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
+    }
+}