116 lines
3.7 KiB
Swift
116 lines
3.7 KiB
Swift
// Copyright (C) 2008 Apple Inc. All Rights Reserved.
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions
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// are met:
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// 1. Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// 2. Redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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//
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// THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY
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// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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import CoreGraphics
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import Foundation
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/// Defines a cubic-bezier where the endpoints are (0, 0) and (1, 1)
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///
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/// The main use case is computing the progress of an animation at a given percent completion. For instance,
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/// for a linear animation, the expected progress at `0.5` is `0.5`.
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///
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/// - Note: This is a Swift port of [Apple's WebKit code](
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/// http://svn.webkit.org/repository/webkit/trunk/Source/WebCore/platform/graphics/UnitBezier.h
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/// )
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///
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struct UnitBezier {
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// MARK: Lifecycle
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init(controlPoint1: CGPoint, controlPoint2: CGPoint) {
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cx = 3.0 * controlPoint1.x
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bx = 3.0 * (controlPoint2.x - controlPoint1.x) - cx
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ax = 1.0 - cx - bx
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cy = 3.0 * controlPoint1.y
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by = 3.0 * (controlPoint2.y - controlPoint1.y) - cy
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ay = 1.0 - cy - by
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}
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// MARK: Internal
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/// Computes the progress `y` value for a given `x` value
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func value(for x: CGFloat, epsilon: CGFloat) -> CGFloat {
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sampleCurveY(solveCurveX(x, epsilon: epsilon))
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}
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// MARK: Private
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private let ax: CGFloat
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private let bx: CGFloat
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private let cx: CGFloat
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private let ay: CGFloat
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private let by: CGFloat
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private let cy: CGFloat
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/// Compute `x(t)` for a given `t`
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private func sampleCurveX(_ t: CGFloat) -> CGFloat {
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// `ax t^3 + bx t^2 + cx t' expanded using Horner's rule.
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((ax * t + bx) * t + cx) * t
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}
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/// Compute `y(t)` for a given `t`
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private func sampleCurveY(_ t: CGFloat) -> CGFloat {
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((ay * t + by) * t + cy) * t
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}
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/// Compute `x'(t)` for a given `t`
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private func sampleCurveDerivativeX(_ t: CGFloat) -> CGFloat {
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(3.0 * ax * t + 2.0 * bx) * t + cx
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}
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/// Given an `x` value solve for the parametric value `t`
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private func solveCurveX(_ x: CGFloat, epsilon: CGFloat) -> CGFloat {
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var t0, t1, t2, x2, d2: CGFloat
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// First try a few iterations of Newton-Raphson -- normally very fast.
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t2 = x
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for _ in 0..<8 {
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x2 = sampleCurveX(t2) - x
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guard abs(x2) >= epsilon else { return t2 }
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d2 = sampleCurveDerivativeX(t2)
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guard abs(d2) >= 1e-6 else { break }
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t2 = t2 - x2 / d2
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}
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// Fall back to the bisection method for reliability.
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t0 = 0.0
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t1 = 1.0
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t2 = x
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guard t2 >= t0 else { return t0 }
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guard t2 <= t1 else { return t1 }
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while t0 < t1 {
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x2 = sampleCurveX(t2)
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guard abs(x2 - x) >= epsilon else { return t2 }
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if x > x2 {
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t0 = t2
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} else {
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t1 = t2
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}
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t2 = (t1 - t0) * 0.5 + t0
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}
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return t2
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}
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}
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