}
+
+} // namespace surface
+} // namespace geometrycentral

From 78cb10b57e2f325b55347a4dadf6c8c2eaa2ef3f Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Thu, 31 Mar 2022 16:10:17 -0400
Subject: [PATCH 02/33] Formatting

---
 include/geometrycentral/surface/remeshing.h |   6 +-
 src/surface/remeshing.cpp                   | 494 +++++++++-----------
 2 files changed, 230 insertions(+), 270 deletions(-)

diff --git a/include/geometrycentral/surface/remeshing.h b/include/geometrycentral/surface/remeshing.h
index ffc370f3..106361d3 100644
--- a/include/geometrycentral/surface/remeshing.h
+++ b/include/geometrycentral/surface/remeshing.h
@@ -10,15 +10,19 @@ namespace surface {
 
 // makes all triangles delaunay
 void fixDelaunay(SurfaceMesh& mesh, VertexPositionGeometry& geometry);
+
 // average positions of vertices based on surrounding vertex positions
 void smoothByLaplacian(SurfaceMesh& mesh, VertexPositionGeometry& geometry);
+
 // average positions of vertices based on surrounding triangle circumenters
 void smoothByCircumcenter(SurfaceMesh& mesh, VertexPositionGeometry& geometry);
+
 // applies splits and collapses to adjust edge lengths based on the curvature
 // flatLength: specifies how long the target edge length should be in flat regions
 // epsilon: controls how much variation in target length occurs due to curvature
 // minLength: specifies the minimum possible length an edge could become
-bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength, double epsilon, double minLength, bool curvatureAdaptive = true);
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength, double epsilon,
+                       double minLength, bool curvatureAdaptive = true);
 
 } // namespace surface
 } // namespace geometrycentral
diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index b3000f02..6c7ccd45 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -5,321 +5,277 @@ namespace surface {
 
 using std::queue;
 
-Vector3 vertexNormal(VertexPositionGeometry& geometry, Vertex v)
-{
-    Vector3 norm = Vector3::zero();
-    for(Corner c : v.adjacentCorners()){
-        norm += geometry.cornerAngle(c) * geometry.faceNormal(c.face());
-    }
-    return normalize(norm);
+Vector3 vertexNormal(VertexPositionGeometry& geometry, Vertex v) {
+  Vector3 norm = Vector3::zero();
+  for (Corner c : v.adjacentCorners()) {
+    norm += geometry.cornerAngle(c) * geometry.faceNormal(c.face());
+  }
+  return normalize(norm);
 }
 
-inline Vector3 projectToPlane(Vector3 v, Vector3 norm)
-{
-    return v - norm * dot(norm, v);
-}
+inline Vector3 projectToPlane(Vector3 v, Vector3 norm) { return v - norm * dot(norm, v); }
 
-inline Vector3 edgeMidpoint(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e)
-{
-    Vector3 endPos1 = geometry.inputVertexPositions[e.halfedge().tailVertex()];
-    Vector3 endPos2 = geometry.inputVertexPositions[e.halfedge().tipVertex()];
-    return (endPos1+endPos2)/2;
+inline Vector3 edgeMidpoint(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e) {
+  Vector3 endPos1 = geometry.vertexPositions[e.halfedge().tailVertex()];
+  Vector3 endPos2 = geometry.vertexPositions[e.halfedge().tipVertex()];
+  return (endPos1 + endPos2) / 2;
 }
 
-Vector3 findCircumcenter(Vector3 p1, Vector3 p2, Vector3 p3)
-{
-    // barycentric coordinates of circumcenter
-    double a = (p3 - p2).norm();
-    double b = (p3 - p1).norm();
-    double c = (p2 - p1).norm();
-    double a2 = a * a;
-    double b2 = b * b;
-    double c2 = c * c;
-    Vector3 O{a2 * (b2 + c2 - a2), b2 * (c2 + a2 - b2), c2 * (a2 + b2 - c2)};
-    // normalize to sum of 1
-    O /= O[0] + O[1] + O[2];
-    // change back to space
-    return O[0] * p1 + O[1] * p2 + O[2] * p3;
+Vector3 findCircumcenter(Vector3 p1, Vector3 p2, Vector3 p3) {
+  // barycentric coordinates of circumcenter
+  double a = (p3 - p2).norm();
+  double b = (p3 - p1).norm();
+  double c = (p2 - p1).norm();
+  double a2 = a * a;
+  double b2 = b * b;
+  double c2 = c * c;
+  Vector3 O{a2 * (b2 + c2 - a2), b2 * (c2 + a2 - b2), c2 * (a2 + b2 - c2)};
+  // normalize to sum of 1
+  O /= O[0] + O[1] + O[2];
+  // change back to space
+  return O[0] * p1 + O[1] * p2 + O[2] * p3;
 }
 
-Vector3 findCircumcenter(VertexPositionGeometry& geometry, Face f)
-{
-    // retrieve the face's vertices
-    int index = 0;
-    Vector3 p[3];
-    for (Vertex v0 : f.adjacentVertices())
-    {
-        p[index] = geometry.inputVertexPositions[v0];
-        index++;
-    }
-    return findCircumcenter(p[0], p[1], p[2]);
+Vector3 findCircumcenter(VertexPositionGeometry& geometry, Face f) {
+  // retrieve the face's vertices
+  int index = 0;
+  Vector3 p[3];
+  for (Vertex v0 : f.adjacentVertices()) {
+    p[index] = geometry.vertexPositions[v0];
+    index++;
+  }
+  return findCircumcenter(p[0], p[1], p[2]);
 }
 
-bool isDelaunay(VertexPositionGeometry& geometry, Edge e)
-{
-    float angle1 = geometry.cornerAngle(e.halfedge().next().next().corner());
-    float angle2 = geometry.cornerAngle(e.halfedge().twin().next().next().corner());
-    return angle1 + angle2 <= PI;
+bool isDelaunay(VertexPositionGeometry& geometry, Edge e) {
+  float angle1 = geometry.cornerAngle(e.halfedge().next().next().corner());
+  float angle2 = geometry.cornerAngle(e.halfedge().twin().next().next().corner());
+  return angle1 + angle2 <= PI;
 }
 
 inline double diamondAngle(Vector3 a, Vector3 b, Vector3 c, Vector3 d) // dihedral angle at edge a-b
 {
-    Vector3 n1 = cross(b-a, c-a);
-    Vector3 n2 = cross(b-d, a-d);
-    return PI-angle(n1, n2);
+  Vector3 n1 = cross(b - a, c - a);
+  Vector3 n2 = cross(b - d, a - d);
+  return PI - angle(n1, n2);
 }
 
-inline bool checkFoldover(Vector3 a, Vector3 b, Vector3 c, Vector3 x, double angle)
-{
-    return diamondAngle(a, b, c, x) < angle;
+inline bool checkFoldover(Vector3 a, Vector3 b, Vector3 c, Vector3 x, double angle) {
+  return diamondAngle(a, b, c, x) < angle;
 }
 
-bool shouldCollapse(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e)
-{
-    std::vector<Halfedge> toCheck;
-    Vertex v1 = e.halfedge().vertex();
-    Vertex v2 = e.halfedge().twin().vertex();
-    Vector3 midpoint = edgeMidpoint(mesh, geometry, e);
-    // find (halfedge) link around the edge, starting with those surrounding v1
-    Halfedge he = v1.halfedge();
-    Halfedge st = he;
-    do{
-        he = he.next();
-        if(he.vertex() != v2 && he.next().vertex() != v2){
-            toCheck.push_back(he);
-        }
-        he = he.next().twin();
+bool shouldCollapse(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e) {
+  std::vector<Halfedge> toCheck;
+  Vertex v1 = e.halfedge().vertex();
+  Vertex v2 = e.halfedge().twin().vertex();
+  Vector3 midpoint = edgeMidpoint(mesh, geometry, e);
+  // find (halfedge) link around the edge, starting with those surrounding v1
+  Halfedge he = v1.halfedge();
+  Halfedge st = he;
+  do {
+    he = he.next();
+    if (he.vertex() != v2 && he.next().vertex() != v2) {
+      toCheck.push_back(he);
     }
-    while(he != st);
-    // link around v2
-    he = v2.halfedge();
-    st = he;
-    do{
-        he = he.next();
-        if(he.vertex() != v1 && he.next().vertex() != v1){
-            toCheck.push_back(he);
-        }
-        he = he.next().twin();
+    he = he.next().twin();
+  } while (he != st);
+  // link around v2
+  he = v2.halfedge();
+  st = he;
+  do {
+    he = he.next();
+    if (he.vertex() != v1 && he.next().vertex() != v1) {
+      toCheck.push_back(he);
     }
-    while(he != st);
-    
-    // see if the point that would form after a collapse would cause a major foldover with surrounding edges
-    for(Halfedge he0 : toCheck){
-        Halfedge heT = he0.twin();
-        Vertex v1 = heT.vertex();
-        Vertex v2 = heT.next().vertex();
-        Vertex v3 = heT.next().next().vertex();
-        Vector3 a = geometry.inputVertexPositions[v1];
-        Vector3 b = geometry.inputVertexPositions[v2];
-        Vector3 c = geometry.inputVertexPositions[v3];
-        if(checkFoldover(a, b, c, midpoint, 2)){
-            return false;
-        }
+    he = he.next().twin();
+  } while (he != st);
+
+  // see if the point that would form after a collapse would cause a major foldover with surrounding edges
+  for (Halfedge he0 : toCheck) {
+    Halfedge heT = he0.twin();
+    Vertex v1 = heT.vertex();
+    Vertex v2 = heT.next().vertex();
+    Vertex v3 = heT.next().next().vertex();
+    Vector3 a = geometry.vertexPositions[v1];
+    Vector3 b = geometry.vertexPositions[v2];
+    Vector3 c = geometry.vertexPositions[v3];
+    if (checkFoldover(a, b, c, midpoint, 2)) {
+      return false;
     }
-    return true;
+  }
+  return true;
 }
 
-double getSmoothMeanCurvature(VertexPositionGeometry& geometry, Vertex v)
-{
-    double A = geometry.vertexDualArea(v);
-    double S = geometry.vertexMeanCurvature(v);
-    double K = S / A;
-    return K;
+double getSmoothMeanCurvature(VertexPositionGeometry& geometry, Vertex v) {
+  double A = geometry.vertexDualArea(v);
+  double S = geometry.vertexMeanCurvature(v);
+  double K = S / A;
+  return K;
 }
 
 // flatLength: specifies how long the target edge length should be in flat regions
 // epsilon: controls how much variation in target length occurs due to curvature
 
-double findMeanTargetL(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e, double flatLength, double epsilon)
-{
-    double averageH = 0;
-    for (Vertex v : e.adjacentVertices()) {
-        averageH += getSmoothMeanCurvature(geometry, v);
-    }
-    averageH /= 2;
-    double L = flatLength * epsilon / (fabs(averageH) + epsilon);
-    return L;
+double findMeanTargetL(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e, double flatLength, double epsilon) {
+  double averageH = 0;
+  for (Vertex v : e.adjacentVertices()) {
+    averageH += getSmoothMeanCurvature(geometry, v);
+  }
+  averageH /= 2;
+  double L = flatLength * epsilon / (fabs(averageH) + epsilon);
+  return L;
 }
 
 
+void fixDelaunay(SurfaceMesh& mesh, VertexPositionGeometry& geometry) {
+  // queue of edges to check if Delaunay
+  queue<Edge> toCheck;
+  // true if edge is currently in toCheck
+  EdgeData<bool> inQueue(mesh);
+  // start with all edges
+  for (Edge e : mesh.edges()) {
+    toCheck.push(e);
+    inQueue[e] = true;
+  }
+  // counter and limit for number of flips
+  int flipMax = 100 * mesh.nVertices();
+  int flipCnt = 0;
+  while (!toCheck.empty() && flipCnt < flipMax) {
+    Edge e = toCheck.front();
+    toCheck.pop();
+    inQueue[e] = false;
+    // if not Delaunay, flip edge and enqueue the surrounding "diamond" edges (if not already)
+    if (!e.isBoundary() && !isDelaunay(geometry, e)) {
+      flipCnt++;
+      Halfedge he = e.halfedge();
+      Halfedge he1 = he.next();
+      Halfedge he2 = he1.next();
+      Halfedge he3 = he.twin().next();
+      Halfedge he4 = he3.next();
 
-void fixDelaunay(SurfaceMesh& mesh, VertexPositionGeometry& geometry)
-{
-    // queue of edges to check if Delaunay
-    queue<Edge> toCheck;
-    // true if edge is currently in toCheck
-    EdgeData<bool> inQueue(mesh);
-    // start with all edges
-    for (Edge e : mesh.edges())
-    {
-        toCheck.push(e);
-        inQueue[e] = true;
-    }
-    // counter and limit for number of flips
-    int flipMax = 100 * mesh.nVertices();
-    int flipCnt = 0;
-    while (!toCheck.empty() && flipCnt < flipMax)
-    {
-        Edge e = toCheck.front();
-        toCheck.pop();
-        inQueue[e] = false;
-        // if not Delaunay, flip edge and enqueue the surrounding "diamond" edges (if not already)
-        if (!e.isBoundary() && !isDelaunay(geometry, e))
-        {
-            flipCnt++;
-            Halfedge he = e.halfedge();
-            Halfedge he1 = he.next();
-            Halfedge he2 = he1.next();
-            Halfedge he3 = he.twin().next();
-            Halfedge he4 = he3.next();
-
-            if (!inQueue[he1.edge()])
-            {
-                toCheck.push(he1.edge());
-                inQueue[he1.edge()] = true;
-            }
-            if (!inQueue[he2.edge()])
-            {
-                toCheck.push(he2.edge());
-                inQueue[he2.edge()] = true;
-            }
-            if (!inQueue[he3.edge()])
-            {
-                toCheck.push(he3.edge());
-                inQueue[he3.edge()] = true;
-            }
-            if (!inQueue[he4.edge()])
-            {
-                toCheck.push(he4.edge());
-                inQueue[he4.edge()] = true;
-            }
-            mesh.flip(e);
-        }
+      if (!inQueue[he1.edge()]) {
+        toCheck.push(he1.edge());
+        inQueue[he1.edge()] = true;
+      }
+      if (!inQueue[he2.edge()]) {
+        toCheck.push(he2.edge());
+        inQueue[he2.edge()] = true;
+      }
+      if (!inQueue[he3.edge()]) {
+        toCheck.push(he3.edge());
+        inQueue[he3.edge()] = true;
+      }
+      if (!inQueue[he4.edge()]) {
+        toCheck.push(he4.edge());
+        inQueue[he4.edge()] = true;
+      }
+      mesh.flip(e);
     }
+  }
 }
 
-void smoothByLaplacian(SurfaceMesh& mesh, VertexPositionGeometry& geometry)
-{
-    // smoothed vertex positions
-    VertexData<Vector3> newVertexPosition(mesh);
-    for (Vertex v : mesh.vertices())
-    {
-        if(v.isBoundary())
-        {
-            newVertexPosition[v] = geometry.inputVertexPositions[v];
-        }
-        else
-        {
-            // calculate average of surrounding vertices
-            newVertexPosition[v] = Vector3::zero();
-            for (Vertex j : v.adjacentVertices())
-            {
-                newVertexPosition[v] += geometry.inputVertexPositions[j];
-            }
-            newVertexPosition[v] /= v.degree();
-            // and project the average to the tangent plane
-            Vector3 updateDirection = newVertexPosition[v] - geometry.inputVertexPositions[v];
-            updateDirection = projectToPlane(updateDirection, vertexNormal(geometry, v));
-            
-            newVertexPosition[v] = geometry.inputVertexPositions[v] + 1*updateDirection;
-        }
-    }
-    // update final vertices
-    for (Vertex v : mesh.vertices())
-    {
-        geometry.inputVertexPositions[v] = newVertexPosition[v];
+void smoothByLaplacian(SurfaceMesh& mesh, VertexPositionGeometry& geometry) {
+  // smoothed vertex positions
+  VertexData<Vector3> newVertexPosition(mesh);
+  for (Vertex v : mesh.vertices()) {
+    if (v.isBoundary()) {
+      newVertexPosition[v] = geometry.vertexPositions[v];
+    } else {
+      // calculate average of surrounding vertices
+      newVertexPosition[v] = Vector3::zero();
+      for (Vertex j : v.adjacentVertices()) {
+        newVertexPosition[v] += geometry.vertexPositions[j];
+      }
+      newVertexPosition[v] /= v.degree();
+      // and project the average to the tangent plane
+      Vector3 updateDirection = newVertexPosition[v] - geometry.vertexPositions[v];
+      updateDirection = projectToPlane(updateDirection, vertexNormal(geometry, v));
+
+      newVertexPosition[v] = geometry.vertexPositions[v] + 1 * updateDirection;
     }
+  }
+  // update final vertices
+  for (Vertex v : mesh.vertices()) {
+    geometry.vertexPositions[v] = newVertexPosition[v];
+  }
 }
 
-void smoothByCircumcenter(SurfaceMesh& mesh, VertexPositionGeometry& geometry)
-{
-    geometry.requireFaceAreas();
-    // smoothed vertex positions
-    VertexData<Vector3> newVertexPosition(mesh);
-    for (Vertex v : mesh.vertices())
-    {
-        newVertexPosition[v] = geometry.inputVertexPositions[v]; // default
-        if(!v.isBoundary())
-        {
-            Vector3 updateDirection = Vector3::zero();
-            for (Face f : v.adjacentFaces())
-            {
-                // add the circumcenter weighted by face area to the update direction
-                Vector3 circum = findCircumcenter(geometry, f);
-                updateDirection += geometry.faceArea(f) * (circum - geometry.inputVertexPositions[v]);
-            }
-            updateDirection /= (3 * geometry.vertexDualArea(v));
-            // project update direction to tangent plane
-            updateDirection = projectToPlane(updateDirection, vertexNormal(geometry, v));
-            Vector3 newPos = geometry.inputVertexPositions[v] + .5 * updateDirection;
-            newVertexPosition[v] = newPos;
-        }
-    }
-    // update final vertices
-    for (Vertex v : mesh.vertices())
-    {
-        geometry.inputVertexPositions[v] = newVertexPosition[v];
+void smoothByCircumcenter(SurfaceMesh& mesh, VertexPositionGeometry& geometry) {
+  geometry.requireFaceAreas();
+  // smoothed vertex positions
+  VertexData<Vector3> newVertexPosition(mesh);
+  for (Vertex v : mesh.vertices()) {
+    newVertexPosition[v] = geometry.vertexPositions[v]; // default
+    if (!v.isBoundary()) {
+      Vector3 updateDirection = Vector3::zero();
+      for (Face f : v.adjacentFaces()) {
+        // add the circumcenter weighted by face area to the update direction
+        Vector3 circum = findCircumcenter(geometry, f);
+        updateDirection += geometry.faceArea(f) * (circum - geometry.vertexPositions[v]);
+      }
+      updateDirection /= (3 * geometry.vertexDualArea(v));
+      // project update direction to tangent plane
+      updateDirection = projectToPlane(updateDirection, vertexNormal(geometry, v));
+      Vector3 newPos = geometry.vertexPositions[v] + .5 * updateDirection;
+      newVertexPosition[v] = newPos;
     }
+  }
+  // update final vertices
+  for (Vertex v : mesh.vertices()) {
+    geometry.vertexPositions[v] = newVertexPosition[v];
+  }
 }
 
 
-bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength, double epsilon, double minLength, bool curvatureAdaptive)
-{
-    bool didSplitOrCollapse = false;
-    // queues of edges to CHECK to change
-    std::vector<Edge> toSplit;
-    std::vector<Edge> toCollapse;
-    
-    for(Edge e : mesh.edges())
-    {
-        toSplit.push_back(e);
-    }
-    
-    // actually splitting
-    while(!toSplit.empty())
-    {
-        Edge e = toSplit.back();
-        toSplit.pop_back();
-        double length_e = geometry.edgeLength(e);
-        double threshold = (curvatureAdaptive) ? findMeanTargetL(mesh, geometry, e, flatLength, epsilon) : flatLength;
-        if(length_e > minLength && length_e > threshold * 1.5)
-        {
-            Vector3 newPos = edgeMidpoint(mesh, geometry, e);
-            Halfedge he = mesh.splitEdgeTriangular(e);
-            didSplitOrCollapse = true;
-            Vertex newV = he.vertex();
-            geometry.inputVertexPositions[newV] = newPos;
-        }
-        else
-        {
-            toCollapse.push_back(e);
-        }                
-        
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength, double epsilon,
+                       double minLength, bool curvatureAdaptive) {
+  bool didSplitOrCollapse = false;
+  // queues of edges to CHECK to change
+  std::vector<Edge> toSplit;
+  std::vector<Edge> toCollapse;
+
+  for (Edge e : mesh.edges()) {
+    toSplit.push_back(e);
+  }
+
+  // actually splitting
+  while (!toSplit.empty()) {
+    Edge e = toSplit.back();
+    toSplit.pop_back();
+    double length_e = geometry.edgeLength(e);
+    double threshold = (curvatureAdaptive) ? findMeanTargetL(mesh, geometry, e, flatLength, epsilon) : flatLength;
+    if (length_e > minLength && length_e > threshold * 1.5) {
+      Vector3 newPos = edgeMidpoint(mesh, geometry, e);
+      Halfedge he = mesh.splitEdgeTriangular(e);
+      didSplitOrCollapse = true;
+      Vertex newV = he.vertex();
+      geometry.vertexPositions[newV] = newPos;
+    } else {
+      toCollapse.push_back(e);
     }
-    // actually collapsing
-    while(!toCollapse.empty())
+  }
+  // actually collapsing
+  while (!toCollapse.empty()) {
+    Edge e = toCollapse.back();
+    toCollapse.pop_back();
+    if (e.halfedge().next().getIndex() != INVALID_IND) // make sure it exists
     {
-        Edge e = toCollapse.back();
-        toCollapse.pop_back();
-        if(e.halfedge().next().getIndex() != INVALID_IND) // make sure it exists
-        {
-            double threshold = (curvatureAdaptive) ? findMeanTargetL(mesh, geometry, e, flatLength, epsilon) : flatLength;
-            if(geometry.edgeLength(e) < threshold * 0.5)
-            {
-                Vector3 newPos = edgeMidpoint(mesh, geometry, e);
-                if(shouldCollapse(mesh, geometry, e)) {
-                    Vertex v = mesh.collapseEdgeTriangular(e);
-                    didSplitOrCollapse = true;
-                    if (v != Vertex()) {
-                        if(!v.isBoundary()) {
-                            geometry.inputVertexPositions[v] = newPos;
-                        }
-                    }
-                }
+      double threshold = (curvatureAdaptive) ? findMeanTargetL(mesh, geometry, e, flatLength, epsilon) : flatLength;
+      if (geometry.edgeLength(e) < threshold * 0.5) {
+        Vector3 newPos = edgeMidpoint(mesh, geometry, e);
+        if (shouldCollapse(mesh, geometry, e)) {
+          Vertex v = mesh.collapseEdgeTriangular(e);
+          didSplitOrCollapse = true;
+          if (v != Vertex()) {
+            if (!v.isBoundary()) {
+              geometry.vertexPositions[v] = newPos;
             }
+          }
         }
+      }
     }
-    return didSplitOrCollapse;
+  }
+  return didSplitOrCollapse;
 }
 
 } // namespace surface

From 7774ac6ac8046a791b90b2f4f5fbfda8b336a75a Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Thu, 31 Mar 2022 17:32:48 -0400
Subject: [PATCH 03/33] Use mutation managers

---
 include/geometrycentral/surface/remeshing.h |  36 ++-
 src/surface/remeshing.cpp                   | 264 +++++++++++---------
 2 files changed, 179 insertions(+), 121 deletions(-)

diff --git a/include/geometrycentral/surface/remeshing.h b/include/geometrycentral/surface/remeshing.h
index 106361d3..82e9b8b7 100644
--- a/include/geometrycentral/surface/remeshing.h
+++ b/include/geometrycentral/surface/remeshing.h
@@ -1,28 +1,46 @@
 #pragma once
 
+#include "geometrycentral/surface/barycentric_coordinate_helpers.h"
 #include "geometrycentral/surface/manifold_surface_mesh.h"
+#include "geometrycentral/surface/mutation_manager.h"
 #include "geometrycentral/surface/vertex_position_geometry.h"
 
-#include <queue>
+#include <deque>
 
 namespace geometrycentral {
 namespace surface {
 
 // makes all triangles delaunay
-void fixDelaunay(SurfaceMesh& mesh, VertexPositionGeometry& geometry);
+// returns the number of flips performed
+size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry);
+size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm);
 
 // average positions of vertices based on surrounding vertex positions
-void smoothByLaplacian(SurfaceMesh& mesh, VertexPositionGeometry& geometry);
+// returns the average amount each vertex was moved by
+double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double stepSize = 1);
+double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
+                         double stepSize = 1);
 
 // average positions of vertices based on surrounding triangle circumenters
-void smoothByCircumcenter(SurfaceMesh& mesh, VertexPositionGeometry& geometry);
+// returns the average amount each vertex was moved by
+double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double stepSize = 1);
+double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
+                            double stepSize = 1);
 
 // applies splits and collapses to adjust edge lengths based on the curvature
-// flatLength: specifies how long the target edge length should be in flat regions
-// epsilon: controls how much variation in target length occurs due to curvature
-// minLength: specifies the minimum possible length an edge could become
-bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength, double epsilon,
-                       double minLength, bool curvatureAdaptive = true);
+// flatLength:          specifies how long the target edge length should be in flat regions
+// curvatureAdaptation: controls how much variation in target length occurs due to curvature. Set curvatureAdaptation to
+//                      0 if you want lengths to be approximately flatLength everywhere
+// minRelativeLength:   specifies the minimum possible length an edge could become. Defined relative to flatLength
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength,
+                       double curvatureAdaptation = 0.2, double minRelativeLength = 0.05);
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
+                       double flatLength, double curvatureAdaptation = 0.2, double minRelativeLength = 0.05);
+
+void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double targetEdgeLength,
+            size_t maxIterations = 10, double curvatureAdaptation = 0.2, double minRelativeLength = 0.05);
+void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm, double targetEdgeLength,
+            size_t maxIterations = 10, double curvatureAdaptation = 0.2, double minRelativeLength = 0.05);
 
 } // namespace surface
 } // namespace geometrycentral
diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index 6c7ccd45..a225bbdd 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -3,8 +3,6 @@
 namespace geometrycentral {
 namespace surface {
 
