epoger@google.com | ec3ed6a | 2011-07-28 14:26:00 +0000 | [diff] [blame] | 1 | /* |
| 2 | * Copyright 2006 The Android Open Source Project |
| 3 | * |
| 4 | * Use of this source code is governed by a BSD-style license that can be |
| 5 | * found in the LICENSE file. |
| 6 | */ |
| 7 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 8 | #include "SkGeometry.h" |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 9 | #include "SkMatrix.h" |
mtklein | c9adb05 | 2015-03-30 10:50:27 -0700 | [diff] [blame] | 10 | #include "SkNx.h" |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 11 | |
reed | 6983f66 | 2015-04-15 18:23:03 -0700 | [diff] [blame] | 12 | #if 0 |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 13 | static Sk2s from_point(const SkPoint& point) { |
| 14 | return Sk2s::Load(&point.fX); |
| 15 | } |
| 16 | |
| 17 | static SkPoint to_point(const Sk2s& x) { |
| 18 | SkPoint point; |
| 19 | x.store(&point.fX); |
| 20 | return point; |
| 21 | } |
reed | 6983f66 | 2015-04-15 18:23:03 -0700 | [diff] [blame] | 22 | #endif |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 23 | |
| 24 | static SkVector to_vector(const Sk2s& x) { |
| 25 | SkVector vector; |
| 26 | x.store(&vector.fX); |
| 27 | return vector; |
| 28 | } |
| 29 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 30 | /** If defined, this makes eval_quad and eval_cubic do more setup (sometimes |
| 31 | involving integer multiplies by 2 or 3, but fewer calls to SkScalarMul. |
| 32 | May also introduce overflow of fixed when we compute our setup. |
| 33 | */ |
reed@google.com | 8f4d230 | 2013-12-17 16:44:46 +0000 | [diff] [blame] | 34 | // #define DIRECT_EVAL_OF_POLYNOMIALS |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 35 | |
| 36 | //////////////////////////////////////////////////////////////////////// |
| 37 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 38 | static int is_not_monotonic(SkScalar a, SkScalar b, SkScalar c) { |
| 39 | SkScalar ab = a - b; |
| 40 | SkScalar bc = b - c; |
reed@google.com | 8f4d230 | 2013-12-17 16:44:46 +0000 | [diff] [blame] | 41 | if (ab < 0) { |
| 42 | bc = -bc; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 43 | } |
reed@google.com | 8f4d230 | 2013-12-17 16:44:46 +0000 | [diff] [blame] | 44 | return ab == 0 || bc < 0; |
| 45 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 46 | |
| 47 | //////////////////////////////////////////////////////////////////////// |
| 48 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 49 | static bool is_unit_interval(SkScalar x) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 50 | return x > 0 && x < SK_Scalar1; |
| 51 | } |
| 52 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 53 | static int valid_unit_divide(SkScalar numer, SkScalar denom, SkScalar* ratio) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 54 | SkASSERT(ratio); |
| 55 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 56 | if (numer < 0) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 57 | numer = -numer; |
| 58 | denom = -denom; |
| 59 | } |
| 60 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 61 | if (denom == 0 || numer == 0 || numer >= denom) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 62 | return 0; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 63 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 64 | |
| 65 | SkScalar r = SkScalarDiv(numer, denom); |
reed@android.com | 1516162 | 2010-03-08 17:44:42 +0000 | [diff] [blame] | 66 | if (SkScalarIsNaN(r)) { |
| 67 | return 0; |
| 68 | } |
