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Math library

Utility functions for math objects.

functions

  • rectanglesOverlap {P1 P2 Q1 Q2 strict} determine if the rectangles defined by the corner points P1 P2 and Q1 Q2. Strict is a bool that indicates if the answer is strictly determined. (From: Cormen, Leiserson, and Rivests' "Algorithms", page 889)
  • regionToBbox {r}: converts a region r to its bounding box, returns a list of {minimum_x minimum_y maximum_x maximum_y}
  • boxCentroid {box}: returns the centroid of the box box
  • boxWidth {box}: returns the width of the box box
  • boxHeight {box}: returns the height of the box box

namespaces

vec2

A vec2 is a 2d vector, i.e. a structure that stores 2 number, and can preform operations upon it. In Tcl they are represented by a list of 2 numbers.

  • add {a b}: adds the respective pairs of x and y values together
  • sub {a b}: subracts the respective pairs of Xb and Yb from Xa and Ya
  • scale {a args}: if args is 1 value, scale both values by it, if it's 2 values, scale Xa by Xargs and Ya by Yargs
  • rotate {a theta}: rotate the values in a by theta
  • distance {a b}: calculates the euclidean distance (the length of a line segment between the two points)
  • normalize {a}: normalizes the vector by dividing each value by the magnitude of the vector
  • dot {a b}: calculate the dot product of the two vectors, basically, calculates how much two vectors point in the same direction.
  • distanceToLineSegment {a v w}: returns the distance to the line segment defined by v and w
  • midpoint {a b}: returns the midpoint of the line segment defined by a b.

region

A region is an arbitrary oriented chunk of a plane. The archetypal region is the region of a program/page, which is the quadrilateral area of space that is covered by that page. A region is defined by a set of vertices and a set of edges among those vertices.

  • create {vertices edges {angle 0}}: create a region with the given vertices and edges, and optional angle.
  • vertices {r}: return the vertices of the region r
  • edges {r}: return the edges of the region r
  • angle {r}: return the angle of the region r
  • width {r}: return the width of the region r in screen space, acounting for rotation.
  • height {r}: return the height of the region r in screen space, acounting for rotation.
  • top {r}: return the vec2 point at the top of the region r
  • left {r}: return the vec2 point to the left of the region r
  • right {r}: return the vec2 point to the right of the region r
  • bottom {r}: return the vec2 point at the bottom of the region r
  • bottomleft {r}: return the vec2 point at the bottom left of the region r
  • bottomright {r}: return the vec2 point at the bottom right of the region r
  • topleft {r}: return the vec2 point at the top left of the region r
  • topright {r}: return the vec2 point at the top right of the region r
  • mapVertices {varname r body}: apply the body for each vector varname in region r
  • distance {r1 r2}: calculate the distance between regions r1 and r2
  • contains {r p}: check if the region r contains the point p
  • intersects {r1 r2}: check if region r1 intersects with region r2
  • centroid {r}: only works for rectangular regions! returns the point that is the centroid of the region r
  • rotate {r angle}: returns a region r' that has been rotated by angle
  • scale {r args}: Accepts values in px, %, and unmarked. If 1 arg, scale all by that arg, otherwise accepts X<unit> width Y<unit> height
  • move {r args}: Moves the region left/right/up/down on the x and y axies of the region, not the global x and y. Args in the format <AMMOUNT><UNIT> <DIRECTION> where unit is one of the units that scale supports, and direction is left/right/up/down.

TODO:

  • Rewrite in C
  • Triangulate a region
  • Average the centroids of all triangles in a region
  • Rename regionToBbox
  • Assert that box is actually a box
  • Optimize scale
  • Allow areas in regions to be filled/unfilled

CC-BY-SA 2023 Arcade Wise (We can change the license if y'all want, I just wanted to avoid copyright issues)