-using std::queue;
-
 Vector3 vertexNormal(VertexPositionGeometry& geometry, Vertex v) {
   Vector3 norm = Vector3::zero();
   for (Corner c : v.adjacentCorners()) {
@@ -29,11 +27,12 @@ Vector3 findCircumcenter(Vector3 p1, Vector3 p2, Vector3 p3) {
   double a2 = a * a;
   double b2 = b * b;
   double c2 = c * c;
-  Vector3 O{a2 * (b2 + c2 - a2), b2 * (c2 + a2 - b2), c2 * (a2 + b2 - c2)};
+  Vector3 circumcenterLoc{a2 * (b2 + c2 - a2), b2 * (c2 + a2 - b2), c2 * (a2 + b2 - c2)};
   // normalize to sum of 1
-  O /= O[0] + O[1] + O[2];
+  circumcenterLoc = normalizeBarycentric(circumcenterLoc);
+
   // change back to space
-  return O[0] * p1 + O[1] * p2 + O[2] * p3;
+  return circumcenterLoc[0] * p1 + circumcenterLoc[1] * p2 + circumcenterLoc[2] * p3;
 }
 
 Vector3 findCircumcenter(VertexPositionGeometry& geometry, Face f) {
@@ -65,37 +64,31 @@ inline bool checkFoldover(Vector3 a, Vector3 b, Vector3 c, Vector3 x, double ang
 }
 
 bool shouldCollapse(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e) {
-  std::vector<Halfedge> toCheck;
+  std::vector<Halfedge> edgesToCheck;
   Vertex v1 = e.halfedge().vertex();
   Vertex v2 = e.halfedge().twin().vertex();
-  Vector3 midpoint = edgeMidpoint(mesh, geometry, e);
+
   // find (halfedge) link around the edge, starting with those surrounding v1
-  Halfedge he = v1.halfedge();
-  Halfedge st = he;
-  do {
-    he = he.next();
-    if (he.vertex() != v2 && he.next().vertex() != v2) {
-      toCheck.push_back(he);
+  for (Halfedge he : v1.outgoingHalfedges()) {
+    if (he.next().tailVertex() != v2 && he.next().tipVertex() != v2) {
+      edgesToCheck.push_back(he.next());
     }
-    he = he.next().twin();
-  } while (he != st);
+  }
+
   // link around v2
-  he = v2.halfedge();
-  st = he;
-  do {
-    he = he.next();
-    if (he.vertex() != v1 && he.next().vertex() != v1) {
-      toCheck.push_back(he);
+  for (Halfedge he : v2.outgoingHalfedges()) {
+    if (he.next().tailVertex() != v1 && he.next().tipVertex() != v1) {
+      edgesToCheck.push_back(he.next());
     }
-    he = he.next().twin();
-  } while (he != st);
+  }
 
   // see if the point that would form after a collapse would cause a major foldover with surrounding edges
-  for (Halfedge he0 : toCheck) {
+  Vector3 midpoint = edgeMidpoint(mesh, geometry, e);
+  for (Halfedge he0 : edgesToCheck) {
     Halfedge heT = he0.twin();
-    Vertex v1 = heT.vertex();
-    Vertex v2 = heT.next().vertex();
-    Vertex v3 = heT.next().next().vertex();
+    Vertex v1 = heT.tailVertex();
+    Vertex v2 = heT.tipVertex();
+    Vertex v3 = heT.next().tipVertex();
     Vector3 a = geometry.vertexPositions[v1];
     Vector3 b = geometry.vertexPositions[v2];
     Vector3 c = geometry.vertexPositions[v3];
@@ -114,121 +107,146 @@ double getSmoothMeanCurvature(VertexPositionGeometry& geometry, Vertex v) {
 }
 
 // flatLength: specifies how long the target edge length should be in flat regions
-// epsilon: controls how much variation in target length occurs due to curvature
-
-double findMeanTargetL(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e, double flatLength, double epsilon) {
+// curvatureAdaptation: controls how much variation in target length occurs due to curvature
+double findMeanTargetL(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e, double flatLength,
+                       double curvatureAdaptation) {
   double averageH = 0;
   for (Vertex v : e.adjacentVertices()) {
     averageH += getSmoothMeanCurvature(geometry, v);
   }
   averageH /= 2;
-  double L = flatLength * epsilon / (fabs(averageH) + epsilon);
+  double L = flatLength / (fabs(averageH) * curvatureAdaptation + 1);
   return L;
 }
 
 
-void fixDelaunay(SurfaceMesh& mesh, VertexPositionGeometry& geometry) {
-  // queue of edges to check if Delaunay
-  queue<Edge> toCheck;
-  // true if edge is currently in toCheck
-  EdgeData<bool> inQueue(mesh);
+size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry) {
+  MutationManager mm(mesh, geometry);
+  return fixDelaunay(mesh, geometry, mm);
+}
+
+size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm) {
+  // Logic duplicated from surface/intrinsic_triangulation.cpp
+
+  std::deque<Edge> edgesToCheck;      // queue of edges to check if Delaunay
+  EdgeData<bool> inQueue(mesh, true); // true if edge is currently in edgesToCheck
+
   // start with all edges
   for (Edge e : mesh.edges()) {
-    toCheck.push(e);
-    inQueue[e] = true;
+    edgesToCheck.push_back(e);
   }
+
   // counter and limit for number of flips
-  int flipMax = 100 * mesh.nVertices();
-  int flipCnt = 0;
-  while (!toCheck.empty() && flipCnt < flipMax) {
-    Edge e = toCheck.front();
-    toCheck.pop();
+  size_t flipMax = 100 * mesh.nVertices();
+  size_t nFlips = 0;
+  while (!edgesToCheck.empty() && nFlips < flipMax) {
+    Edge e = edgesToCheck.front();
+    edgesToCheck.pop_front();
     inQueue[e] = false;
-    // if not Delaunay, flip edge and enqueue the surrounding "diamond" edges (if not already)
-    if (!e.isBoundary() && !isDelaunay(geometry, e)) {
-      flipCnt++;
-      Halfedge he = e.halfedge();
-      Halfedge he1 = he.next();
-      Halfedge he2 = he1.next();
-      Halfedge he3 = he.twin().next();
-      Halfedge he4 = he3.next();
-
-      if (!inQueue[he1.edge()]) {
-        toCheck.push(he1.edge());
-        inQueue[he1.edge()] = true;
-      }
-      if (!inQueue[he2.edge()]) {
-        toCheck.push(he2.edge());
-        inQueue[he2.edge()] = true;
-      }
-      if (!inQueue[he3.edge()]) {
-        toCheck.push(he3.edge());
-        inQueue[he3.edge()] = true;
-      }
-      if (!inQueue[he4.edge()]) {
-        toCheck.push(he4.edge());
-        inQueue[he4.edge()] = true;
+
+    if (e.isBoundary() || isDelaunay(geometry, e)) continue;
+
+    // if not Delaunay, try to flip edge
+    bool wasFlipped = mm.flipEdge(e);
+
+    if (!wasFlipped) continue;
+
+    nFlips++;
+
+    // Add neighbors to queue, as they may need flipping now
+    Halfedge he = e.halfedge();
+    std::array<Edge, 4> neighboringEdges{he.next().edge(), he.next().next().edge(), he.twin().next().edge(),
+                                         he.twin().next().next().edge()};
+    for (Edge nE : neighboringEdges) {
+      if (!inQueue[nE]) {
+        edgesToCheck.push_back(nE);
+        inQueue[nE] = true;
       }
-      mesh.flip(e);
     }
   }
+  return nFlips;
 }
 
-void smoothByLaplacian(SurfaceMesh& mesh, VertexPositionGeometry& geometry) {
-  // smoothed vertex positions
-  VertexData<Vector3> newVertexPosition(mesh);
+double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double stepSize) {
+  MutationManager mm(mesh, geometry);
+  return smoothByLaplacian(mesh, geometry, mm, stepSize);
+}
+
+double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
+                         double stepSize) {
+  VertexData<Vector3> vertexOffsets(mesh);
   for (Vertex v : mesh.vertices()) {
     if (v.isBoundary()) {
-      newVertexPosition[v] = geometry.vertexPositions[v];
+      vertexOffsets[v] = Vector3::zero();
     } else {
       // calculate average of surrounding vertices
-      newVertexPosition[v] = Vector3::zero();
+      Vector3 avgNeighbor = Vector3::zero();
       for (Vertex j : v.adjacentVertices()) {
-        newVertexPosition[v] += geometry.vertexPositions[j];
+        avgNeighbor += geometry.vertexPositions[j];
       }
-      newVertexPosition[v] /= v.degree();
-      // and project the average to the tangent plane
-      Vector3 updateDirection = newVertexPosition[v] - geometry.vertexPositions[v];
-      updateDirection = projectToPlane(updateDirection, vertexNormal(geometry, v));
+      avgNeighbor /= v.degree();
 
-      newVertexPosition[v] = geometry.vertexPositions[v] + 1 * updateDirection;
+      // and project the average to the tangent plane
+      Vector3 updateDirection = avgNeighbor - geometry.vertexPositions[v];
+      vertexOffsets[v] = stepSize * projectToPlane(updateDirection, vertexNormal(geometry, v));
     }
   }
+
   // update final vertices
+  double totalMovement = 0;
   for (Vertex v : mesh.vertices()) {
-    geometry.vertexPositions[v] = newVertexPosition[v];
+    mm.repositionVertex(v, vertexOffsets[v]);
+    totalMovement += vertexOffsets[v].norm();
   }
+  return totalMovement / mesh.nVertices();
+}
+
+double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double stepSize) {
+  MutationManager mm(mesh, geometry);
+  return smoothByCircumcenter(mesh, geometry, mm, stepSize);
 }
 
-void smoothByCircumcenter(SurfaceMesh& mesh, VertexPositionGeometry& geometry) {
+double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
+                            double stepSize) {
   geometry.requireFaceAreas();
-  // smoothed vertex positions
-  VertexData<Vector3> newVertexPosition(mesh);
+  VertexData<Vector3> vertexOffsets(mesh);
   for (Vertex v : mesh.vertices()) {
-    newVertexPosition[v] = geometry.vertexPositions[v]; // default
-    if (!v.isBoundary()) {
-      Vector3 updateDirection = Vector3::zero();
+    if (v.isBoundary()) {
+      vertexOffsets[v] = Vector3::zero();
+    } else {
+      vertexOffsets[v] = Vector3::zero();
       for (Face f : v.adjacentFaces()) {
         // add the circumcenter weighted by face area to the update direction
         Vector3 circum = findCircumcenter(geometry, f);
-        updateDirection += geometry.faceArea(f) * (circum - geometry.vertexPositions[v]);
+        vertexOffsets[v] += geometry.faceArea(f) * (circum - geometry.vertexPositions[v]);
       }
-      updateDirection /= (3 * geometry.vertexDualArea(v));
+      vertexOffsets[v] /= (3 * geometry.vertexDualArea(v));
       // project update direction to tangent plane
-      updateDirection = projectToPlane(updateDirection, vertexNormal(geometry, v));
-      Vector3 newPos = geometry.vertexPositions[v] + .5 * updateDirection;
-      newVertexPosition[v] = newPos;
+      vertexOffsets[v] = stepSize * projectToPlane(vertexOffsets[v], vertexNormal(geometry, v)) / 2.;
     }
   }
+
   // update final vertices
+  double totalMovement = 0;
   for (Vertex v : mesh.vertices()) {
-    geometry.vertexPositions[v] = newVertexPosition[v];
+    mm.repositionVertex(v, vertexOffsets[v]);
+    totalMovement += vertexOffsets[v].norm();
   }
+  return totalMovement / mesh.nVertices();
+}
+
+
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength,
+                       double curvatureAdaptation, double minRelativeLength) {
+  MutationManager mm(mesh, geometry);
+  return adjustEdgeLengths(mesh, geometry, mm, flatLength, curvatureAdaptation, minRelativeLength);
 }
 
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
+                       double flatLength, double curvatureAdaptation, double minRelativeLength) {
+  bool useCurvatureAdaptation = curvatureAdaptation > 0;
+  double minLength = minRelativeLength * flatLength;
 
-bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength, double epsilon,
-                       double minLength, bool curvatureAdaptive) {
   bool didSplitOrCollapse = false;
   // queues of edges to CHECK to change
   std::vector<Edge> toSplit;
@@ -243,40 +261,62 @@ bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geomet
     Edge e = toSplit.back();
     toSplit.pop_back();
     double length_e = geometry.edgeLength(e);
-    double threshold = (curvatureAdaptive) ? findMeanTargetL(mesh, geometry, e, flatLength, epsilon) : flatLength;
+    double threshold =
+        (useCurvatureAdaptation) ? findMeanTargetL(mesh, geometry, e, flatLength, curvatureAdaptation) : flatLength;
     if (length_e > minLength && length_e > threshold * 1.5) {
       Vector3 newPos = edgeMidpoint(mesh, geometry, e);
-      Halfedge he = mesh.splitEdgeTriangular(e);
+      Halfedge he = mm.splitEdge(e, newPos);
       didSplitOrCollapse = true;
-      Vertex newV = he.vertex();
-      geometry.vertexPositions[newV] = newPos;
     } else {
       toCollapse.push_back(e);
     }
   }
+
   // actually collapsing
   while (!toCollapse.empty()) {
     Edge e = toCollapse.back();
     toCollapse.pop_back();
-    if (e.halfedge().next().getIndex() != INVALID_IND) // make sure it exists
-    {
-      double threshold = (curvatureAdaptive) ? findMeanTargetL(mesh, geometry, e, flatLength, epsilon) : flatLength;
-      if (geometry.edgeLength(e) < threshold * 0.5) {
-        Vector3 newPos = edgeMidpoint(mesh, geometry, e);
-        if (shouldCollapse(mesh, geometry, e)) {
-          Vertex v = mesh.collapseEdgeTriangular(e);
-          didSplitOrCollapse = true;
-          if (v != Vertex()) {
-            if (!v.isBoundary()) {
-              geometry.vertexPositions[v] = newPos;
-            }
-          }
-        }
+    if (e == Edge() || e.isDead()) continue; // make sure it exists
+
+    double threshold =
+        (useCurvatureAdaptation) ? findMeanTargetL(mesh, geometry, e, flatLength, curvatureAdaptation) : flatLength;
+    if (geometry.edgeLength(e) < threshold * 0.5) {
+      Vector3 newPos = edgeMidpoint(mesh, geometry, e);
+      if (shouldCollapse(mesh, geometry, e)) {
+        Vertex v = mm.collapseEdge(e, newPos);
+        didSplitOrCollapse = true;
       }
     }
   }
+
+  mesh.compress();
   return didSplitOrCollapse;
 }
 
+void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double targetEdgeLength, size_t maxIterations,
+            double curvatureAdaptation, double minRelativeLength) {
+  MutationManager mm(mesh, geometry);
+  return remesh(mesh, geometry, mm, targetEdgeLength, maxIterations, curvatureAdaptation, minRelativeLength);
+}
+
+void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm, double targetEdgeLength,
+            size_t maxIterations, double curvatureAdaptation, double minRelativeLength) {
+
+  bool doConnectivityChanges = true;
+
+  for (size_t iIt = 0; iIt < maxIterations; iIt++) {
+    if (doConnectivityChanges) {
+      doConnectivityChanges =
+          adjustEdgeLengths(mesh, geometry, mm, targetEdgeLength, curvatureAdaptation, minRelativeLength);
+    }
+
+    size_t nFlips = fixDelaunay(mesh, geometry, mm);
+    double flowDist = smoothByCircumcenter(mesh, geometry);
+
+    // std::cout << iIt << " : " << changedConnectivity << " " << nFlips << " " << flowDist << std::endl;
+    if ((nFlips == 0) && (flowDist < 0.01)) break;
+  }
+}
+
 } // namespace surface
 } // namespace geometrycentral

From c9c4c97c9d9512eec853786a013a64d6a4778ffd Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Thu, 31 Mar 2022 17:37:00 -0400
Subject: [PATCH 04/33] Use cached mean curvature rather than recomputing all
 the time

---
 src/surface/remeshing.cpp | 11 +++++++++--
 1 file changed, 9 insertions(+), 2 deletions(-)

diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index a225bbdd..ab1f2174 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -99,9 +99,10 @@ bool shouldCollapse(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry,
   return true;
 }
 
+// Warning: requires that geometry.vertexDualAreas and geometry.vertexMeanCurvatures are filled in with accurate data
 double getSmoothMeanCurvature(VertexPositionGeometry& geometry, Vertex v) {
-  double A = geometry.vertexDualArea(v);
-  double S = geometry.vertexMeanCurvature(v);
+  double A = geometry.vertexDualAreas[v];
+  double S = geometry.vertexMeanCurvatures[v];
   double K = S / A;
   return K;
 }
@@ -244,6 +245,9 @@ bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geomet
 
 bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
                        double flatLength, double curvatureAdaptation, double minRelativeLength) {
+  geometry.requireVertexDualAreas();
+  geometry.requireVertexMeanCurvatures();
+
   bool useCurvatureAdaptation = curvatureAdaptation > 0;
   double minLength = minRelativeLength * flatLength;
 
@@ -289,6 +293,9 @@ bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geomet
     }
   }
 
+  geometry.unrequireVertexDualAreas();
+  geometry.unrequireVertexMeanCurvatures();
+
   mesh.compress();
   return didSplitOrCollapse;
 }

From 17f8ce7d18f77936b076f7aa97fdeaed08eae194 Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Thu, 31 Mar 2022 17:40:26 -0400
Subject: [PATCH 05/33] Refresh quantities after remeshing

---
 src/surface/remeshing.cpp | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index ab1f2174..c3d31d79 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -323,6 +323,7 @@ void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, Mutatio
     // std::cout << iIt << " : " << changedConnectivity << " " << nFlips << " " << flowDist << std::endl;
     if ((nFlips == 0) && (flowDist < 0.01)) break;
   }
+  geometry.refreshQuantities();
 }
 
 } // namespace surface

From 67e5952f32daaa3795b7f8d4a1ac48567a5441a6 Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Fri, 1 Apr 2022 13:50:14 -0400
Subject: [PATCH 06/33] Add fields to mutation manager to prevent certain
 mutations

---
 .../surface/mutation_manager.h                | 44 ++++++++-
 src/surface/mutation_manager.cpp              | 92 ++++++++++++++++++-
 2 files changed, 132 insertions(+), 4 deletions(-)

diff --git a/include/geometrycentral/surface/mutation_manager.h b/include/geometrycentral/surface/mutation_manager.h
index b912b79b..c2591d53 100644
--- a/include/geometrycentral/surface/mutation_manager.h
+++ b/include/geometrycentral/surface/mutation_manager.h
@@ -106,6 +106,45 @@ class MutationManager {
   // Create a connectivity-only mutation manager, which does not touch any geometry by default
   MutationManager(ManifoldSurfaceMesh& mesh);
 
+  // ======================================================
+  // ======== Constraints
+  // ======================================================
+
+  // Set up callbacks to update edge constraint data following an edge split
+  // TODO: work out sane policies for updating after other operations?
+  void setConstraintCallbacks();
+
+  // Vertices which are allowed to be repositioned.
+  // (set to an array which holds true if a vertex may be moved, and false if it should stay fixed)
+  // Note that this array may be uninitialized, in which case all vertices are allowed to be repositioned
+  // By default, any newly created vertices are repositionable, unless otherwise specified
+  // Warning: this only prevents vertices from being moved by calls to `repositionVertex()`. Even if
+  // repositionableVertices[v] is false, v may be moved by collapsing an incident edge
+  VertexData<bool> repositionableVertices;
+  void setRepositionableVertices(const VertexData<bool>& repositionableVertex, bool defaultValue = true);
+  void clearRepositionableVertices();
+  bool mayRepositionVertex(Vertex v) const;
+
+  EdgeData<bool> splittableEdges;
+  void setSplittableEdges(const EdgeData<bool>& splittableEdge, bool defaultValue = true);
+  void clearSplittableEdges();
+  bool maySplitEdge(Edge e) const;
+
+  EdgeData<bool> collapsibleEdges;
+  void setCollapsibleEdges(const EdgeData<bool>& collapsibleEdge, bool defaultValue = true);
+  void clearCollapsibleEdges();
+  bool mayCollapseEdge(Edge e) const;
+
+  EdgeData<bool> flippableEdges;
+  void setFlippableEdges(const EdgeData<bool>& flippableEdge, bool defaultValue = true);
+  void clearFlippableEdges();
+  bool mayFlipEdge(Edge e) const;
+
+  FaceData<bool> splittableFaces;
+  void setSplittableFaces(const FaceData<bool>& splittableFace, bool defaultValue = true);
+  void clearSplittableFaces();
+  bool maySplitFace(Face f) const;
+
 
   // ======================================================
   // ======== Low-level mutations
@@ -117,7 +156,8 @@ class MutationManager {
   // many of these, since each adds the burden of a corresponding callback policy to update data.
 
   // Move a vertex in 3D space
-  void repositionVertex(Vertex vert, Vector3 offset);
+  // Returns true if vertex was repositioned (May return false if, e.g., repositionalVertices[vert] is false)
+  bool repositionVertex(Vertex vert, Vector3 offset);
 
   // Flip an edge.
   bool flipEdge(Edge e);
@@ -131,6 +171,7 @@ class MutationManager {
   // Returns the new halfedge which points away from the new vertex (so he.vertex() is the new vertex), and is the same
   // direction as e.halfedge() on the original edge. The halfedge direction of the other part of the new split edge is
   // also preserved.
+  // Returns Halfedge() if edge was not split (e.g. if splittableEdges[e] is false)
   Halfedge splitEdge(Edge e, double tSplit);
   Halfedge splitEdge(Edge e, Vector3 newVertexPosition);
   Halfedge splitEdge(Edge e, double tSplit, Vector3 newVertexPosition);
@@ -142,6 +183,7 @@ class MutationManager {
   Vertex collapseEdge(Edge e, double tCollapse, Vector3 newVertexPosition);
 
   // Split a face (i.e. insert a vertex into the face), and return the new vertex
+  // Returns Vertex() if face was not split (e.g. if splittableFaces[f] is false)
   Vertex splitFace(Face f, const std::vector<double>& bSplit);
   Vertex splitFace(Face f, Vector3 newVertexPosition);
   Vertex splitFace(Face f, const std::vector<double>& bSplit, Vector3 newVertexPosition);
diff --git a/src/surface/mutation_manager.cpp b/src/surface/mutation_manager.cpp
index 11f4ccd8..daddb11d 100644
--- a/src/surface/mutation_manager.cpp
+++ b/src/surface/mutation_manager.cpp
@@ -10,15 +10,85 @@ namespace surface {
 // ======================================================
 
 MutationManager::MutationManager(ManifoldSurfaceMesh& mesh_, VertexPositionGeometry& geometry_)
-    : mesh(mesh_), geometry(&geometry_) {}
+    : mesh(mesh_), geometry(&geometry_) {
+  setConstraintCallbacks();
+}
+
+MutationManager::MutationManager(ManifoldSurfaceMesh& mesh_) : mesh(mesh_) { setConstraintCallbacks(); }
+
+// ======================================================
+// ======== Constraints
+// ======================================================
+
+void MutationManager::setConstraintCallbacks() {
+  // == Register a callback to maintain edge constraint data after edge splits
+  auto cacheConstraintsBeforeEdgeSplit = [&](Edge oldE, double tSplit) -> std::array<bool, 3> {
+    bool wasSplittable = maySplitEdge(oldE);
+    bool wasCollapsible = mayCollapseEdge(oldE);
+    bool wasFlippable = mayFlipEdge(oldE);
+    return {wasSplittable, wasCollapsible, wasFlippable};
+  };
+  auto updateConstraintsAfterEdgeSplit = [&](Halfedge newHe1, Halfedge newHe2, double tSplit,
+                                             std::array<bool, 3> oldConstraints) {
+    if (splittableEdges.size() > 0) {
+      splittableEdges[newHe1.edge()] = oldConstraints[0];
+      splittableEdges[newHe2.edge()] = oldConstraints[0];
+    }
+    if (collapsibleEdges.size() > 0) {
+      collapsibleEdges[newHe1.edge()] = oldConstraints[1];
+      collapsibleEdges[newHe2.edge()] = oldConstraints[1];
+    }
+    if (flippableEdges.size() > 0) {
+      flippableEdges[newHe1.edge()] = oldConstraints[2];
+      flippableEdges[newHe2.edge()] = oldConstraints[2];
+    }
+  };
+  registerEdgeSplitHandlers(cacheConstraintsBeforeEdgeSplit, updateConstraintsAfterEdgeSplit);
+}
+
+void MutationManager::setRepositionableVertices(const VertexData<bool>& repositionableVertices_, bool defaultValue) {
+  repositionableVertices = repositionableVertices_;
+  repositionableVertices.setDefault(defaultValue);
+}
+void MutationManager::clearRepositionableVertices() { repositionableVertices = VertexData<bool>(); }
+bool MutationManager::mayRepositionVertex(Vertex v) const {
+  return repositionableVertices.size() == 0 || repositionableVertices[v];
+}
 
-MutationManager::MutationManager(ManifoldSurfaceMesh& mesh_) : mesh(mesh_) {}
+void MutationManager::setSplittableEdges(const EdgeData<bool>& splittableEdges_, bool defaultValue) {
+  splittableEdges = splittableEdges_;
+  splittableEdges.setDefault(defaultValue);
+}
+void MutationManager::clearSplittableEdges() { splittableEdges = EdgeData<bool>(); }
+bool MutationManager::maySplitEdge(Edge e) const { return splittableEdges.size() == 0 || splittableEdges[e]; }
+
+void MutationManager::setCollapsibleEdges(const EdgeData<bool>& collapsibleEdges_, bool defaultValue) {
+  collapsibleEdges = collapsibleEdges_;
+  collapsibleEdges.setDefault(defaultValue);
+}
+void MutationManager::clearCollapsibleEdges() { collapsibleEdges = EdgeData<bool>(); }
+bool MutationManager::mayCollapseEdge(Edge e) const { return collapsibleEdges.size() == 0 || collapsibleEdges[e]; }
+
+void MutationManager::setFlippableEdges(const EdgeData<bool>& flippableEdges_, bool defaultValue) {
+  flippableEdges = flippableEdges_;
+  flippableEdges.setDefault(defaultValue);
+}
+void MutationManager::clearFlippableEdges() { flippableEdges = EdgeData<bool>(); }
+bool MutationManager::mayFlipEdge(Edge e) const { return flippableEdges.size() == 0 || flippableEdges[e]; }
+
+void MutationManager::setSplittableFaces(const FaceData<bool>& splittableFaces_, bool defaultValue) {
+  splittableFaces = splittableFaces_;
+  splittableFaces.setDefault(defaultValue);
+}
+void MutationManager::clearSplittableFaces() { splittableFaces = FaceData<bool>(); }
+bool MutationManager::maySplitFace(Face f) const { return splittableFaces.size() == 0 || splittableFaces[f]; }
 