Mike Klein | 11fca3f | 2014-09-12 12:17:25 -0400 | [diff] [blame] | 69 | SkASSERTF(r >= 0 && r < SK_Scalar1, "numer %f, denom %f, r %f", numer, denom, r); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 70 | if (r == 0) { // catch underflow if numer <<<< denom |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 71 | return 0; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 72 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 73 | *ratio = r; |
| 74 | return 1; |
| 75 | } |
| 76 | |
| 77 | /** From Numerical Recipes in C. |
| 78 | |
| 79 | Q = -1/2 (B + sign(B) sqrt[B*B - 4*A*C]) |
| 80 | x1 = Q / A |
| 81 | x2 = C / Q |
| 82 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 83 | int SkFindUnitQuadRoots(SkScalar A, SkScalar B, SkScalar C, SkScalar roots[2]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 84 | SkASSERT(roots); |
| 85 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 86 | if (A == 0) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 87 | return valid_unit_divide(-C, B, roots); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 88 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 89 | |
| 90 | SkScalar* r = roots; |
| 91 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 92 | SkScalar R = B*B - 4*A*C; |
reed@android.com | 1516162 | 2010-03-08 17:44:42 +0000 | [diff] [blame] | 93 | if (R < 0 || SkScalarIsNaN(R)) { // complex roots |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 94 | return 0; |
reed@android.com | 1516162 | 2010-03-08 17:44:42 +0000 | [diff] [blame] | 95 | } |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 96 | R = SkScalarSqrt(R); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 97 | |
| 98 | SkScalar Q = (B < 0) ? -(B-R)/2 : -(B+R)/2; |
| 99 | r += valid_unit_divide(Q, A, r); |
| 100 | r += valid_unit_divide(C, Q, r); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 101 | if (r - roots == 2) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 102 | if (roots[0] > roots[1]) |
| 103 | SkTSwap<SkScalar>(roots[0], roots[1]); |
| 104 | else if (roots[0] == roots[1]) // nearly-equal? |
| 105 | r -= 1; // skip the double root |
| 106 | } |
| 107 | return (int)(r - roots); |
| 108 | } |
| 109 | |
reed@google.com | 8f4d230 | 2013-12-17 16:44:46 +0000 | [diff] [blame] | 110 | /////////////////////////////////////////////////////////////////////////////// |
| 111 | /////////////////////////////////////////////////////////////////////////////// |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 112 | |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 113 | static Sk2s quad_poly_eval(const Sk2s& A, const Sk2s& B, const Sk2s& C, const Sk2s& t) { |
| 114 | return (A * t + B) * t + C; |
| 115 | } |
| 116 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 117 | static SkScalar eval_quad(const SkScalar src[], SkScalar t) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 118 | SkASSERT(src); |
| 119 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
| 120 | |
| 121 | #ifdef DIRECT_EVAL_OF_POLYNOMIALS |
| 122 | SkScalar C = src[0]; |
| 123 | SkScalar A = src[4] - 2 * src[2] + C; |
| 124 | SkScalar B = 2 * (src[2] - C); |
| 125 | return SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C); |
| 126 | #else |
| 127 | SkScalar ab = SkScalarInterp(src[0], src[2], t); |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 128 | SkScalar bc = SkScalarInterp(src[2], src[4], t); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 129 | return SkScalarInterp(ab, bc, t); |
| 130 | #endif |
| 131 | } |
| 132 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 133 | static SkScalar eval_quad_derivative(const SkScalar src[], SkScalar t) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 134 | SkScalar A = src[4] - 2 * src[2] + src[0]; |
| 135 | SkScalar B = src[2] - src[0]; |
| 136 | |
| 137 | return 2 * SkScalarMulAdd(A, t, B); |
| 138 | } |
| 139 | |
reed | 6983f66 | 2015-04-15 18:23:03 -0700 | [diff] [blame] | 140 | void SkQuadToCoeff(const SkPoint pts[3], SkPoint coeff[3]) { |
