1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
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
}
}
|
