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Diffstat (limited to 'servo/components/style/bezier.rs')
| -rw-r--r-- | servo/components/style/bezier.rs | 176 |
1 files changed, 176 insertions, 0 deletions
diff --git a/servo/components/style/bezier.rs b/servo/components/style/bezier.rs new file mode 100644 index 0000000000..dd520ac0ed --- /dev/null +++ b/servo/components/style/bezier.rs @@ -0,0 +1,176 @@ +/* This Source Code Form is subject to the terms of the Mozilla Public + * License, v. 2.0. If a copy of the MPL was not distributed with this + * file, You can obtain one at https://mozilla.org/MPL/2.0/. */ + +//! Parametric Bézier curves. +//! +//! This is based on `WebCore/platform/graphics/UnitBezier.h` in WebKit. + +#![deny(missing_docs)] + +use crate::values::CSSFloat; + +const NEWTON_METHOD_ITERATIONS: u8 = 8; + +/// A unit cubic Bézier curve, used for timing functions in CSS transitions and animations. +pub struct Bezier { + ax: f64, + bx: f64, + cx: f64, + ay: f64, + by: f64, + cy: f64, +} + +impl Bezier { + /// Calculate the output of a unit cubic Bézier curve from the two middle control points. + /// + /// X coordinate is time, Y coordinate is function advancement. + /// The nominal range for both is 0 to 1. + /// + /// The start and end points are always (0, 0) and (1, 1) so that a transition or animation + /// starts at 0% and ends at 100%. + pub fn calculate_bezier_output( + progress: f64, + epsilon: f64, + x1: f32, + y1: f32, + x2: f32, + y2: f32, + ) -> f64 { + // Check for a linear curve. + if x1 == y1 && x2 == y2 { + return progress; + } + + // Ensure that we return 0 or 1 on both edges. + if progress == 0.0 { + return 0.0; + } + if progress == 1.0 { + return 1.0; + } + + // For negative values, try to extrapolate with tangent (p1 - p0) or, + // if p1 is coincident with p0, with (p2 - p0). + if progress < 0.0 { + if x1 > 0.0 { + return progress * y1 as f64 / x1 as f64; + } + if y1 == 0.0 && x2 > 0.0 { + return progress * y2 as f64 / x2 as f64; + } + // If we can't calculate a sensible tangent, don't extrapolate at all. + return 0.0; + } + + // For values greater than 1, try to extrapolate with tangent (p2 - p3) or, + // if p2 is coincident with p3, with (p1 - p3). + if progress > 1.0 { + if x2 < 1.0 { + return 1.0 + (progress - 1.0) * (y2 as f64 - 1.0) / (x2 as f64 - 1.0); + } + if y2 == 1.0 && x1 < 1.0 { + return 1.0 + (progress - 1.0) * (y1 as f64 - 1.0) / (x1 as f64 - 1.0); + } + // If we can't calculate a sensible tangent, don't extrapolate at all. + return 1.0; + } + + Bezier::new(x1, y1, x2, y2).solve(progress, epsilon) + } + + #[inline] + fn new(x1: CSSFloat, y1: CSSFloat, x2: CSSFloat, y2: CSSFloat) -> Bezier { + let cx = 3. * x1 as f64; + let bx = 3. * (x2 as f64 - x1 as f64) - cx; + + let cy = 3. * y1 as f64; + let by = 3. * (y2 as f64 - y1 as f64) - cy; + + Bezier { + ax: 1.0 - cx - bx, + bx: bx, + cx: cx, + ay: 1.0 - cy - by, + by: by, + cy: cy, + } + } + + #[inline] + fn sample_curve_x(&self, t: f64) -> f64 { + // ax * t^3 + bx * t^2 + cx * t + ((self.ax * t + self.bx) * t + self.cx) * t + } + + #[inline] + fn sample_curve_y(&self, t: f64) -> f64 { + ((self.ay * t + self.by) * t + self.cy) * t + } + + #[inline] + fn sample_curve_derivative_x(&self, t: f64) -> f64 { + (3.0 * self.ax * t + 2.0 * self.bx) * t + self.cx + } + + #[inline] + fn solve_curve_x(&self, x: f64, epsilon: f64) -> f64 { + // Fast path: Use Newton's method. + let mut t = x; + for _ in 0..NEWTON_METHOD_ITERATIONS { + let x2 = self.sample_curve_x(t); + if x2.approx_eq(x, epsilon) { + return t; + } + let dx = self.sample_curve_derivative_x(t); + if dx.approx_eq(0.0, 1e-6) { + break; + } + t -= (x2 - x) / dx; + } + + // Slow path: Use bisection. + let (mut lo, mut hi, mut t) = (0.0, 1.0, x); + + if t < lo { + return lo; + } + if t > hi { + return hi; + } + + while lo < hi { + let x2 = self.sample_curve_x(t); + if x2.approx_eq(x, epsilon) { + return t; + } + if x > x2 { + lo = t + } else { + hi = t + } + t = (hi - lo) / 2.0 + lo + } + + t + } + + /// Solve the bezier curve for a given `x` and an `epsilon`, that should be + /// between zero and one. + #[inline] + fn solve(&self, x: f64, epsilon: f64) -> f64 { + self.sample_curve_y(self.solve_curve_x(x, epsilon)) + } +} + +trait ApproxEq { + fn approx_eq(self, value: Self, epsilon: Self) -> bool; +} + +impl ApproxEq for f64 { + #[inline] + fn approx_eq(self, value: f64, epsilon: f64) -> bool { + (self - value).abs() < epsilon + } +} |