1
2 /*
3 * Copyright 2011 Google Inc.
4 *
5 * Use of this source code is governed by a BSD-style license that can be
6 * found in the LICENSE file.
7 */
8 #include "SkCubicInterval.h"
9
eval_cubic(SkScalar c1,SkScalar c2,SkScalar c3,SkScalar t)10 static SkScalar eval_cubic(SkScalar c1, SkScalar c2, SkScalar c3,
11 SkScalar t) {
12 return SkScalarMul(SkScalarMul(SkScalarMul(c3, t) + c2, t) + c1, t);
13 }
14
find_cubic_t(SkScalar c1,SkScalar c2,SkScalar c3,SkScalar targetX)15 static SkScalar find_cubic_t(SkScalar c1, SkScalar c2, SkScalar c3,
16 SkScalar targetX) {
17 SkScalar minT = 0;
18 SkScalar maxT = SK_Scalar1;
19 SkScalar t;
20
21 for (;;) {
22 t = SkScalarAve(minT, maxT);
23 SkScalar x = eval_cubic(c1, c2, c3, t);
24 if (SkScalarNearlyZero(x - targetX)) {
25 break;
26 }
27 // subdivide the range and try again
28 if (x < targetX) {
29 minT = t;
30 } else {
31 maxT = t;
32 }
33 }
34 return t;
35 }
36
37 /*
38 a(1-t)^3 + 3bt(1-t)^2 + 3ct^2(1-t) + dt^3
39 a: [0, 0]
40 d: [1, 1]
41
42 3bt - 6bt^2 + 3bt^3 + 3ct^2 - 3ct^3 + t^3
43 C1 = t^1: 3b
44 C2 = t^2: 3c - 6b
45 C3 = t^3: 3b - 3c + 1
46
47 ((C3*t + C2)*t + C1)*t
48 */
SkEvalCubicInterval(SkScalar x1,SkScalar y1,SkScalar x2,SkScalar y2,SkScalar unitX)49 SkScalar SkEvalCubicInterval(SkScalar x1, SkScalar y1,
50 SkScalar x2, SkScalar y2,
51 SkScalar unitX) {
52 x1 = SkScalarPin(x1, 0, SK_Scalar1);
53 x2 = SkScalarPin(x2, 0, SK_Scalar1);
54 unitX = SkScalarPin(unitX, 0, SK_Scalar1);
55
56 // First compute our coefficients in X
57 x1 *= 3;
58 x2 *= 3;
59
60 // now search for t given unitX
61 SkScalar t = find_cubic_t(x1, x2 - 2*x1, x1 - x2 + SK_Scalar1, unitX);
62
63 // now evaluate the cubic in Y
64 y1 *= 3;
65 y2 *= 3;
66 return eval_cubic(y1, y2 - 2*y1, y1 - y2 + SK_Scalar1, t);
67 }
68