 // ======================================================
 // ======== Low-level mutations
 // ======================================================
 
-void MutationManager::repositionVertex(Vertex vert, Vector3 offset) {
+bool MutationManager::repositionVertex(Vertex vert, Vector3 offset) {
+  if (!mayRepositionVertex(vert)) return false;
 
   // Invoke callbacks
   for (VertexRepositionPolicy* policy : vertexRepositionPolicies) {
@@ -26,10 +96,12 @@ void MutationManager::repositionVertex(Vertex vert, Vector3 offset) {
   }
 
   geometry->vertexPositions[vert] += offset;
+  return true;
 }
 
 // Flip an edge.
 bool MutationManager::flipEdge(Edge e) {
+  if (!mayFlipEdge(e)) return false;
 
   // First do a test flip to see if its possible
   // TODO implement canFlip() to avoid this
@@ -60,6 +132,8 @@ bool MutationManager::flipEdge(Edge e) {
 }
 
 Halfedge MutationManager::splitEdge(Edge e, double tSplit) {
+  if (!maySplitEdge(e)) return Halfedge();
+
   Vector3 newPos{0., 0., 0.};
   if (geometry) {
     VertexData<Vector3>& pos = geometry->vertexPositions;
@@ -69,6 +143,7 @@ Halfedge MutationManager::splitEdge(Edge e, double tSplit) {
 }
 
 Halfedge MutationManager::splitEdge(Edge e, Vector3 newVertexPosition) {
+  if (!maySplitEdge(e)) return Halfedge();
 
   double tSplit = -1;
   GC_SAFETY_ASSERT(geometry, "must have geometry to split by position");
@@ -84,6 +159,7 @@ Halfedge MutationManager::splitEdge(Edge e, Vector3 newVertexPosition) {
 }
 
 Halfedge MutationManager::splitEdge(Edge e, double tSplit, Vector3 newVertexPosition) {
+  if (!maySplitEdge(e)) return Halfedge();
 
   // Invoke before callbacks
   for (EdgeSplitPolicy* policy : edgeSplitPolicies) {
@@ -109,6 +185,8 @@ Halfedge MutationManager::splitEdge(Edge e, double tSplit, Vector3 newVertexPosi
 // Collapse an edge.
 // Returns the new vertex if the edge could be collapsed, and Vertex() otherwise
 Vertex MutationManager::collapseEdge(Edge e, double tCollapse) {
+  if (!mayCollapseEdge(e)) return Vertex();
+
   Vector3 newPos{0., 0., 0.};
   if (geometry) {
     // Find the nearest tCoord
@@ -119,6 +197,7 @@ Vertex MutationManager::collapseEdge(Edge e, double tCollapse) {
 }
 
 Vertex MutationManager::collapseEdge(Edge e, Vector3 newVertexPosition) {
+  if (!mayCollapseEdge(e)) return Vertex();
 
   double tCollapse = -1;
   GC_SAFETY_ASSERT(geometry, "must have geometry to split by position");
@@ -133,6 +212,7 @@ Vertex MutationManager::collapseEdge(Edge e, Vector3 newVertexPosition) {
   return collapseEdge(e, tCollapse, newVertexPosition);
 }
 Vertex MutationManager::collapseEdge(Edge e, double tCollapse, Vector3 newVertexPosition) {
+  if (!mayCollapseEdge(e)) return Vertex();
 
   // Invoke before callbacks
   // TODO need to handle possiblity that collapse fails -- check before calling
@@ -158,6 +238,8 @@ Vertex MutationManager::collapseEdge(Edge e, double tCollapse, Vector3 newVertex
 
 // Split a face (i.e. insert a vertex into the face)
 Vertex MutationManager::splitFace(Face f, const std::vector<double>& bSplit) {
+  if (!maySplitFace(f)) return Vertex();
+
   Vector3 newPos = Vector3::zero();
   if (geometry) {
     size_t iV = 0;
@@ -172,6 +254,8 @@ Vertex MutationManager::splitFace(Face f, const std::vector<double>& bSplit) {
 }
 
 Vertex MutationManager::splitFace(Face f, Vector3 newVertexPosition) {
+  if (!maySplitFace(f)) return Vertex();
+
   // TODO
   throw std::runtime_error("Face split based on vertex position not implemented yet");
   return Vertex();
@@ -179,6 +263,8 @@ Vertex MutationManager::splitFace(Face f, Vector3 newVertexPosition) {
 
 
 Vertex MutationManager::splitFace(Face f, const std::vector<double>& bSplit, Vector3 newVertexPosition) {
+  if (!maySplitFace(f)) return Vertex();
+
   // Invoke before callbacks
   for (FaceSplitPolicy* policy : faceSplitPolicies) {
     policy->beforeFaceSplit(f, bSplit);

From bc697c3a90ede3d73d25b2822d401464e9be6732 Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Fri, 1 Apr 2022 14:37:15 -0400
Subject: [PATCH 07/33] Use mutation manager throughout remeshing operations

---
 src/surface/remeshing.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index c3d31d79..7dc05704 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -318,7 +318,7 @@ void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, Mutatio
     }
 
     size_t nFlips = fixDelaunay(mesh, geometry, mm);
-    double flowDist = smoothByCircumcenter(mesh, geometry);
+    double flowDist = smoothByCircumcenter(mesh, geometry, mm);
 
     // std::cout << iIt << " : " << changedConnectivity << " " << nFlips << " " << flowDist << std::endl;
     if ((nFlips == 0) && (flowDist < 0.01)) break;

From 917bff51fced0affcecd84e25d60337a81b0e49e Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Fri, 1 Apr 2022 15:27:08 -0400
Subject: [PATCH 08/33] Don't collapse edges incident on fixed vertices

---
 include/geometrycentral/surface/mutation_manager.h |  4 ++--
 src/surface/mutation_manager.cpp                   | 10 +++++++++-
 2 files changed, 11 insertions(+), 3 deletions(-)

diff --git a/include/geometrycentral/surface/mutation_manager.h b/include/geometrycentral/surface/mutation_manager.h
index c2591d53..36827467 100644
--- a/include/geometrycentral/surface/mutation_manager.h
+++ b/include/geometrycentral/surface/mutation_manager.h
@@ -118,8 +118,8 @@ class MutationManager {
   // (set to an array which holds true if a vertex may be moved, and false if it should stay fixed)
   // Note that this array may be uninitialized, in which case all vertices are allowed to be repositioned
   // By default, any newly created vertices are repositionable, unless otherwise specified
-  // Warning: this only prevents vertices from being moved by calls to `repositionVertex()`. Even if
-  // repositionableVertices[v] is false, v may be moved by collapsing an incident edge
+  // Warning: this prevents vertices from being moved by calls to `repositionVertex()`, and also prevents incident edges
+  // from being collapsed (since this might move the vertex)
   VertexData<bool> repositionableVertices;
   void setRepositionableVertices(const VertexData<bool>& repositionableVertex, bool defaultValue = true);
   void clearRepositionableVertices();
diff --git a/src/surface/mutation_manager.cpp b/src/surface/mutation_manager.cpp
index daddb11d..31b84835 100644
--- a/src/surface/mutation_manager.cpp
+++ b/src/surface/mutation_manager.cpp
@@ -67,7 +67,15 @@ void MutationManager::setCollapsibleEdges(const EdgeData<bool>& collapsibleEdges
   collapsibleEdges.setDefault(defaultValue);
 }
 void MutationManager::clearCollapsibleEdges() { collapsibleEdges = EdgeData<bool>(); }
-bool MutationManager::mayCollapseEdge(Edge e) const { return collapsibleEdges.size() == 0 || collapsibleEdges[e]; }
+bool MutationManager::mayCollapseEdge(Edge e) const {
+  if (collapsibleEdges.size() > 0 && !collapsibleEdges[e]) return false;
+  if (repositionableVertices.size() > 0) {
+    for (Vertex v : e.adjacentVertices()) {
+      if (!repositionableVertices[v]) return false;
+    }
+  }
+  return collapsibleEdges.size() == 0 || collapsibleEdges[e];
+}
 
 void MutationManager::setFlippableEdges(const EdgeData<bool>& flippableEdges_, bool defaultValue) {
   flippableEdges = flippableEdges_;

From 2d8173f7f3556e78dff3276f091646e9004f3bbf Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Fri, 1 Apr 2022 15:35:56 -0400
Subject: [PATCH 09/33] Check for success when moving vertices, collapsing
 edges, etc

---
 src/surface/remeshing.cpp | 20 ++++++++++++++------
 1 file changed, 14 insertions(+), 6 deletions(-)

diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index 7dc05704..d5b82ae9 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -196,8 +196,10 @@ double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom
   // update final vertices
   double totalMovement = 0;
   for (Vertex v : mesh.vertices()) {
-    mm.repositionVertex(v, vertexOffsets[v]);
-    totalMovement += vertexOffsets[v].norm();
+    bool didMove = mm.repositionVertex(v, vertexOffsets[v]);
+    if (didMove) {
+      totalMovement += vertexOffsets[v].norm();
+    }
   }
   return totalMovement / mesh.nVertices();
 }
@@ -230,8 +232,10 @@ double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& g
   // update final vertices
   double totalMovement = 0;
   for (Vertex v : mesh.vertices()) {
-    mm.repositionVertex(v, vertexOffsets[v]);
-    totalMovement += vertexOffsets[v].norm();
+    bool didMove = mm.repositionVertex(v, vertexOffsets[v]);
+    if (didMove) {
+      totalMovement += vertexOffsets[v].norm();
+    }
   }
   return totalMovement / mesh.nVertices();
 }
@@ -270,7 +274,9 @@ bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geomet
     if (length_e > minLength && length_e > threshold * 1.5) {
       Vector3 newPos = edgeMidpoint(mesh, geometry, e);
       Halfedge he = mm.splitEdge(e, newPos);
-      didSplitOrCollapse = true;
+      if (he != Halfedge()) {
+        didSplitOrCollapse = true;
+      }
     } else {
       toCollapse.push_back(e);
     }
@@ -288,7 +294,9 @@ bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geomet
       Vector3 newPos = edgeMidpoint(mesh, geometry, e);
       if (shouldCollapse(mesh, geometry, e)) {
         Vertex v = mm.collapseEdge(e, newPos);
-        didSplitOrCollapse = true;
+        if (v != Vertex()) {
+          didSplitOrCollapse = true;
+        }
       }
     }
   }

From e01af886b3584c33f352fea2db29e5c9bdbbb265 Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Wed, 20 Apr 2022 15:08:17 -0400
Subject: [PATCH 10/33] When smoothing, use circumcenter for interior
 triangles, barycenter for boundary triangles

As recommended by Chen & Holst
---
 src/surface/remeshing.cpp | 18 +++++++++++++++++-
 1 file changed, 17 insertions(+), 1 deletion(-)

diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index d5b82ae9..af040338 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -46,6 +46,22 @@ Vector3 findCircumcenter(VertexPositionGeometry& geometry, Face f) {
   return findCircumcenter(p[0], p[1], p[2]);
 }
 
+// Returns the barycenter for faces incident on a nonflippable edge (e.g. a boundary edge), and the circumcenter for all
+// other faces
+Vector3 findODTCenter(VertexPositionGeometry& geom, Face f, MutationManager& mm) {
+  Vector3 p0 = geom.vertexPositions[f.halfedge().tailVertex()];
+  Vector3 p1 = geom.vertexPositions[f.halfedge().tipVertex()];
+  Vector3 p2 = geom.vertexPositions[f.halfedge().next().tipVertex()];
+
+  for (Edge e : f.adjacentEdges()) {
+    if (e.isBoundary() || !mm.mayFlipEdge(e)) {
+      // e is not flippable. return barycenter
+      return (p0 + p1 + p2) / 3.;
+    }
+  }
+  return findCircumcenter(p0, p1, p2);
+}
+
 bool isDelaunay(VertexPositionGeometry& geometry, Edge e) {
   float angle1 = geometry.cornerAngle(e.halfedge().next().next().corner());
   float angle2 = geometry.cornerAngle(e.halfedge().twin().next().next().corner());
@@ -220,7 +236,7 @@ double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& g
       vertexOffsets[v] = Vector3::zero();
       for (Face f : v.adjacentFaces()) {
         // add the circumcenter weighted by face area to the update direction
-        Vector3 circum = findCircumcenter(geometry, f);
+        Vector3 circum = findODTCenter(geometry, f, mm);
         vertexOffsets[v] += geometry.faceArea(f) * (circum - geometry.vertexPositions[v]);
       }
       vertexOffsets[v] /= (3 * geometry.vertexDualArea(v));

From 76555c97c67b3fd5c8a907588be5ebb8feb2e925 Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Thu, 26 May 2022 14:02:22 -0400
Subject: [PATCH 11/33] Add general mesh compress callback

---
 include/geometrycentral/surface/surface_mesh.h | 10 ++++++----
 src/surface/surface_mesh.cpp                   |  8 ++++++--
 2 files changed, 12 insertions(+), 6 deletions(-)

diff --git a/include/geometrycentral/surface/surface_mesh.h b/include/geometrycentral/surface/surface_mesh.h
index 1aacb800..757a81ad 100644
--- a/include/geometrycentral/surface/surface_mesh.h
+++ b/include/geometrycentral/surface/surface_mesh.h
@@ -1,9 +1,9 @@
 #pragma once
 
+#include "geometrycentral/numerical/linear_algebra_types.h"
 #include "geometrycentral/surface/halfedge_element_types.h"
 #include "geometrycentral/utilities/mesh_data.h"
 #include "geometrycentral/utilities/utilities.h"
-#include "geometrycentral/numerical/linear_algebra_types.h"
 
 #include <list>
 #include <memory>
@@ -46,7 +46,8 @@ class SurfaceMesh {
   // The output will preserve the ordering of vertices and faces.
   SurfaceMesh(const std::vector<std::vector<size_t>>& polygons);
 
-  // like above, but with an FxD array input, e.g. Fx3 for triangle mesh or Fx4 for quads. T should be some integer type.
+  // like above, but with an FxD array input, e.g. Fx3 for triangle mesh or Fx4 for quads. T should be some integer
+  // type.
   template <typename T>
   SurfaceMesh(const Eigen::MatrixBase<T>& triangles);
 
@@ -117,13 +118,13 @@ class SurfaceMesh {
   virtual bool isEdgeManifold();
   virtual bool isOriented();
   void printStatistics() const; // print info about element counts to std::cout
-  
+
   // Mesh helper utilities
   Edge connectingEdge(Vertex vA, Vertex vB); // an edge from vA -- vB if one exists; Edge() otherwise
 
   // Get representations of the face vertex indices
   std::vector<std::vector<size_t>> getFaceVertexList();
-  template<typename T>
+  template <typename T>
   DenseMatrix<T> getFaceVertexMatrix(); // all faces must have same degree
 
   std::unique_ptr<SurfaceMesh> copy() const;
@@ -186,6 +187,7 @@ class SurfaceMesh {
   std::list<std::function<void(const std::vector<size_t>&)>> edgePermuteCallbackList;
   std::list<std::function<void(const std::vector<size_t>&)>> halfedgePermuteCallbackList;
   std::list<std::function<void(const std::vector<size_t>&)>> boundaryLoopPermuteCallbackList;
+  std::list<std::function<void(void)>> compressCallbackList;
 
   // Mesh delete callbacks
   // (this unfortunately seems to be necessary; objects which have registered their callbacks above
diff --git a/src/surface/surface_mesh.cpp b/src/surface/surface_mesh.cpp
index 8ad301c7..e7f2ea68 100644
--- a/src/surface/surface_mesh.cpp
+++ b/src/surface/surface_mesh.cpp
@@ -848,10 +848,10 @@ bool SurfaceMesh::flip(Edge eFlip, bool preventSelfEdges) {
   if (preventSelfEdges) {
     // If enabled, make sure it is not a duplicate
     for (Vertex v : vc.adjacentVertices()) {
-      if(v == vd) return false;
+      if (v == vd) return false;
     }
   }
-  
+
   Face fa = ha1.face();
   Face fb = hb1.face();
 
@@ -1908,6 +1908,10 @@ void SurfaceMesh::compress() {
   compressFaces();
   compressVertices();
   isCompressedFlag = true;
+
+  for (auto& f : compressCallbackList) {
+    f();
+  }
 }
 
 

From a00489b9bdeef5b69dd9b39fbc0e9a1b33ad2d22 Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Wed, 8 Jun 2022 16:02:24 -0400
Subject: [PATCH 12/33] Fix normals on important faces

---
 src/surface/remeshing.cpp | 29 +++++++++++++++++++++++------
 1 file changed, 23 insertions(+), 6 deletions(-)

diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index af040338..19fa0c71 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -3,12 +3,28 @@
 namespace geometrycentral {
 namespace surface {
 
-Vector3 vertexNormal(VertexPositionGeometry& geometry, Vertex v) {
-  Vector3 norm = Vector3::zero();
+Vector3 vertexNormal(VertexPositionGeometry& geometry, Vertex v, MutationManager& mm) {
+  Vector3 totalNormal = Vector3::zero();
+  Vector3 fixedFaceNormals = Vector3::zero();
+  bool foundFixedFace = false;
   for (Corner c : v.adjacentCorners()) {
-    norm += geometry.cornerAngle(c) * geometry.faceNormal(c.face());
+    size_t nFixedVertices = 0;
+    for (Vertex w : c.face().adjacentVertices()) {
+      if (!mm.mayRepositionVertex(w)) nFixedVertices++;
+    }
+
+    Vector3 cornerNormal = geometry.cornerAngle(c) * geometry.faceNormal(c.face());
+    if (nFixedVertices >= 2) {
+      fixedFaceNormals += cornerNormal;
+      foundFixedFace = true;
+    }
+    totalNormal += cornerNormal;
+  }
+  if (foundFixedFace) {
+    return normalize(fixedFaceNormals);
+  } else {
+    return normalize(totalNormal);
   }
-  return normalize(norm);
 }
 
 inline Vector3 projectToPlane(Vector3 v, Vector3 norm) { return v - norm * dot(norm, v); }
@@ -205,7 +221,8 @@ double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom
 
       // and project the average to the tangent plane
       Vector3 updateDirection = avgNeighbor - geometry.vertexPositions[v];
-      vertexOffsets[v] = stepSize * projectToPlane(updateDirection, vertexNormal(geometry, v));
+      Vector3 normal = vertexNormal(geometry, v, mm);
+      vertexOffsets[v] = stepSize * projectToPlane(updateDirection, normal);
     }
   }
 
@@ -241,7 +258,7 @@ double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& g
       }
       vertexOffsets[v] /= (3 * geometry.vertexDualArea(v));
       // project update direction to tangent plane
-      vertexOffsets[v] = stepSize * projectToPlane(vertexOffsets[v], vertexNormal(geometry, v)) / 2.;
+      vertexOffsets[v] = stepSize * projectToPlane(vertexOffsets[v], vertexNormal(geometry, v, mm)) / 2.;
     }
   }
 

From 15cddad133ea814b67d27db518f00457f53f1cd4 Mon Sep 17 00:00:00 2001
From: Caleb Brakensiek <69546117+cbrakensiek@users.noreply.github.com>
Date: Sat, 17 Apr 2021 10:46:12 -0700
Subject: [PATCH 13/33] adding remeshing functions

---
 include/geometrycentral/surface/remeshing.h |  24 ++
 src/CMakeLists.txt                          |   2 +
 src/surface/remeshing.cpp                   | 326 ++++++++++++++++++++
 3 files changed, 352 insertions(+)
 create mode 100644 include/geometrycentral/surface/remeshing.h
 create mode 100644 src/surface/remeshing.cpp

