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Computing the bounding box of a BezierPath as bounds
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Lines changed: 188 additions & 0 deletions

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‎Sources/BaseKit/Geometry/Bezier.swift‎

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Original file line numberDiff line numberDiff line change
@@ -71,9 +71,91 @@ public enum Bezier {
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end,
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]
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}
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public static func computeBoundingBoxForLine(start: Point, end: Point) -> Rect {
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var topLeft = start
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var bottomRight = topLeft
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end.expandBounds(topLeft: &topLeft, bottomRight: &bottomRight)
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return Rect(
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x: topLeft.x,
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y: topLeft.y,
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width: bottomRight.x - topLeft.x,
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height: bottomRight.y - topLeft.y
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)
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}
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public static func computeBoundingBoxForCubicBezier(_ bezierPoints: [Point]) -> Rect {
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// Start with the end points
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var (topLeft, _, _) = splitBezier(bezierPoints, ofDegree: 3, at: 0)
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var bottomRight = topLeft
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let (lastPoint, _, _) = splitBezier(bezierPoints, ofDegree: 3, at: 1)
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lastPoint.expandBounds(topLeft: &topLeft, bottomRight: &bottomRight)
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// Find the roots, which should be the extremities
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let xRoots = computeCubicFirstDerivativeRoots(
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a: bezierPoints[0].x,
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b: bezierPoints[1].x,
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c: bezierPoints[2].x,
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d: bezierPoints[3].x
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)
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for t in xRoots {
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if t < 0 || t > 1 {
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continue
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}
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let (location, _, _) = splitBezier(bezierPoints, ofDegree: 3, at: t)
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location.expandBounds(topLeft: &topLeft, bottomRight: &bottomRight)
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}
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let yRoots = computeCubicFirstDerivativeRoots(
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a: bezierPoints[0].y,
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b: bezierPoints[1].y,
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c: bezierPoints[2].y,
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d: bezierPoints[3].y
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)
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for t in yRoots {
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if t < 0 || t > 1 {
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continue
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}
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let (location, _, _) = splitBezier(bezierPoints, ofDegree: 3, at: t)
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location.expandBounds(topLeft: &topLeft, bottomRight: &bottomRight)
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}
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return Rect(
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x: topLeft.x,
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y: topLeft.y,
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width: bottomRight.x - topLeft.x,
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height: bottomRight.y - topLeft.y
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)
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}
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}
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private extension Bezier {
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static func computeCubicFirstDerivativeRoots(a: Real, b: Real, c: Real, d: Real) -> [Real] {
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// See http://processingjs.nihongoresources.com/bezierinfo/#bounds for where the formulas come from
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let denominator = -a + 3.0 * b - 3.0 * c + d
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// If denominator == 0, fall back to
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if denominator.isClose(to: 0.0, threshold: 1e-9) {
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let t = (a - b) / (2.0 * (a - 2.0 * b + c))
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return [t]
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} else {
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let numeratorLeft = -a + 2.0 * b - c
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let v1 = -a * (c - d)
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let v2 = b * b
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let v3 = b * (c + d)
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let v4 = c * c
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let numeratorRight = -1.0 * sqrt(v1 + v2 - v3 + v4)
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let t1 = (numeratorLeft + numeratorRight) / denominator
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let t2 = (numeratorLeft - numeratorRight) / denominator
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return [t1, t2]
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}
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}
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static func convertBezier(_ bezierPoints: [Point], relativeTo point: Point) -> [Point] {
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// c[i] in the paper
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let distanceFromPoint = [

