epoger@google.com | ec3ed6a | 2011-07-28 14:26:00 +0000 | [diff] [blame] | 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 | */ |
reed@android.com | 161b00b | 2009-11-03 15:33:14 +0000 | [diff] [blame] | 8 | #include "SkCubicInterval.h" |
| 9 | |
| 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 | |
| 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 | */ |
| 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); |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame^] | 62 | |
reed@android.com | 161b00b | 2009-11-03 15:33:14 +0000 | [diff] [blame] | 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 | |