diff --git a/include/geometrycentral/surface/remeshing.h b/include/geometrycentral/surface/remeshing.h
new file mode 100644
index 00000000..ffc370f3
--- /dev/null
+++ b/include/geometrycentral/surface/remeshing.h
@@ -0,0 +1,24 @@
+#pragma once
+
+#include "geometrycentral/surface/manifold_surface_mesh.h"
+#include "geometrycentral/surface/vertex_position_geometry.h"
+
+#include <queue>
+
+namespace geometrycentral {
+namespace surface {
+
+// makes all triangles delaunay
+void fixDelaunay(SurfaceMesh& mesh, VertexPositionGeometry& geometry);
+// average positions of vertices based on surrounding vertex positions
+void smoothByLaplacian(SurfaceMesh& mesh, VertexPositionGeometry& geometry);
+// average positions of vertices based on surrounding triangle circumenters
+void smoothByCircumcenter(SurfaceMesh& mesh, VertexPositionGeometry& geometry);
+// applies splits and collapses to adjust edge lengths based on the curvature
+// flatLength: specifies how long the target edge length should be in flat regions
+// epsilon: controls how much variation in target length occurs due to curvature
+// minLength: specifies the minimum possible length an edge could become
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength, double epsilon, double minLength, bool curvatureAdaptive = true);
+
+} // namespace surface
+} // namespace geometrycentral
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index d71b8c1e..c97da2ed 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -43,6 +43,7 @@ SET(SRCS
   surface/fast_marching_method.cpp
   surface/uniformize.cpp
   surface/parameterize.cpp
+  surface/remeshing.cpp
   surface/surgery.cpp
   surface/simple_idt.cpp
   surface/exact_polyhedral_geodesics.cpp
@@ -119,6 +120,7 @@ SET(HEADERS
   ${INCLUDE_ROOT}/surface/parameterize.h
   ${INCLUDE_ROOT}/surface/poisson_disk_sampler.h
   ${INCLUDE_ROOT}/surface/quadric_error_simplification.h
+  ${INCLUDE_ROOT}/surface/remeshing.h
   ${INCLUDE_ROOT}/surface/rich_surface_mesh_data.h
   ${INCLUDE_ROOT}/surface/rich_surface_mesh_data.ipp
   ${INCLUDE_ROOT}/surface/polygon_soup_mesh.h
diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
new file mode 100644
index 00000000..b3000f02
--- /dev/null
+++ b/src/surface/remeshing.cpp
@@ -0,0 +1,326 @@
+#include "geometrycentral/surface/remeshing.h"
+
+namespace geometrycentral {
+namespace surface {
+
+using std::queue;
+
+Vector3 vertexNormal(VertexPositionGeometry& geometry, Vertex v)
+{
+    Vector3 norm = Vector3::zero();
+    for(Corner c : v.adjacentCorners()){
+        norm += geometry.cornerAngle(c) * geometry.faceNormal(c.face());
+    }
+    return normalize(norm);
+}
+
+inline Vector3 projectToPlane(Vector3 v, Vector3 norm)
+{
+    return v - norm * dot(norm, v);
+}
+
+inline Vector3 edgeMidpoint(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e)
+{
+    Vector3 endPos1 = geometry.inputVertexPositions[e.halfedge().tailVertex()];
+    Vector3 endPos2 = geometry.inputVertexPositions[e.halfedge().tipVertex()];
+    return (endPos1+endPos2)/2;
+}
+
+Vector3 findCircumcenter(Vector3 p1, Vector3 p2, Vector3 p3)
+{
+    // barycentric coordinates of circumcenter
+    double a = (p3 - p2).norm();
+    double b = (p3 - p1).norm();
+    double c = (p2 - p1).norm();
+    double a2 = a * a;
+    double b2 = b * b;
+    double c2 = c * c;
+    Vector3 O{a2 * (b2 + c2 - a2), b2 * (c2 + a2 - b2), c2 * (a2 + b2 - c2)};
+    // normalize to sum of 1
+    O /= O[0] + O[1] + O[2];
+    // change back to space
+    return O[0] * p1 + O[1] * p2 + O[2] * p3;
+}
+
+Vector3 findCircumcenter(VertexPositionGeometry& geometry, Face f)
+{
+    // retrieve the face's vertices
+    int index = 0;
+    Vector3 p[3];
+    for (Vertex v0 : f.adjacentVertices())
+    {
+        p[index] = geometry.inputVertexPositions[v0];
+        index++;
+    }
+    return findCircumcenter(p[0], p[1], p[2]);
+}
+
+bool isDelaunay(VertexPositionGeometry& geometry, Edge e)
+{
+    float angle1 = geometry.cornerAngle(e.halfedge().next().next().corner());
+    float angle2 = geometry.cornerAngle(e.halfedge().twin().next().next().corner());
+    return angle1 + angle2 <= PI;
+}
+
+inline double diamondAngle(Vector3 a, Vector3 b, Vector3 c, Vector3 d) // dihedral angle at edge a-b
+{
+    Vector3 n1 = cross(b-a, c-a);
+    Vector3 n2 = cross(b-d, a-d);
+    return PI-angle(n1, n2);
+}
+
+inline bool checkFoldover(Vector3 a, Vector3 b, Vector3 c, Vector3 x, double angle)
+{
+    return diamondAngle(a, b, c, x) < angle;
+}
+
+bool shouldCollapse(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e)
+{
+    std::vector<Halfedge> toCheck;
+    Vertex v1 = e.halfedge().vertex();
+    Vertex v2 = e.halfedge().twin().vertex();
+    Vector3 midpoint = edgeMidpoint(mesh, geometry, e);
+    // find (halfedge) link around the edge, starting with those surrounding v1
+    Halfedge he = v1.halfedge();
+    Halfedge st = he;
+    do{
+        he = he.next();
+        if(he.vertex() != v2 && he.next().vertex() != v2){
+            toCheck.push_back(he);
+        }
+        he = he.next().twin();
+    }
+    while(he != st);
+    // link around v2
+    he = v2.halfedge();
+    st = he;
+    do{
+        he = he.next();
+        if(he.vertex() != v1 && he.next().vertex() != v1){
+            toCheck.push_back(he);
+        }
+        he = he.next().twin();
+    }
+    while(he != st);
+    
+    // see if the point that would form after a collapse would cause a major foldover with surrounding edges
+    for(Halfedge he0 : toCheck){
+        Halfedge heT = he0.twin();
+        Vertex v1 = heT.vertex();
+        Vertex v2 = heT.next().vertex();
+        Vertex v3 = heT.next().next().vertex();
+        Vector3 a = geometry.inputVertexPositions[v1];
+        Vector3 b = geometry.inputVertexPositions[v2];
+        Vector3 c = geometry.inputVertexPositions[v3];
+        if(checkFoldover(a, b, c, midpoint, 2)){
+            return false;
+        }
+    }
+    return true;
+}
+
+double getSmoothMeanCurvature(VertexPositionGeometry& geometry, Vertex v)
+{
+    double A = geometry.vertexDualArea(v);
+    double S = geometry.vertexMeanCurvature(v);
+    double K = S / A;
+    return K;
+}
+
+// flatLength: specifies how long the target edge length should be in flat regions
+// epsilon: controls how much variation in target length occurs due to curvature
+
+double findMeanTargetL(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e, double flatLength, double epsilon)
+{
+    double averageH = 0;
+    for (Vertex v : e.adjacentVertices()) {
+        averageH += getSmoothMeanCurvature(geometry, v);
+    }
+    averageH /= 2;
+    double L = flatLength * epsilon / (fabs(averageH) + epsilon);
+    return L;
+}
+
+
+
+void fixDelaunay(SurfaceMesh& mesh, VertexPositionGeometry& geometry)
+{
+    // queue of edges to check if Delaunay
+    queue<Edge> toCheck;
+    // true if edge is currently in toCheck
+    EdgeData<bool> inQueue(mesh);
+    // start with all edges
+    for (Edge e : mesh.edges())
+    {
+        toCheck.push(e);
+        inQueue[e] = true;
+    }
+    // counter and limit for number of flips
+    int flipMax = 100 * mesh.nVertices();
+    int flipCnt = 0;
+    while (!toCheck.empty() && flipCnt < flipMax)
+    {
+        Edge e = toCheck.front();
+        toCheck.pop();
+        inQueue[e] = false;
+        // if not Delaunay, flip edge and enqueue the surrounding "diamond" edges (if not already)
+        if (!e.isBoundary() && !isDelaunay(geometry, e))
+        {
+            flipCnt++;
+            Halfedge he = e.halfedge();
+            Halfedge he1 = he.next();
+            Halfedge he2 = he1.next();
+            Halfedge he3 = he.twin().next();
+            Halfedge he4 = he3.next();
+
+            if (!inQueue[he1.edge()])
+            {
+                toCheck.push(he1.edge());
+                inQueue[he1.edge()] = true;
+            }
+            if (!inQueue[he2.edge()])
+            {
+                toCheck.push(he2.edge());
+                inQueue[he2.edge()] = true;
+            }
+            if (!inQueue[he3.edge()])
+            {
+                toCheck.push(he3.edge());
+                inQueue[he3.edge()] = true;
+            }
+            if (!inQueue[he4.edge()])
+            {
+                toCheck.push(he4.edge());
+                inQueue[he4.edge()] = true;
+            }
+            mesh.flip(e);
+        }
+    }
+}
+
+void smoothByLaplacian(SurfaceMesh& mesh, VertexPositionGeometry& geometry)
+{
+    // smoothed vertex positions
+    VertexData<Vector3> newVertexPosition(mesh);
+    for (Vertex v : mesh.vertices())
+    {
+        if(v.isBoundary())
+        {
+            newVertexPosition[v] = geometry.inputVertexPositions[v];
+        }
+        else
+        {
+            // calculate average of surrounding vertices
+            newVertexPosition[v] = Vector3::zero();
+            for (Vertex j : v.adjacentVertices())
+            {
+                newVertexPosition[v] += geometry.inputVertexPositions[j];
+            }
+            newVertexPosition[v] /= v.degree();
+            // and project the average to the tangent plane
+            Vector3 updateDirection = newVertexPosition[v] - geometry.inputVertexPositions[v];
+            updateDirection = projectToPlane(updateDirection, vertexNormal(geometry, v));
+            
+            newVertexPosition[v] = geometry.inputVertexPositions[v] + 1*updateDirection;
+        }
+    }
+    // update final vertices
+    for (Vertex v : mesh.vertices())
+    {
+        geometry.inputVertexPositions[v] = newVertexPosition[v];
+    }
+}
+
+void smoothByCircumcenter(SurfaceMesh& mesh, VertexPositionGeometry& geometry)
+{
+    geometry.requireFaceAreas();
+    // smoothed vertex positions
+    VertexData<Vector3> newVertexPosition(mesh);
+    for (Vertex v : mesh.vertices())
+    {
+        newVertexPosition[v] = geometry.inputVertexPositions[v]; // default
+        if(!v.isBoundary())
+        {
+            Vector3 updateDirection = Vector3::zero();
+            for (Face f : v.adjacentFaces())
+            {
+                // add the circumcenter weighted by face area to the update direction
+                Vector3 circum = findCircumcenter(geometry, f);
+                updateDirection += geometry.faceArea(f) * (circum - geometry.inputVertexPositions[v]);
+            }
+            updateDirection /= (3 * geometry.vertexDualArea(v));
+            // project update direction to tangent plane
+            updateDirection = projectToPlane(updateDirection, vertexNormal(geometry, v));
+            Vector3 newPos = geometry.inputVertexPositions[v] + .5 * updateDirection;
+            newVertexPosition[v] = newPos;
+        }
+    }
+    // update final vertices
+    for (Vertex v : mesh.vertices())
+    {
+        geometry.inputVertexPositions[v] = newVertexPosition[v];
+    }
+}
+
+
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength, double epsilon, double minLength, bool curvatureAdaptive)
+{
+    bool didSplitOrCollapse = false;
+    // queues of edges to CHECK to change
+    std::vector<Edge> toSplit;
+    std::vector<Edge> toCollapse;
+    
+    for(Edge e : mesh.edges())
+    {
+        toSplit.push_back(e);
+    }
+    
+    // actually splitting
+    while(!toSplit.empty())
+    {
+        Edge e = toSplit.back();
+        toSplit.pop_back();
+        double length_e = geometry.edgeLength(e);
+        double threshold = (curvatureAdaptive) ? findMeanTargetL(mesh, geometry, e, flatLength, epsilon) : flatLength;
+        if(length_e > minLength && length_e > threshold * 1.5)
+        {
+            Vector3 newPos = edgeMidpoint(mesh, geometry, e);
+            Halfedge he = mesh.splitEdgeTriangular(e);
+            didSplitOrCollapse = true;
+            Vertex newV = he.vertex();
+            geometry.inputVertexPositions[newV] = newPos;
+        }
+        else
+        {
+            toCollapse.push_back(e);
+        }                
+        
+    }
+    // actually collapsing
+    while(!toCollapse.empty())
+    {
+        Edge e = toCollapse.back();
+        toCollapse.pop_back();
+        if(e.halfedge().next().getIndex() != INVALID_IND) // make sure it exists
+        {
+            double threshold = (curvatureAdaptive) ? findMeanTargetL(mesh, geometry, e, flatLength, epsilon) : flatLength;
+            if(geometry.edgeLength(e) < threshold * 0.5)
+            {
+                Vector3 newPos = edgeMidpoint(mesh, geometry, e);
+                if(shouldCollapse(mesh, geometry, e)) {
+                    Vertex v = mesh.collapseEdgeTriangular(e);
+                    didSplitOrCollapse = true;
+                    if (v != Vertex()) {
+                        if(!v.isBoundary()) {
+                            geometry.inputVertexPositions[v] = newPos;
+                        }
+                    }
+                }
+            }
+        }
+    }
+    return didSplitOrCollapse;
+}
+
+} // namespace surface
+} // namespace geometrycentral

From e7756cfac2ff7e06b0b3e44b69b339ba0ae8fe1a Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Thu, 31 Mar 2022 16:10:17 -0400
Subject: [PATCH 14/33] Formatting

---
 include/geometrycentral/surface/remeshing.h |   6 +-
 src/surface/remeshing.cpp                   | 494 +++++++++-----------
 2 files changed, 230 insertions(+), 270 deletions(-)

diff --git a/include/geometrycentral/surface/remeshing.h b/include/geometrycentral/surface/remeshing.h
index ffc370f3..106361d3 100644
--- a/include/geometrycentral/surface/remeshing.h
+++ b/include/geometrycentral/surface/remeshing.h
@@ -10,15 +10,19 @@ namespace surface {
 
 // makes all triangles delaunay
 void fixDelaunay(SurfaceMesh& mesh, VertexPositionGeometry& geometry);
+
 // average positions of vertices based on surrounding vertex positions
 void smoothByLaplacian(SurfaceMesh& mesh, VertexPositionGeometry& geometry);
+
 // average positions of vertices based on surrounding triangle circumenters
 void smoothByCircumcenter(SurfaceMesh& mesh, VertexPositionGeometry& geometry);
+
 // applies splits and collapses to adjust edge lengths based on the curvature
 // flatLength: specifies how long the target edge length should be in flat regions
 // epsilon: controls how much variation in target length occurs due to curvature
 // minLength: specifies the minimum possible length an edge could become
-bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength, double epsilon, double minLength, bool curvatureAdaptive = true);
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength, double epsilon,
+                       double minLength, bool curvatureAdaptive = true);
 
 } // namespace surface
 } // namespace geometrycentral
diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index b3000f02..6c7ccd45 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -5,321 +5,277 @@ namespace surface {
 
 using std::queue;
 
-Vector3 vertexNormal(VertexPositionGeometry& geometry, Vertex v)
-{
-    Vector3 norm = Vector3::zero();
-    for(Corner c : v.adjacentCorners()){
-        norm += geometry.cornerAngle(c) * geometry.faceNormal(c.face());
-    }
-    return normalize(norm);
+Vector3 vertexNormal(VertexPositionGeometry& geometry, Vertex v) {
+  Vector3 norm = Vector3::zero();
+  for (Corner c : v.adjacentCorners()) {
+    norm += geometry.cornerAngle(c) * geometry.faceNormal(c.face());
+  }
+  return normalize(norm);
 }
 
-inline Vector3 projectToPlane(Vector3 v, Vector3 norm)
-{
-    return v - norm * dot(norm, v);
-}
+inline Vector3 projectToPlane(Vector3 v, Vector3 norm) { return v - norm * dot(norm, v); }
 
-inline Vector3 edgeMidpoint(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e)
-{
-    Vector3 endPos1 = geometry.inputVertexPositions[e.halfedge().tailVertex()];
-    Vector3 endPos2 = geometry.inputVertexPositions[e.halfedge().tipVertex()];
-    return (endPos1+endPos2)/2;
+inline Vector3 edgeMidpoint(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e) {
+  Vector3 endPos1 = geometry.vertexPositions[e.halfedge().tailVertex()];
+  Vector3 endPos2 = geometry.vertexPositions[e.halfedge().tipVertex()];
+  return (endPos1 + endPos2) / 2;
 }
 
-Vector3 findCircumcenter(Vector3 p1, Vector3 p2, Vector3 p3)
-{
-    // barycentric coordinates of circumcenter
-    double a = (p3 - p2).norm();
-    double b = (p3 - p1).norm();
-    double c = (p2 - p1).norm();
-    double a2 = a * a;
-    double b2 = b * b;
-    double c2 = c * c;
-    Vector3 O{a2 * (b2 + c2 - a2), b2 * (c2 + a2 - b2), c2 * (a2 + b2 - c2)};
-    // normalize to sum of 1
-    O /= O[0] + O[1] + O[2];
-    // change back to space
-    return O[0] * p1 + O[1] * p2 + O[2] * p3;
+Vector3 findCircumcenter(Vector3 p1, Vector3 p2, Vector3 p3) {
+  // barycentric coordinates of circumcenter
+  double a = (p3 - p2).norm();
+  double b = (p3 - p1).norm();
+  double c = (p2 - p1).norm();
+  double a2 = a * a;
+  double b2 = b * b;
+  double c2 = c * c;
+  Vector3 O{a2 * (b2 + c2 - a2), b2 * (c2 + a2 - b2), c2 * (a2 + b2 - c2)};
+  // normalize to sum of 1
+  O /= O[0] + O[1] + O[2];
+  // change back to space
+  return O[0] * p1 + O[1] * p2 + O[2] * p3;
 }
 
-Vector3 findCircumcenter(VertexPositionGeometry& geometry, Face f)
-{
-    // retrieve the face's vertices
-    int index = 0;
-    Vector3 p[3];
-    for (Vertex v0 : f.adjacentVertices())
-    {
-        p[index] = geometry.inputVertexPositions[v0];
-        index++;
-    }
-    return findCircumcenter(p[0], p[1], p[2]);
+Vector3 findCircumcenter(VertexPositionGeometry& geometry, Face f) {
+  // retrieve the face's vertices
+  int index = 0;
+  Vector3 p[3];
+  for (Vertex v0 : f.adjacentVertices()) {
+    p[index] = geometry.vertexPositions[v0];
+    index++;
+  }
+  return findCircumcenter(p[0], p[1], p[2]);
 }
 
-bool isDelaunay(VertexPositionGeometry& geometry, Edge e)
-{
-    float angle1 = geometry.cornerAngle(e.halfedge().next().next().corner());
-    float angle2 = geometry.cornerAngle(e.halfedge().twin().next().next().corner());
-    return angle1 + angle2 <= PI;
+bool isDelaunay(VertexPositionGeometry& geometry, Edge e) {
+  float angle1 = geometry.cornerAngle(e.halfedge().next().next().corner());
+  float angle2 = geometry.cornerAngle(e.halfedge().twin().next().next().corner());
+  return angle1 + angle2 <= PI;
 }
 
 inline double diamondAngle(Vector3 a, Vector3 b, Vector3 c, Vector3 d) // dihedral angle at edge a-b
 {
-    Vector3 n1 = cross(b-a, c-a);
-    Vector3 n2 = cross(b-d, a-d);
-    return PI-angle(n1, n2);
+  Vector3 n1 = cross(b - a, c - a);
+  Vector3 n2 = cross(b - d, a - d);
+  return PI - angle(n1, n2);
 }
 
-inline bool checkFoldover(Vector3 a, Vector3 b, Vector3 c, Vector3 x, double angle)
-{
-    return diamondAngle(a, b, c, x) < angle;
+inline bool checkFoldover(Vector3 a, Vector3 b, Vector3 c, Vector3 x, double angle) {
+  return diamondAngle(a, b, c, x) < angle;
 }
 
-bool shouldCollapse(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e)
-{
-    std::vector<Halfedge> toCheck;
-    Vertex v1 = e.halfedge().vertex();
-    Vertex v2 = e.halfedge().twin().vertex();
-    Vector3 midpoint = edgeMidpoint(mesh, geometry, e);
-    // find (halfedge) link around the edge, starting with those surrounding v1
-    Halfedge he = v1.halfedge();
-    Halfedge st = he;
-    do{
-        he = he.next();
-        if(he.vertex() != v2 && he.next().vertex() != v2){
-            toCheck.push_back(he);
-        }
-        he = he.next().twin();
+bool shouldCollapse(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e) {
+  std::vector<Halfedge> toCheck;
+  Vertex v1 = e.halfedge().vertex();
+  Vertex v2 = e.halfedge().twin().vertex();
+  Vector3 midpoint = edgeMidpoint(mesh, geometry, e);
+  // find (halfedge) link around the edge, starting with those surrounding v1
+  Halfedge he = v1.halfedge();
+  Halfedge st = he;
+  do {
+    he = he.next();
+    if (he.vertex() != v2 && he.next().vertex() != v2) {
+      toCheck.push_back(he);
     }
-    while(he != st);
-    // link around v2
-    he = v2.halfedge();
-    st = he;
-    do{
-        he = he.next();
-        if(he.vertex() != v1 && he.next().vertex() != v1){
-            toCheck.push_back(he);
-        }
-        he = he.next().twin();
+    he = he.next().twin();
+  } while (he != st);
+  // link around v2
+  he = v2.halfedge();
+  st = he;
+  do {
+    he = he.next();
+    if (he.vertex() != v1 && he.next().vertex() != v1) {
+      toCheck.push_back(he);
     }
-    while(he != st);
-    
-    // see if the point that would form after a collapse would cause a major foldover with surrounding edges
-    for(Halfedge he0 : toCheck){
-        Halfedge heT = he0.twin();
-        Vertex v1 = heT.vertex();
-        Vertex v2 = heT.next().vertex();
-        Vertex v3 = heT.next().next().vertex();
-        Vector3 a = geometry.inputVertexPositions[v1];
-        Vector3 b = geometry.inputVertexPositions[v2];
-        Vector3 c = geometry.inputVertexPositions[v3];
-        if(checkFoldover(a, b, c, midpoint, 2)){
-            return false;
-        }
+    he = he.next().twin();
+  } while (he != st);
+
+  // see if the point that would form after a collapse would cause a major foldover with surrounding edges
+  for (Halfedge he0 : toCheck) {
+    Halfedge heT = he0.twin();
+    Vertex v1 = heT.vertex();
+    Vertex v2 = heT.next().vertex();
+    Vertex v3 = heT.next().next().vertex();
+    Vector3 a = geometry.vertexPositions[v1];
+    Vector3 b = geometry.vertexPositions[v2];
+    Vector3 c = geometry.vertexPositions[v3];
+    if (checkFoldover(a, b, c, midpoint, 2)) {
+      return false;
     }
-    return true;
+  }
+  return true;
 }
 
-double getSmoothMeanCurvature(VertexPositionGeometry& geometry, Vertex v)
-{
-    double A = geometry.vertexDualArea(v);
-    double S = geometry.vertexMeanCurvature(v);
-    double K = S / A;
-    return K;
+double getSmoothMeanCurvature(VertexPositionGeometry& geometry, Vertex v) {
+  double A = geometry.vertexDualArea(v);
+  double S = geometry.vertexMeanCurvature(v);
+  double K = S / A;
+  return K;
 }
 
 // flatLength: specifies how long the target edge length should be in flat regions
 // epsilon: controls how much variation in target length occurs due to curvature
 
-double findMeanTargetL(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e, double flatLength, double epsilon)
-{
-    double averageH = 0;
-    for (Vertex v : e.adjacentVertices()) {
-        averageH += getSmoothMeanCurvature(geometry, v);
-    }
-    averageH /= 2;
-    double L = flatLength * epsilon / (fabs(averageH) + epsilon);
-    return L;
+double findMeanTargetL(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e, double flatLength, double epsilon) {
+  double averageH = 0;
+  for (Vertex v : e.adjacentVertices()) {
+    averageH += getSmoothMeanCurvature(geometry, v);
+  }
+  averageH /= 2;
+  double L = flatLength * epsilon / (fabs(averageH) + epsilon);
+  return L;
 }
 
 
+void fixDelaunay(SurfaceMesh& mesh, VertexPositionGeometry& geometry) {
+  // queue of edges to check if Delaunay
+  queue<Edge> toCheck;
+  // true if edge is currently in toCheck
+  EdgeData<bool> inQueue(mesh);
+  // start with all edges
+  for (Edge e : mesh.edges()) {
+    toCheck.push(e);
+    inQueue[e] = true;
+  }
+  // counter and limit for number of flips
+  int flipMax = 100 * mesh.nVertices();
+  int flipCnt = 0;
+  while (!toCheck.empty() && flipCnt < flipMax) {
+    Edge e = toCheck.front();
+    toCheck.pop();
+    inQueue[e] = false;
+    // if not Delaunay, flip edge and enqueue the surrounding "diamond" edges (if not already)
+    if (!e.isBoundary() && !isDelaunay(geometry, e)) {
+      flipCnt++;
+      Halfedge he = e.halfedge();
+      Halfedge he1 = he.next();
+      Halfedge he2 = he1.next();
+      Halfedge he3 = he.twin().next();
+      Halfedge he4 = he3.next();
 
-void fixDelaunay(SurfaceMesh& mesh, VertexPositionGeometry& geometry)
-{
-    // queue of edges to check if Delaunay
-    queue<Edge> toCheck;
-    // true if edge is currently in toCheck
-    EdgeData<bool> inQueue(mesh);
-    // start with all edges
-    for (Edge e : mesh.edges())
-    {
-        toCheck.push(e);
-        inQueue[e] = true;
-    }
-    // counter and limit for number of flips
-    int flipMax = 100 * mesh.nVertices();
-    int flipCnt = 0;
-    while (!toCheck.empty() && flipCnt < flipMax)
-    {
-        Edge e = toCheck.front();
-        toCheck.pop();
-        inQueue[e] = false;
-        // if not Delaunay, flip edge and enqueue the surrounding "diamond" edges (if not already)
-        if (!e.isBoundary() && !isDelaunay(geometry, e))
-        {
-            flipCnt++;
-            Halfedge he = e.halfedge();
-            Halfedge he1 = he.next();
-            Halfedge he2 = he1.next();
-            Halfedge he3 = he.twin().next();
-            Halfedge he4 = he3.next();
-
-            if (!inQueue[he1.edge()])
-            {
-                toCheck.push(he1.edge());
-                inQueue[he1.edge()] = true;
-            }
-            if (!inQueue[he2.edge()])
-            {
-                toCheck.push(he2.edge());
-                inQueue[he2.edge()] = true;
-            }
-            if (!inQueue[he3.edge()])
-            {
-                toCheck.push(he3.edge());
-                inQueue[he3.edge()] = true;
-            }
-            if (!inQueue[he4.edge()])
-            {
-                toCheck.push(he4.edge());
-                inQueue[he4.edge()] = true;
-            }
-            mesh.flip(e);
-        }
+      if (!inQueue[he1.edge()]) {
+        toCheck.push(he1.edge());
+        inQueue[he1.edge()] = true;
+      }
+      if (!inQueue[he2.edge()]) {
+        toCheck.push(he2.edge());
+        inQueue[he2.edge()] = true;
+      }
+      if (!inQueue[he3.edge()]) {
+        toCheck.push(he3.edge());
+        inQueue[he3.edge()] = true;
+      }
+      if (!inQueue[he4.edge()]) {
+        toCheck.push(he4.edge());
+        inQueue[he4.edge()] = true;
+      }
+      mesh.flip(e);
     }
+  }
 }
 
-void smoothByLaplacian(SurfaceMesh& mesh, VertexPositionGeometry& geometry)
-{
-    // smoothed vertex positions
-    VertexData<Vector3> newVertexPosition(mesh);
-    for (Vertex v : mesh.vertices())
-    {
-        if(v.isBoundary())
-        {
-            newVertexPosition[v] = geometry.inputVertexPositions[v];
-        }
-        else
-        {
-            // calculate average of surrounding vertices
-            newVertexPosition[v] = Vector3::zero();
-            for (Vertex j : v.adjacentVertices())
-            {
-                newVertexPosition[v] += geometry.inputVertexPositions[j];
-            }
-            newVertexPosition[v] /= v.degree();
-            // and project the average to the tangent plane
-            Vector3 updateDirection = newVertexPosition[v] - geometry.inputVertexPositions[v];
-            updateDirection = projectToPlane(updateDirection, vertexNormal(geometry, v));
-            
-            newVertexPosition[v] = geometry.inputVertexPositions[v] + 1*updateDirection;
-        }
-    }
-    // update final vertices
-    for (Vertex v : mesh.vertices())
-    {
-        geometry.inputVertexPositions[v] = newVertexPosition[v];
+void smoothByLaplacian(SurfaceMesh& mesh, VertexPositionGeometry& geometry) {
+  // smoothed vertex positions
+  VertexData<Vector3> newVertexPosition(mesh);
+  for (Vertex v : mesh.vertices()) {
+    if (v.isBoundary()) {
+      newVertexPosition[v] = geometry.vertexPositions[v];
+    } else {
+      // calculate average of surrounding vertices
+      newVertexPosition[v] = Vector3::zero();
+      for (Vertex j : v.adjacentVertices()) {
+        newVertexPosition[v] += geometry.vertexPositions[j];
+      }
+      newVertexPosition[v] /= v.degree();
+      // and project the average to the tangent plane
+      Vector3 updateDirection = newVertexPosition[v] - geometry.vertexPositions[v];
+      updateDirection = projectToPlane(updateDirection, vertexNormal(geometry, v));
+
+      newVertexPosition[v] = geometry.vertexPositions[v] + 1 * updateDirection;
     }
+  }
+  // update final vertices
+  for (Vertex v : mesh.vertices()) {
+    geometry.vertexPositions[v] = newVertexPosition[v];
+  }
 }
 
-void smoothByCircumcenter(SurfaceMesh& mesh, VertexPositionGeometry& geometry)
-{
-    geometry.requireFaceAreas();
-    // smoothed vertex positions
-    VertexData<Vector3> newVertexPosition(mesh);
-    for (Vertex v : mesh.vertices())
-    {
-        newVertexPosition[v] = geometry.inputVertexPositions[v]; // default
-        if(!v.isBoundary())
-        {
-            Vector3 updateDirection = Vector3::zero();
-            for (Face f : v.adjacentFaces())
-            {
-                // add the circumcenter weighted by face area to the update direction
-                Vector3 circum = findCircumcenter(geometry, f);
-                updateDirection += geometry.faceArea(f) * (circum - geometry.inputVertexPositions[v]);
-            }
-            updateDirection /= (3 * geometry.vertexDualArea(v));
-            // project update direction to tangent plane
-            updateDirection = projectToPlane(updateDirection, vertexNormal(geometry, v));
-            Vector3 newPos = geometry.inputVertexPositions[v] + .5 * updateDirection;
-            newVertexPosition[v] = newPos;
-        }
-    }
-    // update final vertices
-    for (Vertex v : mesh.vertices())
-    {
-        geometry.inputVertexPositions[v] = newVertexPosition[v];
+void smoothByCircumcenter(SurfaceMesh& mesh, VertexPositionGeometry& geometry) {
+  geometry.requireFaceAreas();
+  // smoothed vertex positions
+  VertexData<Vector3> newVertexPosition(mesh);
+  for (Vertex v : mesh.vertices()) {
+    newVertexPosition[v] = geometry.vertexPositions[v]; // default
+    if (!v.isBoundary()) {
+      Vector3 updateDirection = Vector3::zero();
+      for (Face f : v.adjacentFaces()) {
+        // add the circumcenter weighted by face area to the update direction
+        Vector3 circum = findCircumcenter(geometry, f);
+        updateDirection += geometry.faceArea(f) * (circum - geometry.vertexPositions[v]);
+      }
+      updateDirection /= (3 * geometry.vertexDualArea(v));
+      // project update direction to tangent plane
+      updateDirection = projectToPlane(updateDirection, vertexNormal(geometry, v));
+      Vector3 newPos = geometry.vertexPositions[v] + .5 * updateDirection;
+      newVertexPosition[v] = newPos;
     }
+  }
+  // update final vertices
+  for (Vertex v : mesh.vertices()) {
+    geometry.vertexPositions[v] = newVertexPosition[v];
+  }
 }
 
