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BezierKit/BezierKitTests/BezierCurve+PolynomialTests.swift
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,78 @@ | ||
| // | ||
| // BezierCurve+PolynomialTests.swift | ||
| // BezierKit | ||
| // | ||
| // Created by Holmes Futrell on 1/22/21. | ||
| // Copyright © 2021 Holmes Futrell. All rights reserved. | ||
| // | ||
|
|
||
| import BezierKit | ||
| import XCTest | ||
|
|
||
| class BezierCurve_PolynomialTests: XCTestCase { | ||
|
|
||
| func testPolynomialLineSegment() { | ||
| let lineSegment = LineSegment(p0: CGPoint(x: 3, y: 4), p1: CGPoint(x: 5, y: 6)) | ||
| XCTAssertEqual(lineSegment.xPolynomial, BernsteinPolynomial1(b0: 3, b1: 5)) | ||
| XCTAssertEqual(lineSegment.yPolynomial, BernsteinPolynomial1(b0: 4, b1: 6)) | ||
| } | ||
|
|
||
| func testPolynomialQuadratic() { | ||
| let quadratic = QuadraticCurve(p0: CGPoint(x: 1, y: 0), | ||
| p1: CGPoint(x: 2, y: -2), | ||
| p2: CGPoint(x: 3, y: -1)) | ||
| XCTAssertEqual(quadratic.xPolynomial, BernsteinPolynomial2(b0: 1, b1: 2, b2: 3)) | ||
| XCTAssertEqual(quadratic.yPolynomial, BernsteinPolynomial2(b0: 0, b1: -2, b2: -1)) | ||
| } | ||
|
|
||
| func testPolynomialCubic() { | ||
| let cubic = CubicCurve(p0: CGPoint(x: 1, y: 0), | ||
| p1: CGPoint(x: 2, y: 2), | ||
| p2: CGPoint(x: 3, y: 1), | ||
| p3: CGPoint(x: 4, y: -1)) | ||
| XCTAssertEqual(cubic.xPolynomial, BernsteinPolynomial3(b0: 1, b1: 2, b2: 3, b3: 4)) | ||
| XCTAssertEqual(cubic.yPolynomial, BernsteinPolynomial3(b0: 0, b1: 2, b2: 1, b3: -1)) | ||
| } | ||
|
|
||
| func testExtremaLine() { | ||
| let l1 = LineSegment(p0: CGPoint(x: 1.0, y: 2.0), p1: CGPoint(x: 4.0, y: 6.0)) | ||
| let (x1, y1, all1) = l1.extrema() | ||
| XCTAssertTrue(x1.isEmpty) | ||
| XCTAssertTrue(y1.isEmpty) | ||
| XCTAssertTrue(all1.isEmpty) | ||
|
|
||
| let l2 = LineSegment(p0: CGPoint(x: 1.0, y: 2.0), p1: CGPoint(x: 4.0, y: 2.0)) | ||
| let (x2, y2, all2) = l2.extrema() | ||
| XCTAssertTrue(x2.isEmpty) | ||
| XCTAssertTrue(y2.isEmpty) | ||
| XCTAssertTrue(all2.isEmpty) | ||
| } | ||
|
|
||
| func testExtremaQuadratic() { | ||
| let f: [CGFloat] = [4, -2, 1] // f(t) = 4t^2 - 2t + 1, which has a local minimum at t = 0.25 | ||
| let g: [CGFloat] = [1, -4, 4] // g(t) = t^2 -4t + 4, which has a local minimum at t = 2 (outside parameter range) | ||
| let q = BezierKitTestHelpers.quadraticCurveFromPolynomials(f, g) | ||
| let (x, y, all) = q.extrema() | ||
| XCTAssertEqual(all.count, 1) | ||
| XCTAssertEqual(all[0], 0.25) | ||
| XCTAssertEqual(x.count, 1) | ||
| XCTAssertEqual(x[0], 0.25) | ||
| XCTAssertTrue(y.isEmpty) | ||
| } | ||
|
|
||
| func testExtremaCubic() { | ||
| let f: [CGFloat] = [1, -1, 0, 0] // f(t) = t^3 - t^2, which has two local minimum at t=0, t=2/3 and an inflection point t=1/3 | ||
| let g: [CGFloat] = [0, 3, -2, 0] // g(t) = 3t^2 - 2t, which has a local minimum at t=1/3 | ||
| let c = BezierKitTestHelpers.cubicCurveFromPolynomials(f, g) | ||
| let (x, y, all) = c.extrema() | ||
| XCTAssertEqual(all.count, 3) | ||
| XCTAssertEqual(all[0], 0.0) | ||
| XCTAssertEqual(all[1], 1.0 / 3.0) | ||
| XCTAssertEqual(all[2], 2.0 / 3.0) | ||
| XCTAssertEqual(x[0], 0.0) | ||
| XCTAssertEqual(x[1], 1.0 / 3.0) | ||
| XCTAssertEqual(x[2], 2.0 / 3.0) | ||
| XCTAssertEqual(y.count, 1) | ||
| XCTAssertEqual(y[0], 1.0 / 3.0) | ||
| } | ||
| } |
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