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 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); 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