 
-bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength, double epsilon, double minLength, bool curvatureAdaptive)
-{
-    bool didSplitOrCollapse = false;
-    // queues of edges to CHECK to change
-    std::vector<Edge> toSplit;
-    std::vector<Edge> toCollapse;
-    
-    for(Edge e : mesh.edges())
-    {
-        toSplit.push_back(e);
-    }
-    
-    // actually splitting
-    while(!toSplit.empty())
-    {
-        Edge e = toSplit.back();
-        toSplit.pop_back();
-        double length_e = geometry.edgeLength(e);
-        double threshold = (curvatureAdaptive) ? findMeanTargetL(mesh, geometry, e, flatLength, epsilon) : flatLength;
-        if(length_e > minLength && length_e > threshold * 1.5)
-        {
-            Vector3 newPos = edgeMidpoint(mesh, geometry, e);
-            Halfedge he = mesh.splitEdgeTriangular(e);
-            didSplitOrCollapse = true;
-            Vertex newV = he.vertex();
-            geometry.inputVertexPositions[newV] = newPos;
-        }
-        else
-        {
-            toCollapse.push_back(e);
-        }                
-        
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength, double epsilon,
+                       double minLength, bool curvatureAdaptive) {
+  bool didSplitOrCollapse = false;
+  // queues of edges to CHECK to change
+  std::vector<Edge> toSplit;
+  std::vector<Edge> toCollapse;
+
+  for (Edge e : mesh.edges()) {
+    toSplit.push_back(e);
+  }
+
+  // actually splitting
+  while (!toSplit.empty()) {
+    Edge e = toSplit.back();
+    toSplit.pop_back();
+    double length_e = geometry.edgeLength(e);
+    double threshold = (curvatureAdaptive) ? findMeanTargetL(mesh, geometry, e, flatLength, epsilon) : flatLength;
+    if (length_e > minLength && length_e > threshold * 1.5) {
+      Vector3 newPos = edgeMidpoint(mesh, geometry, e);
+      Halfedge he = mesh.splitEdgeTriangular(e);
+      didSplitOrCollapse = true;
+      Vertex newV = he.vertex();
+      geometry.vertexPositions[newV] = newPos;
+    } else {
+      toCollapse.push_back(e);
     }
-    // actually collapsing
-    while(!toCollapse.empty())
+  }
+  // actually collapsing
+  while (!toCollapse.empty()) {
+    Edge e = toCollapse.back();
+    toCollapse.pop_back();
+    if (e.halfedge().next().getIndex() != INVALID_IND) // make sure it exists
     {
-        Edge e = toCollapse.back();
-        toCollapse.pop_back();
-        if(e.halfedge().next().getIndex() != INVALID_IND) // make sure it exists
-        {
-            double threshold = (curvatureAdaptive) ? findMeanTargetL(mesh, geometry, e, flatLength, epsilon) : flatLength;
-            if(geometry.edgeLength(e) < threshold * 0.5)
-            {
-                Vector3 newPos = edgeMidpoint(mesh, geometry, e);
-                if(shouldCollapse(mesh, geometry, e)) {
-                    Vertex v = mesh.collapseEdgeTriangular(e);
-                    didSplitOrCollapse = true;
-                    if (v != Vertex()) {
-                        if(!v.isBoundary()) {
-                            geometry.inputVertexPositions[v] = newPos;
-                        }
-                    }
-                }
+      double threshold = (curvatureAdaptive) ? findMeanTargetL(mesh, geometry, e, flatLength, epsilon) : flatLength;
+      if (geometry.edgeLength(e) < threshold * 0.5) {
+        Vector3 newPos = edgeMidpoint(mesh, geometry, e);
+        if (shouldCollapse(mesh, geometry, e)) {
+          Vertex v = mesh.collapseEdgeTriangular(e);
+          didSplitOrCollapse = true;
+          if (v != Vertex()) {
+            if (!v.isBoundary()) {
+              geometry.vertexPositions[v] = newPos;
             }
+          }
         }
+      }
     }
-    return didSplitOrCollapse;
+  }
+  return didSplitOrCollapse;
 }
 
 } // namespace surface

From cf2767702736d876c0f0fafd734f082bded2223e Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Thu, 31 Mar 2022 17:32:48 -0400
Subject: [PATCH 15/33] Use mutation managers

---
 include/geometrycentral/surface/remeshing.h |  36 ++-
 src/surface/remeshing.cpp                   | 264 +++++++++++---------
 2 files changed, 179 insertions(+), 121 deletions(-)

diff --git a/include/geometrycentral/surface/remeshing.h b/include/geometrycentral/surface/remeshing.h
index 106361d3..82e9b8b7 100644
--- a/include/geometrycentral/surface/remeshing.h
+++ b/include/geometrycentral/surface/remeshing.h
@@ -1,28 +1,46 @@
 #pragma once
 
+#include "geometrycentral/surface/barycentric_coordinate_helpers.h"
 #include "geometrycentral/surface/manifold_surface_mesh.h"
+#include "geometrycentral/surface/mutation_manager.h"
 #include "geometrycentral/surface/vertex_position_geometry.h"
 
-#include <queue>
+#include <deque>
 
 namespace geometrycentral {
 namespace surface {
 
 // makes all triangles delaunay
-void fixDelaunay(SurfaceMesh& mesh, VertexPositionGeometry& geometry);
+// returns the number of flips performed
+size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry);
+size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm);
 
 // average positions of vertices based on surrounding vertex positions
-void smoothByLaplacian(SurfaceMesh& mesh, VertexPositionGeometry& geometry);
+// returns the average amount each vertex was moved by
+double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double stepSize = 1);
+double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
+                         double stepSize = 1);
 
 // average positions of vertices based on surrounding triangle circumenters
-void smoothByCircumcenter(SurfaceMesh& mesh, VertexPositionGeometry& geometry);
+// returns the average amount each vertex was moved by
+double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double stepSize = 1);
+double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
+                            double stepSize = 1);
 
 // applies splits and collapses to adjust edge lengths based on the curvature
-// flatLength: specifies how long the target edge length should be in flat regions
-// epsilon: controls how much variation in target length occurs due to curvature
-// minLength: specifies the minimum possible length an edge could become
-bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength, double epsilon,
-                       double minLength, bool curvatureAdaptive = true);
+// flatLength:          specifies how long the target edge length should be in flat regions
+// curvatureAdaptation: controls how much variation in target length occurs due to curvature. Set curvatureAdaptation to
+//                      0 if you want lengths to be approximately flatLength everywhere
+// minRelativeLength:   specifies the minimum possible length an edge could become. Defined relative to flatLength
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength,
+                       double curvatureAdaptation = 0.2, double minRelativeLength = 0.05);
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
+                       double flatLength, double curvatureAdaptation = 0.2, double minRelativeLength = 0.05);
+
+void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double targetEdgeLength,
+            size_t maxIterations = 10, double curvatureAdaptation = 0.2, double minRelativeLength = 0.05);
+void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm, double targetEdgeLength,
+            size_t maxIterations = 10, double curvatureAdaptation = 0.2, double minRelativeLength = 0.05);
 
 } // namespace surface
 } // namespace geometrycentral
diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index 6c7ccd45..a225bbdd 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -3,8 +3,6 @@
 namespace geometrycentral {
 namespace surface {
 
-using std::queue;
-
 Vector3 vertexNormal(VertexPositionGeometry& geometry, Vertex v) {
   Vector3 norm = Vector3::zero();
   for (Corner c : v.adjacentCorners()) {
@@ -29,11 +27,12 @@ Vector3 findCircumcenter(Vector3 p1, Vector3 p2, Vector3 p3) {
   double a2 = a * a;
   double b2 = b * b;
   double c2 = c * c;
-  Vector3 O{a2 * (b2 + c2 - a2), b2 * (c2 + a2 - b2), c2 * (a2 + b2 - c2)};
+  Vector3 circumcenterLoc{a2 * (b2 + c2 - a2), b2 * (c2 + a2 - b2), c2 * (a2 + b2 - c2)};
   // normalize to sum of 1
-  O /= O[0] + O[1] + O[2];
+  circumcenterLoc = normalizeBarycentric(circumcenterLoc);
+
   // change back to space
-  return O[0] * p1 + O[1] * p2 + O[2] * p3;
+  return circumcenterLoc[0] * p1 + circumcenterLoc[1] * p2 + circumcenterLoc[2] * p3;
 }
 
 Vector3 findCircumcenter(VertexPositionGeometry& geometry, Face f) {
@@ -65,37 +64,31 @@ inline bool checkFoldover(Vector3 a, Vector3 b, Vector3 c, Vector3 x, double ang
 }
 
 bool shouldCollapse(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e) {
-  std::vector<Halfedge> toCheck;
+  std::vector<Halfedge> edgesToCheck;
   Vertex v1 = e.halfedge().vertex();
   Vertex v2 = e.halfedge().twin().vertex();
-  Vector3 midpoint = edgeMidpoint(mesh, geometry, e);
+
   // find (halfedge) link around the edge, starting with those surrounding v1
-  Halfedge he = v1.halfedge();
-  Halfedge st = he;
-  do {
-    he = he.next();
-    if (he.vertex() != v2 && he.next().vertex() != v2) {
-      toCheck.push_back(he);
+  for (Halfedge he : v1.outgoingHalfedges()) {
+    if (he.next().tailVertex() != v2 && he.next().tipVertex() != v2) {
+      edgesToCheck.push_back(he.next());
     }
-    he = he.next().twin();
-  } while (he != st);
+  }
+
   // link around v2
-  he = v2.halfedge();
-  st = he;
-  do {
-    he = he.next();
-    if (he.vertex() != v1 && he.next().vertex() != v1) {
-      toCheck.push_back(he);
+  for (Halfedge he : v2.outgoingHalfedges()) {
+    if (he.next().tailVertex() != v1 && he.next().tipVertex() != v1) {
+      edgesToCheck.push_back(he.next());
     }
-    he = he.next().twin();
-  } while (he != st);
+  }
 
   // see if the point that would form after a collapse would cause a major foldover with surrounding edges
-  for (Halfedge he0 : toCheck) {
+  Vector3 midpoint = edgeMidpoint(mesh, geometry, e);
+  for (Halfedge he0 : edgesToCheck) {
     Halfedge heT = he0.twin();
-    Vertex v1 = heT.vertex();
-    Vertex v2 = heT.next().vertex();
-    Vertex v3 = heT.next().next().vertex();
+    Vertex v1 = heT.tailVertex();
+    Vertex v2 = heT.tipVertex();
+    Vertex v3 = heT.next().tipVertex();
     Vector3 a = geometry.vertexPositions[v1];
     Vector3 b = geometry.vertexPositions[v2];
     Vector3 c = geometry.vertexPositions[v3];
@@ -114,121 +107,146 @@ double getSmoothMeanCurvature(VertexPositionGeometry& geometry, Vertex v) {
 }
 
 // flatLength: specifies how long the target edge length should be in flat regions
-// epsilon: controls how much variation in target length occurs due to curvature
-
-double findMeanTargetL(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e, double flatLength, double epsilon) {
+// curvatureAdaptation: controls how much variation in target length occurs due to curvature
+double findMeanTargetL(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e, double flatLength,
+                       double curvatureAdaptation) {
   double averageH = 0;
   for (Vertex v : e.adjacentVertices()) {
     averageH += getSmoothMeanCurvature(geometry, v);
   }
   averageH /= 2;
-  double L = flatLength * epsilon / (fabs(averageH) + epsilon);
+  double L = flatLength / (fabs(averageH) * curvatureAdaptation + 1);
   return L;
 }
 
 
-void fixDelaunay(SurfaceMesh& mesh, VertexPositionGeometry& geometry) {
-  // queue of edges to check if Delaunay
-  queue<Edge> toCheck;
-  // true if edge is currently in toCheck
-  EdgeData<bool> inQueue(mesh);
+size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry) {
+  MutationManager mm(mesh, geometry);
+  return fixDelaunay(mesh, geometry, mm);
+}
+
+size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm) {
+  // Logic duplicated from surface/intrinsic_triangulation.cpp
+
+  std::deque<Edge> edgesToCheck;      // queue of edges to check if Delaunay
+  EdgeData<bool> inQueue(mesh, true); // true if edge is currently in edgesToCheck
+
   // start with all edges
   for (Edge e : mesh.edges()) {
-    toCheck.push(e);
-    inQueue[e] = true;
+    edgesToCheck.push_back(e);
   }
+
   // counter and limit for number of flips
-  int flipMax = 100 * mesh.nVertices();
-  int flipCnt = 0;
-  while (!toCheck.empty() && flipCnt < flipMax) {
-    Edge e = toCheck.front();
-    toCheck.pop();
+  size_t flipMax = 100 * mesh.nVertices();
+  size_t nFlips = 0;
+  while (!edgesToCheck.empty() && nFlips < flipMax) {
+    Edge e = edgesToCheck.front();
+    edgesToCheck.pop_front();
     inQueue[e] = false;
-    // if not Delaunay, flip edge and enqueue the surrounding "diamond" edges (if not already)
-    if (!e.isBoundary() && !isDelaunay(geometry, e)) {
-      flipCnt++;
-      Halfedge he = e.halfedge();
-      Halfedge he1 = he.next();
-      Halfedge he2 = he1.next();
-      Halfedge he3 = he.twin().next();
-      Halfedge he4 = he3.next();
-
-      if (!inQueue[he1.edge()]) {
-        toCheck.push(he1.edge());
-        inQueue[he1.edge()] = true;
-      }
-      if (!inQueue[he2.edge()]) {
-        toCheck.push(he2.edge());
-        inQueue[he2.edge()] = true;
-      }
-      if (!inQueue[he3.edge()]) {
-        toCheck.push(he3.edge());
-        inQueue[he3.edge()] = true;
-      }
-      if (!inQueue[he4.edge()]) {
-        toCheck.push(he4.edge());
-        inQueue[he4.edge()] = true;
+
+    if (e.isBoundary() || isDelaunay(geometry, e)) continue;
+
+    // if not Delaunay, try to flip edge
+    bool wasFlipped = mm.flipEdge(e);
+
+    if (!wasFlipped) continue;
+
+    nFlips++;
+
+    // Add neighbors to queue, as they may need flipping now
+    Halfedge he = e.halfedge();
+    std::array<Edge, 4> neighboringEdges{he.next().edge(), he.next().next().edge(), he.twin().next().edge(),
+                                         he.twin().next().next().edge()};
+    for (Edge nE : neighboringEdges) {
+      if (!inQueue[nE]) {
+        edgesToCheck.push_back(nE);
+        inQueue[nE] = true;
       }
-      mesh.flip(e);
     }
   }
+  return nFlips;
 }
 
-void smoothByLaplacian(SurfaceMesh& mesh, VertexPositionGeometry& geometry) {
-  // smoothed vertex positions
-  VertexData<Vector3> newVertexPosition(mesh);
+double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double stepSize) {
+  MutationManager mm(mesh, geometry);
+  return smoothByLaplacian(mesh, geometry, mm, stepSize);
+}
+
+double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
+                         double stepSize) {
+  VertexData<Vector3> vertexOffsets(mesh);
   for (Vertex v : mesh.vertices()) {
     if (v.isBoundary()) {
-      newVertexPosition[v] = geometry.vertexPositions[v];
+      vertexOffsets[v] = Vector3::zero();
     } else {
       // calculate average of surrounding vertices
-      newVertexPosition[v] = Vector3::zero();
+      Vector3 avgNeighbor = Vector3::zero();
       for (Vertex j : v.adjacentVertices()) {
-        newVertexPosition[v] += geometry.vertexPositions[j];
+        avgNeighbor += geometry.vertexPositions[j];
       }
-      newVertexPosition[v] /= v.degree();
-      // and project the average to the tangent plane
-      Vector3 updateDirection = newVertexPosition[v] - geometry.vertexPositions[v];
-      updateDirection = projectToPlane(updateDirection, vertexNormal(geometry, v));
+      avgNeighbor /= v.degree();
 
-      newVertexPosition[v] = geometry.vertexPositions[v] + 1 * updateDirection;
+      // and project the average to the tangent plane
+      Vector3 updateDirection = avgNeighbor - geometry.vertexPositions[v];
+      vertexOffsets[v] = stepSize * projectToPlane(updateDirection, vertexNormal(geometry, v));
     }
   }
+
   // update final vertices
+  double totalMovement = 0;
   for (Vertex v : mesh.vertices()) {
-    geometry.vertexPositions[v] = newVertexPosition[v];
+    mm.repositionVertex(v, vertexOffsets[v]);
+    totalMovement += vertexOffsets[v].norm();
   }
+  return totalMovement / mesh.nVertices();
+}
+
+double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double stepSize) {
+  MutationManager mm(mesh, geometry);
+  return smoothByCircumcenter(mesh, geometry, mm, stepSize);
 }
 
-void smoothByCircumcenter(SurfaceMesh& mesh, VertexPositionGeometry& geometry) {
+double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
+                            double stepSize) {
   geometry.requireFaceAreas();
-  // smoothed vertex positions
-  VertexData<Vector3> newVertexPosition(mesh);
+  VertexData<Vector3> vertexOffsets(mesh);
   for (Vertex v : mesh.vertices()) {
-    newVertexPosition[v] = geometry.vertexPositions[v]; // default
-    if (!v.isBoundary()) {
-      Vector3 updateDirection = Vector3::zero();
+    if (v.isBoundary()) {
+      vertexOffsets[v] = Vector3::zero();
+    } else {
+      vertexOffsets[v] = Vector3::zero();
       for (Face f : v.adjacentFaces()) {
         // add the circumcenter weighted by face area to the update direction
         Vector3 circum = findCircumcenter(geometry, f);
-        updateDirection += geometry.faceArea(f) * (circum - geometry.vertexPositions[v]);
+        vertexOffsets[v] += geometry.faceArea(f) * (circum - geometry.vertexPositions[v]);
       }
-      updateDirection /= (3 * geometry.vertexDualArea(v));
+      vertexOffsets[v] /= (3 * geometry.vertexDualArea(v));
       // project update direction to tangent plane
-      updateDirection = projectToPlane(updateDirection, vertexNormal(geometry, v));
-      Vector3 newPos = geometry.vertexPositions[v] + .5 * updateDirection;
-      newVertexPosition[v] = newPos;
+      vertexOffsets[v] = stepSize * projectToPlane(vertexOffsets[v], vertexNormal(geometry, v)) / 2.;
     }
   }
+
   // update final vertices
+  double totalMovement = 0;
   for (Vertex v : mesh.vertices()) {
-    geometry.vertexPositions[v] = newVertexPosition[v];
+    mm.repositionVertex(v, vertexOffsets[v]);
+    totalMovement += vertexOffsets[v].norm();
   }
+  return totalMovement / mesh.nVertices();
+}
+
+
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength,
+                       double curvatureAdaptation, double minRelativeLength) {
+  MutationManager mm(mesh, geometry);
+  return adjustEdgeLengths(mesh, geometry, mm, flatLength, curvatureAdaptation, minRelativeLength);
 }
 
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
+                       double flatLength, double curvatureAdaptation, double minRelativeLength) {
+  bool useCurvatureAdaptation = curvatureAdaptation > 0;
+  double minLength = minRelativeLength * flatLength;
 
-bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength, double epsilon,
-                       double minLength, bool curvatureAdaptive) {
   bool didSplitOrCollapse = false;
   // queues of edges to CHECK to change
   std::vector<Edge> toSplit;
@@ -243,40 +261,62 @@ bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geomet
     Edge e = toSplit.back();
     toSplit.pop_back();
     double length_e = geometry.edgeLength(e);
-    double threshold = (curvatureAdaptive) ? findMeanTargetL(mesh, geometry, e, flatLength, epsilon) : flatLength;
+    double threshold =
+        (useCurvatureAdaptation) ? findMeanTargetL(mesh, geometry, e, flatLength, curvatureAdaptation) : flatLength;
     if (length_e > minLength && length_e > threshold * 1.5) {
       Vector3 newPos = edgeMidpoint(mesh, geometry, e);
-      Halfedge he = mesh.splitEdgeTriangular(e);
+      Halfedge he = mm.splitEdge(e, newPos);
       didSplitOrCollapse = true;
-      Vertex newV = he.vertex();
-      geometry.vertexPositions[newV] = newPos;
     } else {
       toCollapse.push_back(e);
     }
   }
+
   // actually collapsing
   while (!toCollapse.empty()) {
     Edge e = toCollapse.back();
     toCollapse.pop_back();
-    if (e.halfedge().next().getIndex() != INVALID_IND) // make sure it exists
-    {
-      double threshold = (curvatureAdaptive) ? findMeanTargetL(mesh, geometry, e, flatLength, epsilon) : flatLength;
-      if (geometry.edgeLength(e) < threshold * 0.5) {
-        Vector3 newPos = edgeMidpoint(mesh, geometry, e);
-        if (shouldCollapse(mesh, geometry, e)) {
-          Vertex v = mesh.collapseEdgeTriangular(e);
-          didSplitOrCollapse = true;
-          if (v != Vertex()) {
-            if (!v.isBoundary()) {
-              geometry.vertexPositions[v] = newPos;
-            }
-          }
-        }
+    if (e == Edge() || e.isDead()) continue; // make sure it exists
+
+    double threshold =
+        (useCurvatureAdaptation) ? findMeanTargetL(mesh, geometry, e, flatLength, curvatureAdaptation) : flatLength;
+    if (geometry.edgeLength(e) < threshold * 0.5) {
+      Vector3 newPos = edgeMidpoint(mesh, geometry, e);
+      if (shouldCollapse(mesh, geometry, e)) {
+        Vertex v = mm.collapseEdge(e, newPos);
+        didSplitOrCollapse = true;
       }
     }
   }
+
+  mesh.compress();
   return didSplitOrCollapse;
 }
 
+void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double targetEdgeLength, size_t maxIterations,
+            double curvatureAdaptation, double minRelativeLength) {
+  MutationManager mm(mesh, geometry);
+  return remesh(mesh, geometry, mm, targetEdgeLength, maxIterations, curvatureAdaptation, minRelativeLength);
+}
+
+void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm, double targetEdgeLength,
+            size_t maxIterations, double curvatureAdaptation, double minRelativeLength) {
+
+  bool doConnectivityChanges = true;
+
+  for (size_t iIt = 0; iIt < maxIterations; iIt++) {
+    if (doConnectivityChanges) {
+      doConnectivityChanges =
+          adjustEdgeLengths(mesh, geometry, mm, targetEdgeLength, curvatureAdaptation, minRelativeLength);
+    }
+
+    size_t nFlips = fixDelaunay(mesh, geometry, mm);
+    double flowDist = smoothByCircumcenter(mesh, geometry);
+
+    // std::cout << iIt << " : " << changedConnectivity << " " << nFlips << " " << flowDist << std::endl;
+    if ((nFlips == 0) && (flowDist < 0.01)) break;
+  }
+}
+
 } // namespace surface
 } // namespace geometrycentral

From 6960cae507e91b5c1bc937806363810c33a0306f Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Thu, 31 Mar 2022 17:37:00 -0400
Subject: [PATCH 16/33] Use cached mean curvature rather than recomputing all
 the time

---
 src/surface/remeshing.cpp | 11 +++++++++--
 1 file changed, 9 insertions(+), 2 deletions(-)

diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index a225bbdd..ab1f2174 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -99,9 +99,10 @@ bool shouldCollapse(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry,
   return true;
 }
 
+// Warning: requires that geometry.vertexDualAreas and geometry.vertexMeanCurvatures are filled in with accurate data
 double getSmoothMeanCurvature(VertexPositionGeometry& geometry, Vertex v) {
-  double A = geometry.vertexDualArea(v);
-  double S = geometry.vertexMeanCurvature(v);
+  double A = geometry.vertexDualAreas[v];
+  double S = geometry.vertexMeanCurvatures[v];
   double K = S / A;
   return K;
 }
@@ -244,6 +245,9 @@ bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geomet
 
 bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
                        double flatLength, double curvatureAdaptation, double minRelativeLength) {
+  geometry.requireVertexDualAreas();
+  geometry.requireVertexMeanCurvatures();
+
   bool useCurvatureAdaptation = curvatureAdaptation > 0;
   double minLength = minRelativeLength * flatLength;
 
@@ -289,6 +293,9 @@ bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geomet
     }
   }
 
+  geometry.unrequireVertexDualAreas();
+  geometry.unrequireVertexMeanCurvatures();
+
   mesh.compress();
   return didSplitOrCollapse;
 }

From c8db0a367a6e04d0c9fcf89c1e3a48045440c168 Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Thu, 31 Mar 2022 17:40:26 -0400
Subject: [PATCH 17/33] Refresh quantities after remeshing

---
 src/surface/remeshing.cpp | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index ab1f2174..c3d31d79 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -323,6 +323,7 @@ void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, Mutatio
     // std::cout << iIt << " : " << changedConnectivity << " " << nFlips << " " << flowDist << std::endl;
     if ((nFlips == 0) && (flowDist < 0.01)) break;
   }
+  geometry.refreshQuantities();
 }
 
 } // namespace surface

From 132443718c34043f5293ffd7388a80d12aca9841 Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Fri, 1 Apr 2022 13:50:14 -0400
Subject: [PATCH 18/33] Add fields to mutation manager to prevent certain
 mutations

---
 .../surface/mutation_manager.h                | 44 ++++++++-
 src/surface/mutation_manager.cpp              | 92 ++++++++++++++++++-
 2 files changed, 132 insertions(+), 4 deletions(-)

diff --git a/include/geometrycentral/surface/mutation_manager.h b/include/geometrycentral/surface/mutation_manager.h
index b912b79b..c2591d53 100644
--- a/include/geometrycentral/surface/mutation_manager.h
+++ b/include/geometrycentral/surface/mutation_manager.h
@@ -106,6 +106,45 @@ class MutationManager {
   // Create a connectivity-only mutation manager, which does not touch any geometry by default
   MutationManager(ManifoldSurfaceMesh& mesh);
 
+  // ======================================================
+  // ======== Constraints
+  // ======================================================
+
+  // Set up callbacks to update edge constraint data following an edge split
+  // TODO: work out sane policies for updating after other operations?
+  void setConstraintCallbacks();
+
+  // Vertices which are allowed to be repositioned.
+  // (set to an array which holds true if a vertex may be moved, and false if it should stay fixed)
+  // Note that this array may be uninitialized, in which case all vertices are allowed to be repositioned
+  // By default, any newly created vertices are repositionable, unless otherwise specified
+  // Warning: this only prevents vertices from being moved by calls to `repositionVertex()`. Even if
+  // repositionableVertices[v] is false, v may be moved by collapsing an incident edge
+  VertexData<bool> repositionableVertices;
+  void setRepositionableVertices(const VertexData<bool>& repositionableVertex, bool defaultValue = true);
+  void clearRepositionableVertices();
+  bool mayRepositionVertex(Vertex v) const;
+
+  EdgeData<bool> splittableEdges;
+  void setSplittableEdges(const EdgeData<bool>& splittableEdge, bool defaultValue = true);
+  void clearSplittableEdges();
+  bool maySplitEdge(Edge e) const;
+
+  EdgeData<bool> collapsibleEdges;
+  void setCollapsibleEdges(const EdgeData<bool>& collapsibleEdge, bool defaultValue = true);
+  void clearCollapsibleEdges();
+  bool mayCollapseEdge(Edge e) const;
+
+  EdgeData<bool> flippableEdges;
+  void setFlippableEdges(const EdgeData<bool>& flippableEdge, bool defaultValue = true);
+  void clearFlippableEdges();
+  bool mayFlipEdge(Edge e) const;
+
+  FaceData<bool> splittableFaces;
+  void setSplittableFaces(const FaceData<bool>& splittableFace, bool defaultValue = true);
+  void clearSplittableFaces();
+  bool maySplitFace(Face f) const;
+
 
   // ======================================================
   // ======== Low-level mutations
@@ -117,7 +156,8 @@ class MutationManager {
   // many of these, since each adds the burden of a corresponding callback policy to update data.
 