‎Sources/BaseKit/Geometry/BezierPath.swift‎

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Original file line numberDiff line numberDiff line change
@@ -168,6 +168,45 @@ public struct BezierPath: Hashable, BezierPathRepresentable, Codable, Sendable {
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}
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}
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public var bounds: Rect {
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var rect: Rect? = nil
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var currentPoint: Point? = nil
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var startPoint: Point? = nil
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for element in elements {
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switch element {
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case let .move(to: point):
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startPoint = point
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currentPoint = point
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case let .line(to: point):
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if let currentPoint {
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let bounds = Bezier.computeBoundingBoxForLine(start: currentPoint, end: point)
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rect = rect.union(bounds)
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}
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currentPoint = point
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case let .curve(to: point, control1: control1, control2: control2):
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if let currentPoint {
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let bounds = Bezier.computeBoundingBoxForCubicBezier([
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currentPoint, control1, control2, point
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])
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rect = rect.union(bounds)
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}
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currentPoint = point
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case .closeSubpath:
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if let startPoint, let currentPoint, startPoint != currentPoint {
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// Draw a line between ending point and starting point
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let bounds = Bezier.computeBoundingBoxForLine(start: currentPoint, end: startPoint)
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rect = rect.union(bounds)
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}
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currentPoint = nil
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startPoint = nil
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}
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}
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return rect ?? .zero
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}
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public func reversed() -> BezierPath {
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var subpaths = [[BezierPath.Element]]()
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var currentSubpath = [BezierPath.Element]()

‎Sources/BaseKit/Geometry/Rect.swift‎

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@@ -46,4 +46,15 @@ public struct Rect: Hashable, Codable, Sendable {
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public func contains(_ point: Point) -> Bool {
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point.x >= minX && point.x <= maxX && point.y >= minY && point.y <= maxY
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}
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public func isClose(to other: Rect, threshold: Real) -> Bool {
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origin.isClose(to: other.origin, threshold: threshold)
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&& size.isClose(to: other.size, threshold: threshold)
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}
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}
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public extension Optional where Wrapped == Rect {
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func union(_ other: Rect) -> Rect {
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map { $0.union(other) } ?? other
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}
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}

‎Sources/BaseKit/Geometry/Size.swift‎

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@@ -16,4 +16,9 @@ public struct Size: Hashable, Codable, Sendable {
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let heightDelta = size.height - height
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return sqrt(widthDelta * widthDelta + heightDelta * heightDelta)
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}
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public func isClose(to other: Size, threshold: Real) -> Bool {
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width.isClose(to: other.width, threshold: threshold)
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&& height.isClose(to: other.height, threshold: threshold)
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}
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}

‎Sources/BaseKit/Geometry/Transform.swift‎

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@@ -50,6 +50,12 @@ public extension Transform {
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)
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}
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init(rotate angle: Real, anchor: Point) {
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self = Transform(translateX: anchor.x, translateY: anchor.y)
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.concatenating(Transform(rotate: angle))
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.concatenating(Transform(translateX: -anchor.x, translateY: -anchor.y))
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}
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init(skewX angle: Real) {
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self.init(c: tan(angle))
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}

‎Tests/BaseKitTests/Geometry/BezierPathTests.swift‎

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@@ -0,0 +1,45 @@
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import Testing
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@testable import BaseKit
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struct BezierPathTests {
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@Test
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func testBoundsWithEllipse() {
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let ellipse = BezierPath(ellipseIn: Rect(x: 25, y: 50, width: 50, height: 75))
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let bounds = ellipse.bounds
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let expected = Rect(x: 25, y: 50, width: 50, height: 75)
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#expect(bounds == expected)
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}
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@Test
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func testBoundsWithRectangle() {
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let rect = BezierPath(rect: Rect(x: 25, y: 50, width: 50, height: 75))
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let bounds = rect.bounds
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let expected = Rect(x: 25, y: 50, width: 50, height: 75)
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#expect(bounds == expected)
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}
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@Test
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func testBoundsWithRotatedCircle() {
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var circle = BezierPath(ellipseIn: Rect(x: 25, y: 50, width: 50, height: 50))
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circle.transform(Transform(rotate: Real.pi / 4.0, anchor: Point(x: 50, y: 75)))
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let bounds = circle.bounds
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let expected = Rect(x: 25, y: 50, width: 50, height: 50)
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#expect(bounds.isClose(to: expected, threshold: 1e-6))
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}
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@Test
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func testBoundsWithRotatedSquare() {
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let center = Point(x: 50, y: 75)
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var square = BezierPath(rect: Rect(x: 25, y: 50, width: 50, height: 50))
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square.transform(Transform(rotate: Real.pi / 4.0, anchor: center))
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let bounds = square.bounds
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let radius: Real = 35.35533906
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let expected = Rect(
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x: center.x - radius,
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y: center.y - radius,
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width: radius * 2,
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height: radius * 2
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)
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#expect(bounds.isClose(to: expected, threshold: 1e-6))
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}
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}

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