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Merge pull request #94 from hfutrell/intersection-via-implicitization
Intersection via implicitization
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BezierKit/BezierKitTests/BezierCurve+ImplicitizationTests.swift
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| // | ||
| // BezierCurve+ImplicitizationTests.swift | ||
| // BezierKit | ||
| // | ||
| // Created by Holmes Futrell on 5/10/21. | ||
| // Copyright © 2021 Holmes Futrell. All rights reserved. | ||
| // | ||
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| @testable import BezierKit | ||
| import XCTest | ||
|
|
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| class BezierCurve_ImplicitizationTests: XCTestCase { | ||
|
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| func testLineSegmentImplicitization() { | ||
| let lineSegment = LineSegment(p0: CGPoint(x: 1, y: 2), p1: CGPoint(x: 4, y: 3)) | ||
| let implicitLine = lineSegment.implicitPolynomial | ||
| XCTAssertEqual(implicitLine.value(at: lineSegment.startingPoint), 0) | ||
| XCTAssertEqual(implicitLine.value(at: lineSegment.endingPoint), 0) | ||
| XCTAssertEqual(implicitLine.value(at: lineSegment.point(at: 0.25)), 0) | ||
| XCTAssertEqual(implicitLine.value(at: CGPoint(x: 0, y: 5)), 10) | ||
| XCTAssertEqual(implicitLine.value(at: CGPoint(x: 2, y: -1)), -10) | ||
| // check the implicit line composed with a parametric line | ||
| let otherLineSegment = LineSegment(p0: CGPoint(x: 0, y: 5), p1: CGPoint(x: 2, y: -1)) | ||
| let xPolynomial = BernsteinPolynomialN(coefficients: otherLineSegment.xPolynomial.coefficients) | ||
| let yPolynomial = BernsteinPolynomialN(coefficients: otherLineSegment.yPolynomial.coefficients) | ||
| let polynomialComposedWithLine = implicitLine.value(xPolynomial, yPolynomial) | ||
| XCTAssertEqual(polynomialComposedWithLine.value(at: 0), 10) | ||
| XCTAssertEqual(polynomialComposedWithLine.value(at: 1), -10) | ||
| } | ||
|
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| func testQuadraticCurveImplicitization() { | ||
| let quadraticCurve = QuadraticCurve(p0: CGPoint(x: 0, y: 2), | ||
| p1: CGPoint(x: 1, y: 0), | ||
| p2: CGPoint(x: 2, y: 2)) | ||
| let implicitQuadratic = quadraticCurve.implicitPolynomial | ||
| XCTAssertEqual(implicitQuadratic.value(at: quadraticCurve.startingPoint), 0) | ||
| XCTAssertEqual(implicitQuadratic.value(at: quadraticCurve.endingPoint), 0) | ||
| XCTAssertEqual(implicitQuadratic.value(at: quadraticCurve.point(at: 0.25)), 0) | ||
| let valueAbove = implicitQuadratic.value(at: CGPoint(x: 1, y: 2)) | ||
| let valueBelow = implicitQuadratic.value(at: CGPoint(x: 1, y: 0)) | ||
| XCTAssertGreaterThan(valueAbove, 0) | ||
| XCTAssertLessThan(valueBelow, 0) | ||
| // check the implicit quadratic composed with an parametric quadratic | ||
| let otherQuadratic = QuadraticCurve(p0: CGPoint(x: 1, y: 2), | ||
| p1: CGPoint(x: 1, y: 1), | ||
| p2: CGPoint(x: 1, y: 0)) | ||
| let polynomialComposedWithQuadratic = implicitQuadratic.value(otherQuadratic.xPolynomial, otherQuadratic.yPolynomial) | ||
| XCTAssertEqual(polynomialComposedWithQuadratic.value(at: 0), valueAbove) | ||
| XCTAssertEqual(polynomialComposedWithQuadratic.value(at: 0.5), 0) | ||
| XCTAssertEqual(polynomialComposedWithQuadratic.value(at: 1), valueBelow) | ||
| } | ||
|
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| func testCubicImplicitization() { | ||
| let cubicCurve = CubicCurve(p0: CGPoint(x: 0, y: 0), | ||
| p1: CGPoint(x: 1, y: 1), | ||
| p2: CGPoint(x: 2, y: 0), | ||
| p3: CGPoint(x: 3, y: 1)) | ||
| let implicitCubic = cubicCurve.implicitPolynomial | ||
| XCTAssertEqual(implicitCubic.value(at: cubicCurve.startingPoint), 0) | ||
| XCTAssertEqual(implicitCubic.value(at: cubicCurve.endingPoint), 0) | ||
| XCTAssertEqual(implicitCubic.value(at: cubicCurve.point(at: 0.25)), 0) | ||
| let valueAbove = implicitCubic.value(at: CGPoint(x: 1, y: 1)) | ||
| let valueBelow = implicitCubic.value(at: CGPoint(x: 2, y: 0)) | ||
| XCTAssertGreaterThan(valueAbove, 0) | ||
| XCTAssertLessThan(valueBelow, 0) | ||
| // check the implicit quadratic composed with a parametric line | ||
| let lineSegment = LineSegment(p0: CGPoint(x: 1, y: 1), p1: CGPoint(x: 2, y: 0)) | ||
| let polynomialComposedWithLineSegment = implicitCubic.value(lineSegment.xPolynomial, lineSegment.yPolynomial) | ||
| XCTAssertEqual(polynomialComposedWithLineSegment.value(at: 0), valueAbove) | ||
| XCTAssertEqual(polynomialComposedWithLineSegment.value(at: 1), valueBelow) | ||
| XCTAssertEqual(polynomialComposedWithLineSegment.value(at: 0.5), 0) | ||
| } | ||
| } |
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