   // Move a vertex in 3D space
-  void repositionVertex(Vertex vert, Vector3 offset);
+  // Returns true if vertex was repositioned (May return false if, e.g., repositionalVertices[vert] is false)
+  bool repositionVertex(Vertex vert, Vector3 offset);
 
   // Flip an edge.
   bool flipEdge(Edge e);
@@ -131,6 +171,7 @@ class MutationManager {
   // Returns the new halfedge which points away from the new vertex (so he.vertex() is the new vertex), and is the same
   // direction as e.halfedge() on the original edge. The halfedge direction of the other part of the new split edge is
   // also preserved.
+  // Returns Halfedge() if edge was not split (e.g. if splittableEdges[e] is false)
   Halfedge splitEdge(Edge e, double tSplit);
   Halfedge splitEdge(Edge e, Vector3 newVertexPosition);
   Halfedge splitEdge(Edge e, double tSplit, Vector3 newVertexPosition);
@@ -142,6 +183,7 @@ class MutationManager {
   Vertex collapseEdge(Edge e, double tCollapse, Vector3 newVertexPosition);
 
   // Split a face (i.e. insert a vertex into the face), and return the new vertex
+  // Returns Vertex() if face was not split (e.g. if splittableFaces[f] is false)
   Vertex splitFace(Face f, const std::vector<double>& bSplit);
   Vertex splitFace(Face f, Vector3 newVertexPosition);
   Vertex splitFace(Face f, const std::vector<double>& bSplit, Vector3 newVertexPosition);
diff --git a/src/surface/mutation_manager.cpp b/src/surface/mutation_manager.cpp
index 11f4ccd8..daddb11d 100644
--- a/src/surface/mutation_manager.cpp
+++ b/src/surface/mutation_manager.cpp
@@ -10,15 +10,85 @@ namespace surface {
 // ======================================================
 
 MutationManager::MutationManager(ManifoldSurfaceMesh& mesh_, VertexPositionGeometry& geometry_)
-    : mesh(mesh_), geometry(&geometry_) {}
+    : mesh(mesh_), geometry(&geometry_) {
+  setConstraintCallbacks();
+}
+
+MutationManager::MutationManager(ManifoldSurfaceMesh& mesh_) : mesh(mesh_) { setConstraintCallbacks(); }
+
+// ======================================================
+// ======== Constraints
+// ======================================================
+
+void MutationManager::setConstraintCallbacks() {
+  // == Register a callback to maintain edge constraint data after edge splits
+  auto cacheConstraintsBeforeEdgeSplit = [&](Edge oldE, double tSplit) -> std::array<bool, 3> {
+    bool wasSplittable = maySplitEdge(oldE);
+    bool wasCollapsible = mayCollapseEdge(oldE);
+    bool wasFlippable = mayFlipEdge(oldE);
+    return {wasSplittable, wasCollapsible, wasFlippable};
+  };
+  auto updateConstraintsAfterEdgeSplit = [&](Halfedge newHe1, Halfedge newHe2, double tSplit,
+                                             std::array<bool, 3> oldConstraints) {
+    if (splittableEdges.size() > 0) {
+      splittableEdges[newHe1.edge()] = oldConstraints[0];
+      splittableEdges[newHe2.edge()] = oldConstraints[0];
+    }
+    if (collapsibleEdges.size() > 0) {
+      collapsibleEdges[newHe1.edge()] = oldConstraints[1];
+      collapsibleEdges[newHe2.edge()] = oldConstraints[1];
+    }
+    if (flippableEdges.size() > 0) {
+      flippableEdges[newHe1.edge()] = oldConstraints[2];
+      flippableEdges[newHe2.edge()] = oldConstraints[2];
+    }
+  };
+  registerEdgeSplitHandlers(cacheConstraintsBeforeEdgeSplit, updateConstraintsAfterEdgeSplit);
+}
+
+void MutationManager::setRepositionableVertices(const VertexData<bool>& repositionableVertices_, bool defaultValue) {
+  repositionableVertices = repositionableVertices_;
+  repositionableVertices.setDefault(defaultValue);
+}
+void MutationManager::clearRepositionableVertices() { repositionableVertices = VertexData<bool>(); }
+bool MutationManager::mayRepositionVertex(Vertex v) const {
+  return repositionableVertices.size() == 0 || repositionableVertices[v];
+}
 
-MutationManager::MutationManager(ManifoldSurfaceMesh& mesh_) : mesh(mesh_) {}
+void MutationManager::setSplittableEdges(const EdgeData<bool>& splittableEdges_, bool defaultValue) {
+  splittableEdges = splittableEdges_;
+  splittableEdges.setDefault(defaultValue);
+}
+void MutationManager::clearSplittableEdges() { splittableEdges = EdgeData<bool>(); }
+bool MutationManager::maySplitEdge(Edge e) const { return splittableEdges.size() == 0 || splittableEdges[e]; }
+
+void MutationManager::setCollapsibleEdges(const EdgeData<bool>& collapsibleEdges_, bool defaultValue) {
+  collapsibleEdges = collapsibleEdges_;
+  collapsibleEdges.setDefault(defaultValue);
+}
+void MutationManager::clearCollapsibleEdges() { collapsibleEdges = EdgeData<bool>(); }
+bool MutationManager::mayCollapseEdge(Edge e) const { return collapsibleEdges.size() == 0 || collapsibleEdges[e]; }
+
+void MutationManager::setFlippableEdges(const EdgeData<bool>& flippableEdges_, bool defaultValue) {
+  flippableEdges = flippableEdges_;
+  flippableEdges.setDefault(defaultValue);
+}
+void MutationManager::clearFlippableEdges() { flippableEdges = EdgeData<bool>(); }
+bool MutationManager::mayFlipEdge(Edge e) const { return flippableEdges.size() == 0 || flippableEdges[e]; }
+
+void MutationManager::setSplittableFaces(const FaceData<bool>& splittableFaces_, bool defaultValue) {
+  splittableFaces = splittableFaces_;
+  splittableFaces.setDefault(defaultValue);
+}
+void MutationManager::clearSplittableFaces() { splittableFaces = FaceData<bool>(); }
+bool MutationManager::maySplitFace(Face f) const { return splittableFaces.size() == 0 || splittableFaces[f]; }
 
 // ======================================================
 // ======== Low-level mutations
 // ======================================================
 
-void MutationManager::repositionVertex(Vertex vert, Vector3 offset) {
+bool MutationManager::repositionVertex(Vertex vert, Vector3 offset) {
+  if (!mayRepositionVertex(vert)) return false;
 
   // Invoke callbacks
   for (VertexRepositionPolicy* policy : vertexRepositionPolicies) {
@@ -26,10 +96,12 @@ void MutationManager::repositionVertex(Vertex vert, Vector3 offset) {
   }
 
   geometry->vertexPositions[vert] += offset;
+  return true;
 }
 
 // Flip an edge.
 bool MutationManager::flipEdge(Edge e) {
+  if (!mayFlipEdge(e)) return false;
 
   // First do a test flip to see if its possible
   // TODO implement canFlip() to avoid this
@@ -60,6 +132,8 @@ bool MutationManager::flipEdge(Edge e) {
 }
 
 Halfedge MutationManager::splitEdge(Edge e, double tSplit) {
+  if (!maySplitEdge(e)) return Halfedge();
+
   Vector3 newPos{0., 0., 0.};
   if (geometry) {
     VertexData<Vector3>& pos = geometry->vertexPositions;
@@ -69,6 +143,7 @@ Halfedge MutationManager::splitEdge(Edge e, double tSplit) {
 }
 
 Halfedge MutationManager::splitEdge(Edge e, Vector3 newVertexPosition) {
+  if (!maySplitEdge(e)) return Halfedge();
 
   double tSplit = -1;
   GC_SAFETY_ASSERT(geometry, "must have geometry to split by position");
@@ -84,6 +159,7 @@ Halfedge MutationManager::splitEdge(Edge e, Vector3 newVertexPosition) {
 }
 
 Halfedge MutationManager::splitEdge(Edge e, double tSplit, Vector3 newVertexPosition) {
+  if (!maySplitEdge(e)) return Halfedge();
 
   // Invoke before callbacks
   for (EdgeSplitPolicy* policy : edgeSplitPolicies) {
@@ -109,6 +185,8 @@ Halfedge MutationManager::splitEdge(Edge e, double tSplit, Vector3 newVertexPosi
 // Collapse an edge.
 // Returns the new vertex if the edge could be collapsed, and Vertex() otherwise
 Vertex MutationManager::collapseEdge(Edge e, double tCollapse) {
+  if (!mayCollapseEdge(e)) return Vertex();
+
   Vector3 newPos{0., 0., 0.};
   if (geometry) {
     // Find the nearest tCoord
@@ -119,6 +197,7 @@ Vertex MutationManager::collapseEdge(Edge e, double tCollapse) {
 }
 
 Vertex MutationManager::collapseEdge(Edge e, Vector3 newVertexPosition) {
+  if (!mayCollapseEdge(e)) return Vertex();
 
   double tCollapse = -1;
   GC_SAFETY_ASSERT(geometry, "must have geometry to split by position");
@@ -133,6 +212,7 @@ Vertex MutationManager::collapseEdge(Edge e, Vector3 newVertexPosition) {
   return collapseEdge(e, tCollapse, newVertexPosition);
 }
 Vertex MutationManager::collapseEdge(Edge e, double tCollapse, Vector3 newVertexPosition) {
+  if (!mayCollapseEdge(e)) return Vertex();
 
   // Invoke before callbacks
   // TODO need to handle possiblity that collapse fails -- check before calling
@@ -158,6 +238,8 @@ Vertex MutationManager::collapseEdge(Edge e, double tCollapse, Vector3 newVertex
 
 // Split a face (i.e. insert a vertex into the face)
 Vertex MutationManager::splitFace(Face f, const std::vector<double>& bSplit) {
+  if (!maySplitFace(f)) return Vertex();
+
   Vector3 newPos = Vector3::zero();
   if (geometry) {
     size_t iV = 0;
@@ -172,6 +254,8 @@ Vertex MutationManager::splitFace(Face f, const std::vector<double>& bSplit) {
 }
 
 Vertex MutationManager::splitFace(Face f, Vector3 newVertexPosition) {
+  if (!maySplitFace(f)) return Vertex();
+
   // TODO
   throw std::runtime_error("Face split based on vertex position not implemented yet");
   return Vertex();
@@ -179,6 +263,8 @@ Vertex MutationManager::splitFace(Face f, Vector3 newVertexPosition) {
 
 
 Vertex MutationManager::splitFace(Face f, const std::vector<double>& bSplit, Vector3 newVertexPosition) {
+  if (!maySplitFace(f)) return Vertex();
+
   // Invoke before callbacks
   for (FaceSplitPolicy* policy : faceSplitPolicies) {
     policy->beforeFaceSplit(f, bSplit);

From 483d0308da34c740c8c0e3c651825077d76860ca Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Fri, 1 Apr 2022 14:37:15 -0400
Subject: [PATCH 19/33] Use mutation manager throughout remeshing operations

---
 src/surface/remeshing.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index c3d31d79..7dc05704 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -318,7 +318,7 @@ void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, Mutatio
     }
 
     size_t nFlips = fixDelaunay(mesh, geometry, mm);
-    double flowDist = smoothByCircumcenter(mesh, geometry);
+    double flowDist = smoothByCircumcenter(mesh, geometry, mm);
 
     // std::cout << iIt << " : " << changedConnectivity << " " << nFlips << " " << flowDist << std::endl;
     if ((nFlips == 0) && (flowDist < 0.01)) break;

From 9fa35de120ae88947a1d0e0463339a99ea8f810d Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Fri, 1 Apr 2022 15:27:08 -0400
Subject: [PATCH 20/33] Don't collapse edges incident on fixed vertices

---
 include/geometrycentral/surface/mutation_manager.h |  4 ++--
 src/surface/mutation_manager.cpp                   | 10 +++++++++-
 2 files changed, 11 insertions(+), 3 deletions(-)

diff --git a/include/geometrycentral/surface/mutation_manager.h b/include/geometrycentral/surface/mutation_manager.h
index c2591d53..36827467 100644
--- a/include/geometrycentral/surface/mutation_manager.h
+++ b/include/geometrycentral/surface/mutation_manager.h
@@ -118,8 +118,8 @@ class MutationManager {
   // (set to an array which holds true if a vertex may be moved, and false if it should stay fixed)
   // Note that this array may be uninitialized, in which case all vertices are allowed to be repositioned
   // By default, any newly created vertices are repositionable, unless otherwise specified
-  // Warning: this only prevents vertices from being moved by calls to `repositionVertex()`. Even if
-  // repositionableVertices[v] is false, v may be moved by collapsing an incident edge
+  // Warning: this prevents vertices from being moved by calls to `repositionVertex()`, and also prevents incident edges
+  // from being collapsed (since this might move the vertex)
   VertexData<bool> repositionableVertices;
   void setRepositionableVertices(const VertexData<bool>& repositionableVertex, bool defaultValue = true);
   void clearRepositionableVertices();
diff --git a/src/surface/mutation_manager.cpp b/src/surface/mutation_manager.cpp
index daddb11d..31b84835 100644
--- a/src/surface/mutation_manager.cpp
+++ b/src/surface/mutation_manager.cpp
@@ -67,7 +67,15 @@ void MutationManager::setCollapsibleEdges(const EdgeData<bool>& collapsibleEdges
   collapsibleEdges.setDefault(defaultValue);
 }
 void MutationManager::clearCollapsibleEdges() { collapsibleEdges = EdgeData<bool>(); }
-bool MutationManager::mayCollapseEdge(Edge e) const { return collapsibleEdges.size() == 0 || collapsibleEdges[e]; }
+bool MutationManager::mayCollapseEdge(Edge e) const {
+  if (collapsibleEdges.size() > 0 && !collapsibleEdges[e]) return false;
+  if (repositionableVertices.size() > 0) {
+    for (Vertex v : e.adjacentVertices()) {
+      if (!repositionableVertices[v]) return false;
+    }
+  }
+  return collapsibleEdges.size() == 0 || collapsibleEdges[e];
+}
 
 void MutationManager::setFlippableEdges(const EdgeData<bool>& flippableEdges_, bool defaultValue) {
   flippableEdges = flippableEdges_;

From 9e0096e0a0cbfc54169224c112c4354b5a49867f Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Fri, 1 Apr 2022 15:35:56 -0400
Subject: [PATCH 21/33] Check for success when moving vertices, collapsing
 edges, etc

---
 src/surface/remeshing.cpp | 20 ++++++++++++++------
 1 file changed, 14 insertions(+), 6 deletions(-)

diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index 7dc05704..d5b82ae9 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -196,8 +196,10 @@ double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom
   // update final vertices
   double totalMovement = 0;
   for (Vertex v : mesh.vertices()) {
-    mm.repositionVertex(v, vertexOffsets[v]);
-    totalMovement += vertexOffsets[v].norm();
+    bool didMove = mm.repositionVertex(v, vertexOffsets[v]);
+    if (didMove) {
+      totalMovement += vertexOffsets[v].norm();
+    }
   }
   return totalMovement / mesh.nVertices();
 }
@@ -230,8 +232,10 @@ double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& g
   // update final vertices
   double totalMovement = 0;
   for (Vertex v : mesh.vertices()) {
-    mm.repositionVertex(v, vertexOffsets[v]);
-    totalMovement += vertexOffsets[v].norm();
+    bool didMove = mm.repositionVertex(v, vertexOffsets[v]);
+    if (didMove) {
+      totalMovement += vertexOffsets[v].norm();
+    }
   }
   return totalMovement / mesh.nVertices();
 }
@@ -270,7 +274,9 @@ bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geomet
     if (length_e > minLength && length_e > threshold * 1.5) {
       Vector3 newPos = edgeMidpoint(mesh, geometry, e);
       Halfedge he = mm.splitEdge(e, newPos);
-      didSplitOrCollapse = true;
+      if (he != Halfedge()) {
+        didSplitOrCollapse = true;
+      }
     } else {
       toCollapse.push_back(e);
     }
@@ -288,7 +294,9 @@ bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geomet
       Vector3 newPos = edgeMidpoint(mesh, geometry, e);
       if (shouldCollapse(mesh, geometry, e)) {
         Vertex v = mm.collapseEdge(e, newPos);
-        didSplitOrCollapse = true;
+        if (v != Vertex()) {
+          didSplitOrCollapse = true;
+        }
       }
     }
   }

From 711ca68565b6f6bbd4a95a67ef0856b3b6cdb543 Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Wed, 20 Apr 2022 15:08:17 -0400
Subject: [PATCH 22/33] When smoothing, use circumcenter for interior
 triangles, barycenter for boundary triangles

As recommended by Chen & Holst
---
 src/surface/remeshing.cpp | 18 +++++++++++++++++-
 1 file changed, 17 insertions(+), 1 deletion(-)

diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index d5b82ae9..af040338 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -46,6 +46,22 @@ Vector3 findCircumcenter(VertexPositionGeometry& geometry, Face f) {
   return findCircumcenter(p[0], p[1], p[2]);
 }
 
+// Returns the barycenter for faces incident on a nonflippable edge (e.g. a boundary edge), and the circumcenter for all
+// other faces
+Vector3 findODTCenter(VertexPositionGeometry& geom, Face f, MutationManager& mm) {
+  Vector3 p0 = geom.vertexPositions[f.halfedge().tailVertex()];
+  Vector3 p1 = geom.vertexPositions[f.halfedge().tipVertex()];
+  Vector3 p2 = geom.vertexPositions[f.halfedge().next().tipVertex()];
+
+  for (Edge e : f.adjacentEdges()) {
+    if (e.isBoundary() || !mm.mayFlipEdge(e)) {
+      // e is not flippable. return barycenter
+      return (p0 + p1 + p2) / 3.;
+    }
+  }
+  return findCircumcenter(p0, p1, p2);
+}
+
 bool isDelaunay(VertexPositionGeometry& geometry, Edge e) {
   float angle1 = geometry.cornerAngle(e.halfedge().next().next().corner());
   float angle2 = geometry.cornerAngle(e.halfedge().twin().next().next().corner());
@@ -220,7 +236,7 @@ double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& g
       vertexOffsets[v] = Vector3::zero();
       for (Face f : v.adjacentFaces()) {
         // add the circumcenter weighted by face area to the update direction
-        Vector3 circum = findCircumcenter(geometry, f);
+        Vector3 circum = findODTCenter(geometry, f, mm);
         vertexOffsets[v] += geometry.faceArea(f) * (circum - geometry.vertexPositions[v]);
       }
       vertexOffsets[v] /= (3 * geometry.vertexDualArea(v));

From 181795528ef64c5a7a89bad2758a6c0547acd58b Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Thu, 26 May 2022 14:02:22 -0400
Subject: [PATCH 23/33] Add general mesh compress callback

---
 include/geometrycentral/surface/surface_mesh.h | 1 +
 src/surface/surface_mesh.cpp                   | 4 ++++
 2 files changed, 5 insertions(+)

diff --git a/include/geometrycentral/surface/surface_mesh.h b/include/geometrycentral/surface/surface_mesh.h
index 03dd23a5..42fe6971 100644
--- a/include/geometrycentral/surface/surface_mesh.h
+++ b/include/geometrycentral/surface/surface_mesh.h
@@ -193,6 +193,7 @@ class SurfaceMesh {
   std::list<std::function<void(const std::vector<size_t>&)>> edgePermuteCallbackList;
   std::list<std::function<void(const std::vector<size_t>&)>> halfedgePermuteCallbackList;
   std::list<std::function<void(const std::vector<size_t>&)>> boundaryLoopPermuteCallbackList;
+  std::list<std::function<void(void)>> compressCallbackList;
 
   // Mesh delete callbacks
   // (this unfortunately seems to be necessary; objects which have registered their callbacks above
diff --git a/src/surface/surface_mesh.cpp b/src/surface/surface_mesh.cpp
index 5f66a220..4d0bdebe 100644
--- a/src/surface/surface_mesh.cpp
+++ b/src/surface/surface_mesh.cpp
@@ -1940,6 +1940,10 @@ void SurfaceMesh::compress() {
   compressFaces();
   compressVertices();
   isCompressedFlag = true;
+
+  for (auto& f : compressCallbackList) {
+    f();
+  }
 }
 
 

From e355fc380e1450a223053a0954bc5708ab974777 Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Wed, 8 Jun 2022 16:02:24 -0400
Subject: [PATCH 24/33] Fix normals on important faces

---
 src/surface/remeshing.cpp | 29 +++++++++++++++++++++++------
 1 file changed, 23 insertions(+), 6 deletions(-)

diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index af040338..19fa0c71 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -3,12 +3,28 @@
 namespace geometrycentral {
 namespace surface {
 
-Vector3 vertexNormal(VertexPositionGeometry& geometry, Vertex v) {
-  Vector3 norm = Vector3::zero();
+Vector3 vertexNormal(VertexPositionGeometry& geometry, Vertex v, MutationManager& mm) {
+  Vector3 totalNormal = Vector3::zero();
+  Vector3 fixedFaceNormals = Vector3::zero();
+  bool foundFixedFace = false;
   for (Corner c : v.adjacentCorners()) {
-    norm += geometry.cornerAngle(c) * geometry.faceNormal(c.face());
+    size_t nFixedVertices = 0;
+    for (Vertex w : c.face().adjacentVertices()) {
+      if (!mm.mayRepositionVertex(w)) nFixedVertices++;
+    }
+
+    Vector3 cornerNormal = geometry.cornerAngle(c) * geometry.faceNormal(c.face());
+    if (nFixedVertices >= 2) {
+      fixedFaceNormals += cornerNormal;
+      foundFixedFace = true;
+    }
+    totalNormal += cornerNormal;
+  }
+  if (foundFixedFace) {
+    return normalize(fixedFaceNormals);
+  } else {
+    return normalize(totalNormal);
   }
-  return normalize(norm);
 }
 
 inline Vector3 projectToPlane(Vector3 v, Vector3 norm) { return v - norm * dot(norm, v); }
@@ -205,7 +221,8 @@ double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom
 
       // and project the average to the tangent plane
       Vector3 updateDirection = avgNeighbor - geometry.vertexPositions[v];
-      vertexOffsets[v] = stepSize * projectToPlane(updateDirection, vertexNormal(geometry, v));
+      Vector3 normal = vertexNormal(geometry, v, mm);
+      vertexOffsets[v] = stepSize * projectToPlane(updateDirection, normal);
     }
   }
 
@@ -241,7 +258,7 @@ double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& g
       }
       vertexOffsets[v] /= (3 * geometry.vertexDualArea(v));
       // project update direction to tangent plane
-      vertexOffsets[v] = stepSize * projectToPlane(vertexOffsets[v], vertexNormal(geometry, v)) / 2.;
+      vertexOffsets[v] = stepSize * projectToPlane(vertexOffsets[v], vertexNormal(geometry, v, mm)) / 2.;
     }
   }
 

From 1fb1c98004957e8a59f6d36e2adfe9712517b026 Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Wed, 5 Oct 2022 09:24:17 -0400
Subject: [PATCH 25/33] Turn off remeshing by default

---
 include/geometrycentral/surface/remeshing.h | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/include/geometrycentral/surface/remeshing.h b/include/geometrycentral/surface/remeshing.h
index 82e9b8b7..ec5c191f 100644
--- a/include/geometrycentral/surface/remeshing.h
+++ b/include/geometrycentral/surface/remeshing.h
@@ -35,12 +35,12 @@ double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& g
 bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength,
                        double curvatureAdaptation = 0.2, double minRelativeLength = 0.05);
 bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
-                       double flatLength, double curvatureAdaptation = 0.2, double minRelativeLength = 0.05);
+                       double flatLength, double curvatureAdaptation = 0., double minRelativeLength = 0.05);
 
 void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double targetEdgeLength,
-            size_t maxIterations = 10, double curvatureAdaptation = 0.2, double minRelativeLength = 0.05);
+            size_t maxIterations = 10, double curvatureAdaptation = 0., double minRelativeLength = 0.05);
 void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm, double targetEdgeLength,
-            size_t maxIterations = 10, double curvatureAdaptation = 0.2, double minRelativeLength = 0.05);
+            size_t maxIterations = 10, double curvatureAdaptation = 0., double minRelativeLength = 0.05);
 
 } // namespace surface
 } // namespace geometrycentral

From b13d4c8893078ec5d9d4300d85256b9c89a6691f Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Wed, 5 Oct 2022 09:40:42 -0400
Subject: [PATCH 26/33] Tweak comments, and default args

---
 include/geometrycentral/surface/remeshing.h | 41 ++++++++------
 src/surface/remeshing.cpp                   | 63 ++++++++++++---------
 2 files changed, 62 insertions(+), 42 deletions(-)

diff --git a/include/geometrycentral/surface/remeshing.h b/include/geometrycentral/surface/remeshing.h
index ec5c191f..efb42b25 100644
--- a/include/geometrycentral/surface/remeshing.h
+++ b/include/geometrycentral/surface/remeshing.h
@@ -10,37 +10,46 @@
 namespace geometrycentral {
 namespace surface {
 
