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Merge pull request #94 from hfutrell/intersection-via-implicitization
Intersection via implicitization
2 parents 13b6bb7 + 2ec6cc4 commit 385af8c

16 files changed

+817
-46
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‎BezierKit/BezierKit.xcodeproj/project.pbxproj

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‎BezierKit/BezierKitTests/BezierCurve+ImplicitizationTests.swift

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//
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// BezierCurve+ImplicitizationTests.swift
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// BezierKit
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//
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// Created by Holmes Futrell on 5/10/21.
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// Copyright © 2021 Holmes Futrell. All rights reserved.
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//
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@testable import BezierKit
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import XCTest
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class BezierCurve_ImplicitizationTests: XCTestCase {
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func testLineSegmentImplicitization() {
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let lineSegment = LineSegment(p0: CGPoint(x: 1, y: 2), p1: CGPoint(x: 4, y: 3))
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let implicitLine = lineSegment.implicitPolynomial
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XCTAssertEqual(implicitLine.value(at: lineSegment.startingPoint), 0)
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XCTAssertEqual(implicitLine.value(at: lineSegment.endingPoint), 0)
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XCTAssertEqual(implicitLine.value(at: lineSegment.point(at: 0.25)), 0)
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XCTAssertEqual(implicitLine.value(at: CGPoint(x: 0, y: 5)), 10)
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XCTAssertEqual(implicitLine.value(at: CGPoint(x: 2, y: -1)), -10)
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// check the implicit line composed with a parametric line
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let otherLineSegment = LineSegment(p0: CGPoint(x: 0, y: 5), p1: CGPoint(x: 2, y: -1))
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let xPolynomial = BernsteinPolynomialN(coefficients: otherLineSegment.xPolynomial.coefficients)
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let yPolynomial = BernsteinPolynomialN(coefficients: otherLineSegment.yPolynomial.coefficients)
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let polynomialComposedWithLine = implicitLine.value(xPolynomial, yPolynomial)
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XCTAssertEqual(polynomialComposedWithLine.value(at: 0), 10)
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XCTAssertEqual(polynomialComposedWithLine.value(at: 1), -10)
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}
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func testQuadraticCurveImplicitization() {
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let quadraticCurve = QuadraticCurve(p0: CGPoint(x: 0, y: 2),
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p1: CGPoint(x: 1, y: 0),
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p2: CGPoint(x: 2, y: 2))
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let implicitQuadratic = quadraticCurve.implicitPolynomial
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XCTAssertEqual(implicitQuadratic.value(at: quadraticCurve.startingPoint), 0)
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XCTAssertEqual(implicitQuadratic.value(at: quadraticCurve.endingPoint), 0)
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XCTAssertEqual(implicitQuadratic.value(at: quadraticCurve.point(at: 0.25)), 0)
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let valueAbove = implicitQuadratic.value(at: CGPoint(x: 1, y: 2))
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let valueBelow = implicitQuadratic.value(at: CGPoint(x: 1, y: 0))
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XCTAssertGreaterThan(valueAbove, 0)
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XCTAssertLessThan(valueBelow, 0)
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// check the implicit quadratic composed with an parametric quadratic
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let otherQuadratic = QuadraticCurve(p0: CGPoint(x: 1, y: 2),
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p1: CGPoint(x: 1, y: 1),
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p2: CGPoint(x: 1, y: 0))
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let polynomialComposedWithQuadratic = implicitQuadratic.value(otherQuadratic.xPolynomial, otherQuadratic.yPolynomial)
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XCTAssertEqual(polynomialComposedWithQuadratic.value(at: 0), valueAbove)
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XCTAssertEqual(polynomialComposedWithQuadratic.value(at: 0.5), 0)
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XCTAssertEqual(polynomialComposedWithQuadratic.value(at: 1), valueBelow)
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}
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func testCubicImplicitization() {
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let cubicCurve = CubicCurve(p0: CGPoint(x: 0, y: 0),
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p1: CGPoint(x: 1, y: 1),
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p2: CGPoint(x: 2, y: 0),
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p3: CGPoint(x: 3, y: 1))
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let implicitCubic = cubicCurve.implicitPolynomial
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XCTAssertEqual(implicitCubic.value(at: cubicCurve.startingPoint), 0)
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XCTAssertEqual(implicitCubic.value(at: cubicCurve.endingPoint), 0)
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XCTAssertEqual(implicitCubic.value(at: cubicCurve.point(at: 0.25)), 0)
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let valueAbove = implicitCubic.value(at: CGPoint(x: 1, y: 1))
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let valueBelow = implicitCubic.value(at: CGPoint(x: 2, y: 0))
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XCTAssertGreaterThan(valueAbove, 0)
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XCTAssertLessThan(valueBelow, 0)
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// check the implicit quadratic composed with a parametric line
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let lineSegment = LineSegment(p0: CGPoint(x: 1, y: 1), p1: CGPoint(x: 2, y: 0))
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let polynomialComposedWithLineSegment = implicitCubic.value(lineSegment.xPolynomial, lineSegment.yPolynomial)
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XCTAssertEqual(polynomialComposedWithLineSegment.value(at: 0), valueAbove)
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XCTAssertEqual(polynomialComposedWithLineSegment.value(at: 1), valueBelow)
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XCTAssertEqual(polynomialComposedWithLineSegment.value(at: 0.5), 0)
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}
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}

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