-// makes all triangles delaunay
-// returns the number of flips performed
+// Improve mesh using repeated rounds of edge flipping, vertex position smoothing, and edge splits/collapses
+//   targetEdgeLength:    the target edge length in flat regions. If `targetEdgeLength` is negative, the target edge
+//                        length is set to the input mesh's mean edge length
+//   maxIterations:       the maximum number of iterations to run for
+//   curvatureAdaptation: how much variation in target length occurs due to curvature. Set curvatureAdaptation
+//                        to 0 if you want lengths to be approximately flatLength everywhere
+//   minRelativeLength:   the minimum possible length an edge could become. Defined relative to
+//                        targetEdgeLength
+void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double targetEdgeLength = -1,
+            size_t maxIterations = 10, double curvatureAdaptation = 0., double minRelativeLength = 0.05);
+void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
+            double targetEdgeLength = -1, size_t maxIterations = 10, double curvatureAdaptation = 0.,
+            double minRelativeLength = 0.05);
+
+// Try to make all triangles delaunay
+// Returns the number of flips performed
 size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry);
 size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm);
 
-// average positions of vertices based on surrounding vertex positions
-// returns the average amount each vertex was moved by
+// Average positions of vertices based on surrounding vertex positions
+// Returns the average amount each vertex was moved by
 double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double stepSize = 1);
 double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
                          double stepSize = 1);
 
-// average positions of vertices based on surrounding triangle circumenters
-// returns the average amount each vertex was moved by
+// Average positions of vertices based on surrounding triangle circumenters as in [Chen & Holst 2011]
+// Returns the average amount each vertex was moved by
 double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double stepSize = 1);
 double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
                             double stepSize = 1);
 
-// applies splits and collapses to adjust edge lengths based on the curvature
-// flatLength:          specifies how long the target edge length should be in flat regions
-// curvatureAdaptation: controls how much variation in target length occurs due to curvature. Set curvatureAdaptation to
-//                      0 if you want lengths to be approximately flatLength everywhere
-// minRelativeLength:   specifies the minimum possible length an edge could become. Defined relative to flatLength
+// Apply splits and collapses to adjust edge lengths based on the curvature
+//   flatLength:          how long the target edge length should be in flat regions
+//   curvatureAdaptation: how much variation in target length occurs due to curvature. Set curvatureAdaptation
+//                        to 0 if you want lengths to be approximately flatLength everywhere
+//   minRelativeLength:   the minimum possible length an edge could become. Defined relative to flatLength
 bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength,
                        double curvatureAdaptation = 0.2, double minRelativeLength = 0.05);
 bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
                        double flatLength, double curvatureAdaptation = 0., double minRelativeLength = 0.05);
 
-void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double targetEdgeLength,
-            size_t maxIterations = 10, double curvatureAdaptation = 0., double minRelativeLength = 0.05);
-void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm, double targetEdgeLength,
-            size_t maxIterations = 10, double curvatureAdaptation = 0., double minRelativeLength = 0.05);
-
 } // namespace surface
 } // namespace geometrycentral
diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index 19fa0c71..ab2318cb 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -3,6 +3,43 @@
 namespace geometrycentral {
 namespace surface {
 
+void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double targetEdgeLength, size_t maxIterations,
+            double curvatureAdaptation, double minRelativeLength) {
+  MutationManager mm(mesh, geometry);
+  return remesh(mesh, geometry, mm, targetEdgeLength, maxIterations, curvatureAdaptation, minRelativeLength);
+}
+
+void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm, double targetEdgeLength,
+            size_t maxIterations, double curvatureAdaptation, double minRelativeLength) {
+  if (targetEdgeLength < 0) {
+    double meanLength = 0;
+    geometry->requireEdgeLengths();
+    for (Edge e : mesh->edges()) {
+      meanLength += geometry->edgeLengths[e];
+    }
+    geometry->unrequireEdgeLengths();
+    meanLength /= mesh->nEdges();
+
+    targetEdgeLength = meanLength;
+  }
+
+  bool doConnectivityChanges = true;
+
+  for (size_t iIt = 0; iIt < maxIterations; iIt++) {
+    if (doConnectivityChanges) {
+      doConnectivityChanges =
+          adjustEdgeLengths(mesh, geometry, mm, targetEdgeLength, curvatureAdaptation, minRelativeLength);
+    }
+
+    size_t nFlips = fixDelaunay(mesh, geometry, mm);
+    double flowDist = smoothByCircumcenter(mesh, geometry, mm);
+
+    // std::cout << iIt << " : " << changedConnectivity << " " << nFlips << " " << flowDist << std::endl;
+    if ((nFlips == 0) && (flowDist < 0.01)) break;
+  }
+  geometry.refreshQuantities();
+}
+
 Vector3 vertexNormal(VertexPositionGeometry& geometry, Vertex v, MutationManager& mm) {
   Vector3 totalNormal = Vector3::zero();
   Vector3 fixedFaceNormals = Vector3::zero();
@@ -341,31 +378,5 @@ bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geomet
   return didSplitOrCollapse;
 }
 
-void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double targetEdgeLength, size_t maxIterations,
-            double curvatureAdaptation, double minRelativeLength) {
-  MutationManager mm(mesh, geometry);
-  return remesh(mesh, geometry, mm, targetEdgeLength, maxIterations, curvatureAdaptation, minRelativeLength);
-}
-
-void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm, double targetEdgeLength,
-            size_t maxIterations, double curvatureAdaptation, double minRelativeLength) {
-
-  bool doConnectivityChanges = true;
-
-  for (size_t iIt = 0; iIt < maxIterations; iIt++) {
-    if (doConnectivityChanges) {
-      doConnectivityChanges =
-          adjustEdgeLengths(mesh, geometry, mm, targetEdgeLength, curvatureAdaptation, minRelativeLength);
-    }
-
-    size_t nFlips = fixDelaunay(mesh, geometry, mm);
-    double flowDist = smoothByCircumcenter(mesh, geometry, mm);
-
-    // std::cout << iIt << " : " << changedConnectivity << " " << nFlips << " " << flowDist << std::endl;
-    if ((nFlips == 0) && (flowDist < 0.01)) break;
-  }
-  geometry.refreshQuantities();
-}
-
 } // namespace surface
 } // namespace geometrycentral

From 1eb2fe4c1c77875106d251463bc90a8ba0418598 Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Wed, 5 Oct 2022 09:52:15 -0400
Subject: [PATCH 27/33] Remove weird fixed face normal stuff

---
 src/surface/remeshing.cpp | 27 ++++++---------------------
 1 file changed, 6 insertions(+), 21 deletions(-)

diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index ab2318cb..36204788 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -13,12 +13,12 @@ void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, Mutatio
             size_t maxIterations, double curvatureAdaptation, double minRelativeLength) {
   if (targetEdgeLength < 0) {
     double meanLength = 0;
-    geometry->requireEdgeLengths();
-    for (Edge e : mesh->edges()) {
-      meanLength += geometry->edgeLengths[e];
+    geometry.requireEdgeLengths();
+    for (Edge e : mesh.edges()) {
+      meanLength += geometry.edgeLengths[e];
     }
-    geometry->unrequireEdgeLengths();
-    meanLength /= mesh->nEdges();
+    geometry.unrequireEdgeLengths();
+    meanLength /= mesh.nEdges();
 
     targetEdgeLength = meanLength;
   }
@@ -42,26 +42,11 @@ void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, Mutatio
 
 Vector3 vertexNormal(VertexPositionGeometry& geometry, Vertex v, MutationManager& mm) {
   Vector3 totalNormal = Vector3::zero();
-  Vector3 fixedFaceNormals = Vector3::zero();
-  bool foundFixedFace = false;
   for (Corner c : v.adjacentCorners()) {
-    size_t nFixedVertices = 0;
-    for (Vertex w : c.face().adjacentVertices()) {
-      if (!mm.mayRepositionVertex(w)) nFixedVertices++;
-    }
-
     Vector3 cornerNormal = geometry.cornerAngle(c) * geometry.faceNormal(c.face());
-    if (nFixedVertices >= 2) {
-      fixedFaceNormals += cornerNormal;
-      foundFixedFace = true;
-    }
     totalNormal += cornerNormal;
   }
-  if (foundFixedFace) {
-    return normalize(fixedFaceNormals);
-  } else {
-    return normalize(totalNormal);
-  }
+  return normalize(totalNormal);
 }
 
 inline Vector3 projectToPlane(Vector3 v, Vector3 norm) { return v - norm * dot(norm, v); }

From e4d2899aaf787e570d12fe6422194661495da904 Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Fri, 9 Dec 2022 14:51:40 -0500
Subject: [PATCH 28/33] Allow relative target length

---
 include/geometrycentral/surface/remeshing.h | 2 +-
 src/surface/remeshing.cpp                   | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/include/geometrycentral/surface/remeshing.h b/include/geometrycentral/surface/remeshing.h
index efb42b25..050f447e 100644
--- a/include/geometrycentral/surface/remeshing.h
+++ b/include/geometrycentral/surface/remeshing.h
@@ -12,7 +12,7 @@ namespace surface {
 
 // Improve mesh using repeated rounds of edge flipping, vertex position smoothing, and edge splits/collapses
 //   targetEdgeLength:    the target edge length in flat regions. If `targetEdgeLength` is negative, the target edge
-//                        length is set to the input mesh's mean edge length
+//                        length is set to relative the input mesh's mean edge length
 //   maxIterations:       the maximum number of iterations to run for
 //   curvatureAdaptation: how much variation in target length occurs due to curvature. Set curvatureAdaptation
 //                        to 0 if you want lengths to be approximately flatLength everywhere
diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index 36204788..61dd8904 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -20,7 +20,7 @@ void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, Mutatio
     geometry.unrequireEdgeLengths();
     meanLength /= mesh.nEdges();
 
-    targetEdgeLength = meanLength;
+    targetEdgeLength = abs(targetEdgeLength * meanLength);
   }
 
   bool doConnectivityChanges = true;

From a6f6d1713095b434b4488e455b736d5438f05cc6 Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Fri, 9 Dec 2022 15:50:03 -0500
Subject: [PATCH 29/33] Add options struct, boundary condition options

---
 include/geometrycentral/surface/remeshing.h |  66 ++---
 src/surface/remeshing.cpp                   | 281 +++++++++++---------
 2 files changed, 193 insertions(+), 154 deletions(-)

diff --git a/include/geometrycentral/surface/remeshing.h b/include/geometrycentral/surface/remeshing.h
index 547084df..8e35a31e 100644
--- a/include/geometrycentral/surface/remeshing.h
+++ b/include/geometrycentral/surface/remeshing.h
@@ -10,46 +10,52 @@
 namespace geometrycentral {
 namespace surface {
 
+enum class RemeshBoundaryCondition { Fixed, Tangential, Free };
+enum class RemeshSmoothStyle { Circumcentric, Laplacian };
+
+struct RemeshOptions {
+  double targetEdgeLength = -1; // the target edge length in flat regions. If `targetEdgeLength` is negative, the target
+                                // edge length is set to relative the input mesh's mean edge length
+  size_t maxIterations = 10;    // the maximum number of iterations to run for
+  double curvatureAdaptation = 0;  // how much target length should vary due to curvature. Set curvatureAdaptation
+                                   // to 0 if you want lengths to be approximately targetEdgeLength everywhere
+  double minRelativeLength = 0.05; // the minimum possible length an edge could become. Defined relative to
+                                   // targetEdgeLength
+  RemeshSmoothStyle smoothStyle = RemeshSmoothStyle::Circumcentric; // smoothing function to use
+  RemeshBoundaryCondition boundaryCondition =
+      RemeshBoundaryCondition::Tangential; // allowed movement of boundary vertices
+};
+extern const RemeshOptions defaultRemeshOptions;
+
 // Improve mesh using repeated rounds of edge flipping, vertex position smoothing, and edge splits/collapses
-//   targetEdgeLength:    the target edge length in flat regions. If `targetEdgeLength` is negative, the target edge
-//                        length is set to relative the input mesh's mean edge length
-//   maxIterations:       the maximum number of iterations to run for
-//   curvatureAdaptation: how much variation in target length occurs due to curvature. Set curvatureAdaptation
-//                        to 0 if you want lengths to be approximately flatLength everywhere
-//   minRelativeLength:   the minimum possible length an edge could become. Defined relative to
-//                        targetEdgeLength
-void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double targetEdgeLength = -1,
-            size_t maxIterations = 10, double curvatureAdaptation = 0., double minRelativeLength = 0.05);
-void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
-            double targetEdgeLength = -1, size_t maxIterations = 10, double curvatureAdaptation = 0.,
-            double minRelativeLength = 0.05);
-
-// Try to make all triangles delaunay
+void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, RemeshOptions options = defaultRemeshOptions);
+void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, MutationManager& mm,
+            RemeshOptions options = defaultRemeshOptions);
+
+// Try to make all triangles Delaunay
 // Returns the number of flips performed
-size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry);
-size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm);
+size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom);
+size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, MutationManager& mm);
 
 // Average positions of vertices based on surrounding vertex positions
 // Returns the average amount each vertex was moved by
-double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double stepSize = 1);
-double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
-                         double stepSize = 1);
+double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, double stepSize = 1,
+                         RemeshBoundaryCondition bc = RemeshBoundaryCondition::Tangential);
+double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, MutationManager& mm,
+                         double stepSize = 1, RemeshBoundaryCondition bc = RemeshBoundaryCondition::Tangential);
 
 // Average positions of vertices based on surrounding triangle circumenters as in [Chen & Holst 2011]
 // Returns the average amount each vertex was moved by
-double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double stepSize = 1);
-double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
-                            double stepSize = 1);
+double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, double stepSize = 1,
+                            RemeshBoundaryCondition bc = RemeshBoundaryCondition::Tangential);
+double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, MutationManager& mm,
+                            double stepSize = 1, RemeshBoundaryCondition bc = RemeshBoundaryCondition::Tangential);
 
 // applies splits and collapses to adjust edge lengths based on the curvature
-// flatLength:          specifies how long the target edge length should be in flat regions
-// curvatureAdaptation: controls how much variation in target length occurs due to curvature. Set curvatureAdaptation to
-//                      0 if you want lengths to be approximately flatLength everywhere
-// minRelativeLength:   specifies the minimum possible length an edge could become. Defined relative to flatLength
-bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength,
-                       double curvatureAdaptation = 0.2, double minRelativeLength = 0.05);
-bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
-                       double flatLength, double curvatureAdaptation = 0.2, double minRelativeLength = 0.05);
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom,
+                       RemeshOptions options = defaultRemeshOptions);
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, MutationManager& mm,
+                       RemeshOptions options = defaultRemeshOptions);
 
 } // namespace surface
 } // namespace geometrycentral
diff --git a/src/surface/remeshing.cpp b/src/surface/remeshing.cpp
index b86aec08..fa73e070 100644
--- a/src/surface/remeshing.cpp
+++ b/src/surface/remeshing.cpp
@@ -3,57 +3,85 @@
 namespace geometrycentral {
 namespace surface {
 
-void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double targetEdgeLength, size_t maxIterations,
-            double curvatureAdaptation, double minRelativeLength) {
-  MutationManager mm(mesh, geometry);
-  return remesh(mesh, geometry, mm, targetEdgeLength, maxIterations, curvatureAdaptation, minRelativeLength);
+// The default trace options
+const RemeshOptions defaultRemeshOptions;
+
+void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, RemeshOptions options) {
+  MutationManager mm(mesh, geom);
+  return remesh(mesh, geom, mm, options);
 }
 
-void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm, double targetEdgeLength,
-            size_t maxIterations, double curvatureAdaptation, double minRelativeLength) {
-  if (targetEdgeLength < 0) {
+void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, MutationManager& mm, RemeshOptions options) {
+  if (options.targetEdgeLength < 0) {
     double meanLength = 0;
-    geometry.requireEdgeLengths();
+    geom.requireEdgeLengths();
     for (Edge e : mesh.edges()) {
-      meanLength += geometry.edgeLengths[e];
+      meanLength += geom.edgeLengths[e];
     }
-    geometry.unrequireEdgeLengths();
+    geom.unrequireEdgeLengths();
     meanLength /= mesh.nEdges();
 
-    targetEdgeLength = abs(targetEdgeLength * meanLength);
+    options.targetEdgeLength = abs(options.targetEdgeLength * meanLength);
   }
 
   bool doConnectivityChanges = true;
 
-  for (size_t iIt = 0; iIt < maxIterations; iIt++) {
+  for (size_t iIt = 0; iIt < options.maxIterations; iIt++) {
     if (doConnectivityChanges) {
-      doConnectivityChanges =
-          adjustEdgeLengths(mesh, geometry, mm, targetEdgeLength, curvatureAdaptation, minRelativeLength);
+      doConnectivityChanges = adjustEdgeLengths(mesh, geom, mm, options);
     }
 
-    size_t nFlips = fixDelaunay(mesh, geometry, mm);
-    double flowDist = smoothByCircumcenter(mesh, geometry, mm);
+    size_t nFlips = fixDelaunay(mesh, geom, mm);
+    double flowDist;
+    switch (options.smoothStyle) {
+    case RemeshSmoothStyle::Circumcentric:
+      flowDist = smoothByCircumcenter(mesh, geom, mm, 1, options.boundaryCondition);
+      break;
+    case RemeshSmoothStyle::Laplacian:
+      flowDist = smoothByLaplacian(mesh, geom, mm, 1, options.boundaryCondition);
+      break;
+    }
 
     // std::cout << iIt << " : " << changedConnectivity << " " << nFlips << " " << flowDist << std::endl;
     if ((nFlips == 0) && (flowDist < 0.01)) break;
   }
-  geometry.refreshQuantities();
+  geom.refreshQuantities();
 }
 
-Vector3 vertexNormal(VertexPositionGeometry& geometry, Vertex v, MutationManager& mm) {
+Vector3 vertexNormal(VertexPositionGeometry& geom, Vertex v, MutationManager& mm) {
   Vector3 totalNormal = Vector3::zero();
   for (Corner c : v.adjacentCorners()) {
-    Vector3 cornerNormal = geometry.cornerAngle(c) * geometry.faceNormal(c.face());
+    Vector3 cornerNormal = geom.cornerAngle(c) * geom.faceNormal(c.face());
     totalNormal += cornerNormal;
   }
   return normalize(totalNormal);
 }
 
+Vector3 boundaryVertexTangent(VertexPositionGeometry& geom, Vertex v, MutationManager& mm) {
+  if (v.isBoundary()) {
+    auto edgeVec = [&](Edge e) -> Vector3 {
+      return (geom.vertexPositions[e.halfedge().tipVertex()] - geom.vertexPositions[e.halfedge().tailVertex()])
+          .normalize();
+    };
+
+    Vector3 totalTangent = Vector3::zero();
+    for (Edge e : v.adjacentEdges()) {
+      if (e.isBoundary()) {
+        totalTangent += edgeVec(e);
+      }
+    }
+    return totalTangent.normalize();
+  } else {
+    return Vector3::zero();
+  }
+}
+
 inline Vector3 projectToPlane(Vector3 v, Vector3 norm) { return v - norm * dot(norm, v); }
+inline Vector3 projectToLine(Vector3 v, Vector3 tangent) { return tangent * dot(tangent, v); }
 
-inline Vector3 edgeMidpoint(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e) {
-  Vector3 endPos1 = geometry.vertexPositions[e.halfedge().tailVertex()];
-  Vector3 endPos2 = geometry.vertexPositions[e.halfedge().tipVertex()];
+inline Vector3 edgeMidpoint(SurfaceMesh& mesh, VertexPositionGeometry& geom, Edge e) {
+  Vector3 endPos1 = geom.vertexPositions[e.halfedge().tailVertex()];
+  Vector3 endPos2 = geom.vertexPositions[e.halfedge().tipVertex()];
   return (endPos1 + endPos2) / 2;
 }
 
@@ -73,12 +101,12 @@ Vector3 findCircumcenter(Vector3 p1, Vector3 p2, Vector3 p3) {
   return circumcenterLoc[0] * p1 + circumcenterLoc[1] * p2 + circumcenterLoc[2] * p3;
 }
 
-Vector3 findCircumcenter(VertexPositionGeometry& geometry, Face f) {
+Vector3 findCircumcenter(VertexPositionGeometry& geom, Face f) {
   // retrieve the face's vertices
   int index = 0;
   Vector3 p[3];
   for (Vertex v0 : f.adjacentVertices()) {
-    p[index] = geometry.vertexPositions[v0];
+    p[index] = geom.vertexPositions[v0];
     index++;
   }
   return findCircumcenter(p[0], p[1], p[2]);
@@ -100,9 +128,9 @@ Vector3 findODTCenter(VertexPositionGeometry& geom, Face f, MutationManager& mm)
   return findCircumcenter(p0, p1, p2);
 }
 
-bool isDelaunay(VertexPositionGeometry& geometry, Edge e) {
-  float angle1 = geometry.cornerAngle(e.halfedge().next().next().corner());
-  float angle2 = geometry.cornerAngle(e.halfedge().twin().next().next().corner());
+bool isDelaunay(VertexPositionGeometry& geom, Edge e) {
+  float angle1 = geom.cornerAngle(e.halfedge().next().next().corner());
+  float angle2 = geom.cornerAngle(e.halfedge().twin().next().next().corner());
   return angle1 + angle2 <= PI;
 }
 
@@ -117,7 +145,7 @@ inline bool checkFoldover(Vector3 a, Vector3 b, Vector3 c, Vector3 x, double ang
   return diamondAngle(a, b, c, x) < angle;
 }
 
-bool shouldCollapse(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e) {
+bool shouldCollapse(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, Edge e) {
   std::vector<Halfedge> edgesToCheck;
   Vertex v1 = e.halfedge().vertex();
   Vertex v2 = e.halfedge().twin().vertex();
@@ -137,15 +165,15 @@ bool shouldCollapse(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry,
   }
 
   // see if the point that would form after a collapse would cause a major foldover with surrounding edges
-  Vector3 midpoint = edgeMidpoint(mesh, geometry, e);
+  Vector3 midpoint = edgeMidpoint(mesh, geom, e);
   for (Halfedge he0 : edgesToCheck) {
     Halfedge heT = he0.twin();
     Vertex v1 = heT.tailVertex();
     Vertex v2 = heT.tipVertex();
     Vertex v3 = heT.next().tipVertex();
-    Vector3 a = geometry.vertexPositions[v1];
-    Vector3 b = geometry.vertexPositions[v2];
-    Vector3 c = geometry.vertexPositions[v3];
+    Vector3 a = geom.vertexPositions[v1];
+    Vector3 b = geom.vertexPositions[v2];
+    Vector3 c = geom.vertexPositions[v3];
     if (checkFoldover(a, b, c, midpoint, 2)) {
       return false;
     }
@@ -153,21 +181,21 @@ bool shouldCollapse(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry,
   return true;
 }
 
-// Warning: requires that geometry.vertexDualAreas and geometry.vertexMeanCurvatures are filled in with accurate data
-double getSmoothMeanCurvature(VertexPositionGeometry& geometry, Vertex v) {
-  double A = geometry.vertexDualAreas[v];
-  double S = geometry.vertexMeanCurvatures[v];
+// Warning: requires that geom.vertexDualAreas and geom.vertexMeanCurvatures are filled in with accurate data
+double getSmoothMeanCurvature(VertexPositionGeometry& geom, Vertex v) {
+  double A = geom.vertexDualAreas[v];
+  double S = geom.vertexMeanCurvatures[v];
   double K = S / A;
   return K;
 }
 
 // flatLength: specifies how long the target edge length should be in flat regions
 // curvatureAdaptation: controls how much variation in target length occurs due to curvature
-double findMeanTargetL(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge e, double flatLength,
+double findMeanTargetL(SurfaceMesh& mesh, VertexPositionGeometry& geom, Edge e, double flatLength,
                        double curvatureAdaptation) {
   double averageH = 0;
   for (Vertex v : e.adjacentVertices()) {
-    averageH += getSmoothMeanCurvature(geometry, v);
+    averageH += getSmoothMeanCurvature(geom, v);
   }
   averageH /= 2;
   double L = flatLength / (fabs(averageH) * curvatureAdaptation + 1);
@@ -175,12 +203,12 @@ double findMeanTargetL(SurfaceMesh& mesh, VertexPositionGeometry& geometry, Edge
 }
 
 
-size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry) {
-  MutationManager mm(mesh, geometry);
-  return fixDelaunay(mesh, geometry, mm);
+size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom) {
+  MutationManager mm(mesh, geom);
+  return fixDelaunay(mesh, geom, mm);
 }
 
-size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm) {
+size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, MutationManager& mm) {
   // Logic duplicated from surface/intrinsic_triangulation.cpp
 
   std::deque<Edge> edgesToCheck;      // queue of edges to check if Delaunay
@@ -199,7 +227,7 @@ size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry,
     edgesToCheck.pop_front();
     inQueue[e] = false;
 
-    if (e.isBoundary() || isDelaunay(geometry, e)) continue;
+    if (e.isBoundary() || isDelaunay(geom, e)) continue;
 
     // if not Delaunay, try to flip edge
     bool wasFlipped = mm.flipEdge(e);
@@ -222,30 +250,46 @@ size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry,
   return nFlips;
 }
 
-double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double stepSize) {
-  MutationManager mm(mesh, geometry);
-  return smoothByLaplacian(mesh, geometry, mm, stepSize);
+double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, double stepSize,
+                         RemeshBoundaryCondition bc) {
+  MutationManager mm(mesh, geom);
+  return smoothByLaplacian(mesh, geom, mm, stepSize, bc);
 }
 
-double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
-                         double stepSize) {
+double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, MutationManager& mm, double stepSize,
+                         RemeshBoundaryCondition bc) {
   VertexData<Vector3> vertexOffsets(mesh);
   for (Vertex v : mesh.vertices()) {
+    // calculate average of surrounding vertices
+    Vector3 avgNeighbor = Vector3::zero();
+    for (Vertex j : v.adjacentVertices()) {
+      avgNeighbor += geom.vertexPositions[j];
+    }
+    avgNeighbor /= v.degree();
+
+    Vector3 updateDirection = avgNeighbor - geom.vertexPositions[v];
+
+    // project updateDirection onto space of allowed movements
+    Vector3 stepDir;
     if (v.isBoundary()) {
-      vertexOffsets[v] = Vector3::zero();
-    } else {
-      // calculate average of surrounding vertices
-      Vector3 avgNeighbor = Vector3::zero();
-      for (Vertex j : v.adjacentVertices()) {
-        avgNeighbor += geometry.vertexPositions[j];
+      switch (bc) {
+      case RemeshBoundaryCondition::Fixed:
+        stepDir = Vector3::zero();
+        break;
+      case RemeshBoundaryCondition::Tangential:
+        // for free boundary vertices, project the average to the boundary tangent line
+        stepDir = projectToLine(updateDirection, boundaryVertexTangent(geom, v, mm));
+        break;
+      case RemeshBoundaryCondition::Free:
+        // for free boundary vertices, project the average to the surface tangent plane
+        stepDir = projectToPlane(updateDirection, vertexNormal(geom, v, mm));
+        break;
       }
-      avgNeighbor /= v.degree();
-
-      // and project the average to the tangent plane
-      Vector3 updateDirection = avgNeighbor - geometry.vertexPositions[v];
-      Vector3 normal = vertexNormal(geometry, v, mm);
-      vertexOffsets[v] = stepSize * projectToPlane(updateDirection, normal);
+    } else {
+      // for interior vertices, project the average to the tangent plane
+      stepDir = projectToPlane(updateDirection, vertexNormal(geom, v, mm));
     }
+    vertexOffsets[v] = stepSize * stepDir;
   }
 
   // update final vertices
@@ -259,29 +303,46 @@ double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom
   return totalMovement / mesh.nVertices();
 }
 
-double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double stepSize) {
-  MutationManager mm(mesh, geometry);
-  return smoothByCircumcenter(mesh, geometry, mm, stepSize);
+double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, double stepSize,
+                            RemeshBoundaryCondition bc) {
+  MutationManager mm(mesh, geom);
+  return smoothByCircumcenter(mesh, geom, mm, stepSize, bc);
 }
 
-double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
-                            double stepSize) {
-  geometry.requireFaceAreas();
+double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, MutationManager& mm,
+                            double stepSize, RemeshBoundaryCondition bc) {
+  geom.requireFaceAreas();
   VertexData<Vector3> vertexOffsets(mesh);
   for (Vertex v : mesh.vertices()) {
+    Vector3 updateDirection = Vector3::zero();
+    for (Face f : v.adjacentFaces()) {
+      // add the circumcenter weighted by face area to the update direction
+      Vector3 circum = findODTCenter(geom, f, mm);
+      updateDirection += geom.faceArea(f) * (circum - geom.vertexPositions[v]);
+    }
+    updateDirection /= (6 * geom.vertexDualArea(v));
+
+    // project updateDirection onto space of allowed movements
+    Vector3 stepDir;
     if (v.isBoundary()) {
-      vertexOffsets[v] = Vector3::zero();
-    } else {
-      vertexOffsets[v] = Vector3::zero();
-      for (Face f : v.adjacentFaces()) {
-        // add the circumcenter weighted by face area to the update direction
-        Vector3 circum = findODTCenter(geometry, f, mm);
-        vertexOffsets[v] += geometry.faceArea(f) * (circum - geometry.vertexPositions[v]);
+      switch (bc) {
+      case RemeshBoundaryCondition::Fixed:
+        stepDir = Vector3::zero();
+        break;
+      case RemeshBoundaryCondition::Tangential:
+        // for free boundary vertices, project the average to the boundary tangent line
+        stepDir = projectToLine(updateDirection, boundaryVertexTangent(geom, v, mm));
+        break;
+      case RemeshBoundaryCondition::Free:
+        // for free boundary vertices, project the average to the surface tangent plane
+        stepDir = projectToPlane(updateDirection, vertexNormal(geom, v, mm));
+        break;
       }
-      vertexOffsets[v] /= (3 * geometry.vertexDualArea(v));
-      // project update direction to tangent plane
-      vertexOffsets[v] = stepSize * projectToPlane(vertexOffsets[v], vertexNormal(geometry, v, mm)) / 2.;
+    } else {
+      // for interior vertices, project the average to the tangent plane
+      stepDir = projectToPlane(updateDirection, vertexNormal(geom, v, mm));
     }
+    vertexOffsets[v] = stepSize * stepDir;
   }
 
   // update final vertices
@@ -293,22 +354,23 @@ double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& g
     }
   }
   return totalMovement / mesh.nVertices();
-}
+} // namespace surface
 
 
-bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double flatLength,
-                       double curvatureAdaptation, double minRelativeLength) {
-  MutationManager mm(mesh, geometry);
-  return adjustEdgeLengths(mesh, geometry, mm, flatLength, curvatureAdaptation, minRelativeLength);
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, RemeshOptions options) {
+  MutationManager mm(mesh, geom);
+  return adjustEdgeLengths(mesh, geom, mm, options);
 }
 
-bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm,
-                       double flatLength, double curvatureAdaptation, double minRelativeLength) {
-  geometry.requireVertexDualAreas();
-  geometry.requireVertexMeanCurvatures();
+bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, MutationManager& mm,
+                       RemeshOptions options) {
+  geom.requireVertexDualAreas();
+  geom.requireVertexMeanCurvatures();
 
+  double curvatureAdaptation = options.curvatureAdaptation;
   bool useCurvatureAdaptation = curvatureAdaptation > 0;
-  double minLength = minRelativeLength * flatLength;
+  double flatLength = options.targetEdgeLength;
+  double minLength = options.minRelativeLength * options.targetEdgeLength;
 
   bool didSplitOrCollapse = false;
   // queues of edges to CHECK to change
@@ -323,11 +385,11 @@ bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geomet
   while (!toSplit.empty()) {
     Edge e = toSplit.back();
     toSplit.pop_back();
-    double length_e = geometry.edgeLength(e);
+    double length_e = geom.edgeLength(e);
     double threshold =
-        (useCurvatureAdaptation) ? findMeanTargetL(mesh, geometry, e, flatLength, curvatureAdaptation) : flatLength;
+        (useCurvatureAdaptation) ? findMeanTargetL(mesh, geom, e, flatLength, curvatureAdaptation) : flatLength;
     if (length_e > minLength && length_e > threshold * 1.5) {
-      Vector3 newPos = edgeMidpoint(mesh, geometry, e);
+      Vector3 newPos = edgeMidpoint(mesh, geom, e);
       Halfedge he = mm.splitEdge(e, newPos);
       if (he != Halfedge()) {
         didSplitOrCollapse = true;
@@ -344,10 +406,10 @@ bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geomet
     if (e == Edge() || e.isDead()) continue; // make sure it exists
 
     double threshold =
-        (useCurvatureAdaptation) ? findMeanTargetL(mesh, geometry, e, flatLength, curvatureAdaptation) : flatLength;
-    if (geometry.edgeLength(e) < threshold * 0.5) {
-      Vector3 newPos = edgeMidpoint(mesh, geometry, e);
-      if (shouldCollapse(mesh, geometry, e)) {
+        (useCurvatureAdaptation) ? findMeanTargetL(mesh, geom, e, flatLength, curvatureAdaptation) : flatLength;
+    if (geom.edgeLength(e) < threshold * 0.5) {
+      Vector3 newPos = edgeMidpoint(mesh, geom, e);
+      if (shouldCollapse(mesh, geom, e)) {
         Vertex v = mm.collapseEdge(e, newPos);
         if (v != Vertex()) {
           didSplitOrCollapse = true;
@@ -356,41 +418,12 @@ bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geomet
     }
   }
 
-  geometry.unrequireVertexDualAreas();
-  geometry.unrequireVertexMeanCurvatures();
+  geom.unrequireVertexDualAreas();
+  geom.unrequireVertexMeanCurvatures();
 
   mesh.compress();
   return didSplitOrCollapse;
 }
 
-<<<<<<< HEAD
-=======
-void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, double targetEdgeLength, size_t maxIterations,
-            double curvatureAdaptation, double minRelativeLength) {
-  MutationManager mm(mesh, geometry);
-  return remesh(mesh, geometry, mm, targetEdgeLength, maxIterations, curvatureAdaptation, minRelativeLength);
-}
-
-void remesh(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geometry, MutationManager& mm, double targetEdgeLength,
-            size_t maxIterations, double curvatureAdaptation, double minRelativeLength) {
-
-  bool doConnectivityChanges = true;
-
-  for (size_t iIt = 0; iIt < maxIterations; iIt++) {
-    if (doConnectivityChanges) {
-      doConnectivityChanges =
-          adjustEdgeLengths(mesh, geometry, mm, targetEdgeLength, curvatureAdaptation, minRelativeLength);
-    }
-
-    size_t nFlips = fixDelaunay(mesh, geometry, mm);
-    double flowDist = smoothByCircumcenter(mesh, geometry, mm);
-
-    // std::cout << iIt << " : " << changedConnectivity << " " << nFlips << " " << flowDist << std::endl;
-    if ((nFlips == 0) && (flowDist < 0.01)) break;
-  }
-  geometry.refreshQuantities();
-}
-
->>>>>>> a00489b9bdeef5b69dd9b39fbc0e9a1b33ad2d22
 } // namespace surface
 } // namespace geometrycentral

From ead543b85eae34eceb004a2dc32a702c7b165cd8 Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Fri, 9 Dec 2022 15:57:45 -0500
Subject: [PATCH 30/33] Alphebetize algorithms

---
 docs/mkdocs.yml | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/docs/mkdocs.yml b/docs/mkdocs.yml
index d99ec6ad..f8d6ea7f 100644
--- a/docs/mkdocs.yml
+++ b/docs/mkdocs.yml
@@ -76,15 +76,15 @@ nav:
       - 'Barycentric Vector': 'surface/utilities/barycentric_vector.md'
     - Algorithms: 
       - 'Direction Fields' : 'surface/algorithms/direction_fields.md'
+      - 'Flip Geodesics' : 'surface/algorithms/flip_geodesics.md'
       - 'Geodesic Distance' : 'surface/algorithms/geodesic_distance.md'
-      - 'Tracing Geodesic Paths' : 'surface/algorithms/geodesic_paths.md'
-      - 'Vector Heat Method' : 'surface/algorithms/vector_heat_method.md'
-      - 'Surface Centers' : 'surface/algorithms/surface_centers.md'
-      - 'Surface Sampling' : 'surface/algorithms/surface_sampling.md'
       - 'Geodesic Centroidal Voronoi Tessellations' : 'surface/algorithms/geodesic_voronoi_tessellations.md'
-      - 'Robust Geometry' : 'surface/algorithms/robust_geometry.md'
-      - 'Flip Geodesics' : 'surface/algorithms/flip_geodesics.md'
       - 'Parameterization' : 'surface/algorithms/parameterization.md'
+      - 'Robust Geometry' : 'surface/algorithms/robust_geometry.md'
+      - 'Surface Centers' : 'surface/algorithms/surface_centers.md'
+      - 'Surface Sampling' : 'surface/algorithms/surface_sampling.md'
+      - 'Tracing Geodesic Paths' : 'surface/algorithms/geodesic_paths.md'
+      - 'Vector Heat Method' : 'surface/algorithms/vector_heat_method.md'
     - Intrinsic Triangulations:
       - 'Basics' : 'surface/intrinsic_triangulations/basics.md'
       - 'Common Subdivision' : 'surface/intrinsic_triangulations/common_subdivision.md'

From 0d6f26ef36b9d6a2f54b78f16dae1323692eca56 Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Fri, 9 Dec 2022 16:23:35 -0500
Subject: [PATCH 31/33] Start remeshing docs

---
 .../media/spot-triangulation-original.png     | Bin 0 -> 603784 bytes
 .../media/spot-triangulation-remeshed.png     | Bin 0 -> 520181 bytes
 docs/docs/surface/algorithms/remeshing.md     |  34 ++++++++++++++++++
 docs/mkdocs.yml                               |   1 +
 include/geometrycentral/surface/remeshing.h   |   2 +-
 5 files changed, 36 insertions(+), 1 deletion(-)
 create mode 100644 docs/docs/media/spot-triangulation-original.png
 create mode 100644 docs/docs/media/spot-triangulation-remeshed.png
 create mode 100644 docs/docs/surface/algorithms/remeshing.md

diff --git a/docs/docs/media/spot-triangulation-original.png b/docs/docs/media/spot-triangulation-original.png
new file mode 100644
index 0000000000000000000000000000000000000000..9c544601ec2b6c385111c2df0b0d060599e00aa5
GIT binary patch
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diff --git a/docs/docs/surface/algorithms/remeshing.md b/docs/docs/surface/algorithms/remeshing.md
new file mode 100644
index 00000000..e04fb6ab
--- /dev/null
+++ b/docs/docs/surface/algorithms/remeshing.md
@@ -0,0 +1,34 @@
+
+| Original | Remeshed |
+| - | - |
+|![finely_triangulated_spot](/media/spot-triangulation-original.png){: style="max-width: 20em; display: block; margin-left: auto; margin-right: auto;"}|![coarsely_triangulated_spot](/media/spot-triangulation-remeshed.png){: style="max-width: 20em; display: block; margin-left: auto; margin-right: auto;"}
+
+
+??? func "`#!cpp void remesh(ManifoldSurfaceMesh& mesh, IntrinsicGeometryInterface& geom, RemeshOptions options = defaultRemeshOptions)`"
+
+    Remesh a mesh using vertex smoothing along with edge splits, collapses, and flips. Options are passed as a [RemeshOptions](#options) object.
+    
+??? func "`#!cpp void remesh(ManifoldSurfaceMesh& mesh, IntrinsicGeometryInterface& geom, MutationManager& mm, RemeshOptions options = defaultRemeshOptions)`"
+
+    Remesh a mesh using vertex smoothing along with edge splits, collapses, and flips. Options are passed as a [RemeshOptions](#options) object.
+    All mesh mutations are performed through a `MutationManager` object, which can e.g. keep special vertices fixed or run callback functions when certain mesh mutations occur.
+
+## Vertex Smoothing
+Vertex 
+
+## Boundary Conditions
+
+## Helper Types
+### Options
+Options are passed in to `remesh` via a `RemeshOptions` object.
+
+| Field                                              | Default value                         | Meaning                                                                                                                                                    |
+|----------------------------------------------------|---------------------------------------|------------------------------------------------------------------------------------------------------------------------------------------------------------|
+| `#!cpp double targetEdgeLength`                   | `-1`                                  | the target edge length in flat regions. If `targetEdgeLength` is negative, the target edge length is set to relative the input mesh's mean edge length     |
+| `#!cpp size_t maxIterations`                      | `10`                                  | the maximum number of iterations to run for                                                                                                                |
+| `#!cpp double curvatureAdaptation`                | `0`                                   | how much target length should vary due to curvature. Set curvatureAdaptation to 0 if you want edge lengths to be approximately targetEdgeLength everywhere |
+| `#!cpp double minRelativeLength`                  | `0.05`                                | the minimum possible edge length allowed in the output mesh. Defined relative to targetEdgeLength                                                          |
+| `#!cpp RemeshSmoothStyle smoothStyle`             | `RemeshSmoothStyle::Circumcentric`    | the type of vertex smoothing to use (either `RemeshSmoothStyle::Circumcentric` or `RemeshSmoothStyle::Laplacian`)                                          |
+| `#!cpp RemeshBoundaryCondition boundaryCondition` | `RemeshBoundaryCondition::Tangential` | the type of motions allowed for boundary vertices (either `RemeshBoundaryCondition::Fixed`, `RemeshBoundaryCondition::Tangential` or `RemeshBoundaryCondition::Free`)                            |
+
+
diff --git a/docs/mkdocs.yml b/docs/mkdocs.yml
index f8d6ea7f..653a2000 100644
--- a/docs/mkdocs.yml
+++ b/docs/mkdocs.yml
@@ -80,6 +80,7 @@ nav:
       - 'Geodesic Distance' : 'surface/algorithms/geodesic_distance.md'
       - 'Geodesic Centroidal Voronoi Tessellations' : 'surface/algorithms/geodesic_voronoi_tessellations.md'
       - 'Parameterization' : 'surface/algorithms/parameterization.md'
+      - 'Remeshing' : 'surface/algorithms/remeshing.md'
       - 'Robust Geometry' : 'surface/algorithms/robust_geometry.md'
       - 'Surface Centers' : 'surface/algorithms/surface_centers.md'
       - 'Surface Sampling' : 'surface/algorithms/surface_sampling.md'
diff --git a/include/geometrycentral/surface/remeshing.h b/include/geometrycentral/surface/remeshing.h
index 8e35a31e..65d7e7f7 100644
--- a/include/geometrycentral/surface/remeshing.h
+++ b/include/geometrycentral/surface/remeshing.h
@@ -19,7 +19,7 @@ struct RemeshOptions {
   size_t maxIterations = 10;    // the maximum number of iterations to run for
   double curvatureAdaptation = 0;  // how much target length should vary due to curvature. Set curvatureAdaptation
                                    // to 0 if you want lengths to be approximately targetEdgeLength everywhere
-  double minRelativeLength = 0.05; // the minimum possible length an edge could become. Defined relative to
+  double minRelativeLength = 0.05; // the minimum possible edge length allowed in the output mesh. Defined relative to
                                    // targetEdgeLength
   RemeshSmoothStyle smoothStyle = RemeshSmoothStyle::Circumcentric; // smoothing function to use
   RemeshBoundaryCondition boundaryCondition =

From e964e19bd56333504d901cac6babdcd68cbc6c89 Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Sat, 10 Dec 2022 15:08:08 -0500
Subject: [PATCH 32/33] Document all functions

---
 docs/docs/surface/algorithms/remeshing.md | 76 +++++++++++++++++++++--
 1 file changed, 71 insertions(+), 5 deletions(-)

diff --git a/docs/docs/surface/algorithms/remeshing.md b/docs/docs/surface/algorithms/remeshing.md
index e04fb6ab..8c1e916c 100644
--- a/docs/docs/surface/algorithms/remeshing.md
+++ b/docs/docs/surface/algorithms/remeshing.md
@@ -3,20 +3,84 @@
 | - | - |
 |![finely_triangulated_spot](/media/spot-triangulation-original.png){: style="max-width: 20em; display: block; margin-left: auto; margin-right: auto;"}|![coarsely_triangulated_spot](/media/spot-triangulation-remeshed.png){: style="max-width: 20em; display: block; margin-left: auto; margin-right: auto;"}
 
+These routines try to improve mesh quality using repeated rounds of [vertex position smoothing](#tangential-vertex-smoothing), [edge flipping](#extrinsic-delaunay-flipping), and [edge splits/collapses](#edge-length-adjustment).
 
-??? func "`#!cpp void remesh(ManifoldSurfaceMesh& mesh, IntrinsicGeometryInterface& geom, RemeshOptions options = defaultRemeshOptions)`"
+??? func "`#!cpp void remesh(ManifoldSurfaceMesh& mesh, IntrinsicGeometryInterface& geom, RemeshOptions options = defaultRemeshOptions);`"
 
     Remesh a mesh using vertex smoothing along with edge splits, collapses, and flips. Options are passed as a [RemeshOptions](#options) object.
     
-??? func "`#!cpp void remesh(ManifoldSurfaceMesh& mesh, IntrinsicGeometryInterface& geom, MutationManager& mm, RemeshOptions options = defaultRemeshOptions)`"
+??? func "`#!cpp void remesh(ManifoldSurfaceMesh& mesh, IntrinsicGeometryInterface& geom, MutationManager& mm, RemeshOptions options = defaultRemeshOptions);`"
 
     Remesh a mesh using vertex smoothing along with edge splits, collapses, and flips. Options are passed as a [RemeshOptions](#options) object.
     All mesh mutations are performed through a `MutationManager` object, which can e.g. keep special vertices fixed or run callback functions when certain mesh mutations occur.
 
-## Vertex Smoothing
-Vertex 
+## Tangential Vertex Smoothing
+Vertex smoothing moves each vertex towards the average of its neighborhood. This average can be computed in two ways: in *circumentric* smoothing, every vertex is moved towards the area-weighted average of the circumcenters of its neighboring faces (as in [[Chen & Holst 2011]](https://www.sciencedirect.com/science/article/abs/pii/S0045782510003117)), whereas in *Laplacian* smoothing, every vertex is moved towards the average of the positions of its neighboring vertices.
 
-## Boundary Conditions
+In either case we perform *tangential smoothing*, meaning that we only move vertices tangentially along the surface. 
+
+??? func "`#!cpp double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, double stepSize = 1, RemeshBoundaryCondition bc = RemeshBoundaryCondition::Tangential);`"
+                         
+    Move each vertex tangentially towards the area-weighted average of its neighboring face circumcenters.
+    Returns the average amount that each vertex was moved by.
+    
+??? func "`#!cpp double smoothByCircumcenter(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, MutationManager& mm, double stepSize = 1, RemeshBoundaryCondition bc = RemeshBoundaryCondition::Tangential);`"
+    
+    Move each vertex tangentially towards the area-weighted average of its neighboring face circumcenters
+    , using the provided `MutationManager` to move the vertices
+    Returns the average amount that each vertex was moved by.
+
+??? func "`#!cpp double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, double stepSize = 1, RemeshBoundaryCondition bc = RemeshBoundaryCondition::Tangential);`"
+                         
+    Move each vertex tangentially towards the average of its neighbors
+    Returns the average amount that each vertex was moved by.
+??? func "`#!cpp double smoothByLaplacian(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, MutationManager& mm, double stepSize = 1, RemeshBoundaryCondition bc = RemeshBoundaryCondition::Tangential);`"
+    
+    Move each vertex tangentially towards the average of its neighbors, using the provided `MutationManager` to move the vertices
+    Returns the average amount that each vertex was moved by.
+
+### Boundary Conditions
+The boundary conditions for smoothing can be set to `RemeshBoundaryCondition::Tangential`, `RemeshBoundaryCondition::Fixed`, or `RemeshBoundaryCondition::Free`. Tangential smoothing allows boundary vertices to move along the tangent direction to the boundary curve, fixed smoothing fixes the boundary vertices, and free smoothing allows boundary vertices to move along any direction in the surface's tangent plane. Leaving boundary vertices free allows the mesh to degenerate, so it is not recommended unless you impose additional constraints.
+
+## Extrinsic Delaunay Flipping
+Delaunay flipping performs edge flips to improve triangle quality.
+
+!!! warning "No guarantees"
+
+    Unlike the [intrinsic Delaunay flipping routines](/surface/intrinsic_triangulations/basics/#high-level-mutators), extrinsic flipping algorithms are not guaranteed to produce a Delaunay mesh. Nonetheless, these edge flips generally improve triangle quality in practice.
+    
+??? func "`#!cpp size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom);`"
+
+    Try to make all triangles Delaunay using extrinsic edge flips.
+    Returns the number of flips performed.
+    
+??? func "`#!cpp size_t fixDelaunay(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, MutationManager& mm);`"
+    Try to make all triangles Delaunay using extrinsic edge flips, using the provided `MutationManager` to flip edges.
+    Returns the number of flips performed.
+    
+## Edge Length Adjustment
+These routines perform edge splits and collapses to drive mesh edge lengths towards a target value. If curvature adaptation is enabled, this target length is made shorter in high-curvature areas, leading to more resolution there.
+
+??? func "`#!cpp bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, RemeshOptions options = defaultRemeshOptions);`"
+
+    Apply splits and collapses to adjust edge lengths.
+   
+    Reads the following options from `options`, with the following default values and meanings:
+    
+    * `#!cpp double options.targetEdgeLength = -1`: the target edge length in flat regions. If `targetEdgeLength` is negative, the target length is set relative to the input mesh's mean length.
+    * `#!cpp double options.curvatureAdaptation = 0`: how much target edge length should vary due to curvature. Set `curvatureAdaptation` to zero if you want edge lengths to be approximately `targetEdgeLength` everywhere.
+    * `#!cpp double options.minRelativeLength = 0.05`: the minimum possible edge length in the output mesh. Defined relative to `targetEdgeLength`.
+
+??? func "`#!cpp bool adjustEdgeLengths(ManifoldSurfaceMesh& mesh, VertexPositionGeometry& geom, MutationManager& mm, RemeshOptions options = defaultRemeshOptions);`"
+
+    Apply splits and collapses to adjust edge lengths.
+    All splits and collapses are performed using the provided `MutationManager`.
+   
+    Reads the following options from `options`, with the following default values and meanings:
+    
+    * `#!cpp double options.targetEdgeLength = -1`: the target edge length in flat regions. If `targetEdgeLength` is negative, the target length is set relative to the input mesh's mean length.
+    * `#!cpp double options.curvatureAdaptation = 0`: how much target edge length should vary due to curvature. Set `curvatureAdaptation` to zero if you want edge lengths to be approximately `targetEdgeLength` everywhere.
+    * `#!cpp double options.minRelativeLength = 0.05`: the minimum possible edge length in the output mesh. Defined relative to `targetEdgeLength`.
 
 ## Helper Types
 ### Options
@@ -31,4 +95,6 @@ Options are passed in to `remesh` via a `RemeshOptions` object.
 | `#!cpp RemeshSmoothStyle smoothStyle`             | `RemeshSmoothStyle::Circumcentric`    | the type of vertex smoothing to use (either `RemeshSmoothStyle::Circumcentric` or `RemeshSmoothStyle::Laplacian`)                                          |
 | `#!cpp RemeshBoundaryCondition boundaryCondition` | `RemeshBoundaryCondition::Tangential` | the type of motions allowed for boundary vertices (either `RemeshBoundaryCondition::Fixed`, `RemeshBoundaryCondition::Tangential` or `RemeshBoundaryCondition::Free`)                            |
 
+!!! warning "'Fixed' boundary may still move slightly"
 
+    Setting `boundaryCondition` to `RemeshBoundaryCondition::Fixed` only fixes boundary vertices during vertex smoothing. Boundary edges may still be split or collapsed during edge length adjustment, which can also cause the boundary to move slightly. To stop all motion of the boundary, you can pass in a `MutationManager` which marks all boundary edges as not splittable or collapsible.

From 561171583f70c8e871105814971003d060df1217 Mon Sep 17 00:00:00 2001
From: Mark Gillespie <mark.gillespie81@gmail.com>
Date: Mon, 12 Dec 2022 09:32:30 -0500
Subject: [PATCH 33/33] Silence deprecated copy warnings

---
 test/CMakeLists.txt | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
index f8ef6d7e..598d6667 100644
--- a/test/CMakeLists.txt
+++ b/test/CMakeLists.txt
@@ -81,6 +81,12 @@ FetchContent_MakeAvailable(googletest)
 
 set_property(TARGET gtest PROPERTY CXX_STANDARD 11)
 
+# silence warning about deprecated copies in gtest
+# https://github.com/abseil/abseil-cpp/issues/948#issuecomment-846592426
+if(NOT "${CMAKE_CXX_COMPILER_ID}" STREQUAL "MSVC")
+  target_compile_options(gtest INTERFACE -Wno-deprecated-copy)
+endif()
+
 
 ### Set (hardcode) a variable for where to find the assets
 set(REL_ASSETS_DIR "${CMAKE_CURRENT_SOURCE_DIR}/assets/")