| 141 | Sk2s p0 = from_point(pts[0]); |
| 142 | Sk2s p1 = from_point(pts[1]); |
| 143 | Sk2s p2 = from_point(pts[2]); |
| 144 | |
| 145 | Sk2s p1minus2 = p1 - p0; |
| 146 | |
| 147 | coeff[0] = to_point(p2 - p1 - p1 + p0); // A * t^2 |
| 148 | coeff[1] = to_point(p1minus2 + p1minus2); // B * t |
| 149 | coeff[2] = pts[0]; // C |
| 150 | } |
| 151 | |
reed | 65cb2cd | 2015-03-19 10:18:47 -0700 | [diff] [blame] | 152 | void SkEvalQuadAt(const SkPoint src[3], SkScalar t, SkPoint* pt, SkVector* tangent) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 153 | SkASSERT(src); |
| 154 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
mtklein | 950e986 | 2015-03-19 12:03:29 -0700 | [diff] [blame] | 155 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 156 | if (pt) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 157 | pt->set(eval_quad(&src[0].fX, t), eval_quad(&src[0].fY, t)); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 158 | } |
| 159 | if (tangent) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 160 | tangent->set(eval_quad_derivative(&src[0].fX, t), |
| 161 | eval_quad_derivative(&src[0].fY, t)); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 162 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 163 | } |
| 164 | |
reed | 65cb2cd | 2015-03-19 10:18:47 -0700 | [diff] [blame] | 165 | SkPoint SkEvalQuadAt(const SkPoint src[3], SkScalar t) { |
| 166 | SkASSERT(src); |
| 167 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
| 168 | |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 169 | const Sk2s t2(t); |
mtklein | 950e986 | 2015-03-19 12:03:29 -0700 | [diff] [blame] | 170 | |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 171 | Sk2s P0 = from_point(src[0]); |
| 172 | Sk2s P1 = from_point(src[1]); |
| 173 | Sk2s P2 = from_point(src[2]); |
mtklein | 950e986 | 2015-03-19 12:03:29 -0700 | [diff] [blame] | 174 | |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 175 | Sk2s B = P1 - P0; |
| 176 | Sk2s A = P2 - P1 - B; |
mtklein | 950e986 | 2015-03-19 12:03:29 -0700 | [diff] [blame] | 177 | |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 178 | return to_point((A * t2 + B+B) * t2 + P0); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 179 | } |
| 180 | |
reed | 40b7dd5 | 2015-03-20 06:01:08 -0700 | [diff] [blame] | 181 | SkVector SkEvalQuadTangentAt(const SkPoint src[3], SkScalar t) { |
| 182 | SkASSERT(src); |
| 183 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
| 184 | |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 185 | Sk2s P0 = from_point(src[0]); |
| 186 | Sk2s P1 = from_point(src[1]); |
| 187 | Sk2s P2 = from_point(src[2]); |
reed | 40b7dd5 | 2015-03-20 06:01:08 -0700 | [diff] [blame] | 188 | |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 189 | Sk2s B = P1 - P0; |
| 190 | Sk2s A = P2 - P1 - B; |
| 191 | Sk2s T = A * Sk2s(t) + B; |
reed | 40b7dd5 | 2015-03-20 06:01:08 -0700 | [diff] [blame] | 192 | |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 193 | return to_vector(T + T); |
reed | 40b7dd5 | 2015-03-20 06:01:08 -0700 | [diff] [blame] | 194 | } |
| 195 | |
reed | 40b7dd5 | 2015-03-20 06:01:08 -0700 | [diff] [blame] | 196 | static inline Sk2s interp(const Sk2s& v0, const Sk2s& v1, const Sk2s& t) { |
| 197 | return v0 + (v1 - v0) * t; |
| 198 | } |
| 199 | |
reed | c08330f | 2015-03-26 07:26:08 -0700 | [diff] [blame] | 200 | void SkChopQuadAt(const SkPoint src[3], SkPoint dst[5], SkScalar t) { |
reed | 40b7dd5 | 2015-03-20 06:01:08 -0700 | [diff] [blame] | 201 | SkASSERT(t > 0 && t < SK_Scalar1); |
| 202 | |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 203 | Sk2s p0 = from_point(src[0]); |
| 204 | Sk2s p1 = from_point(src[1]); |
| 205 | Sk2s p2 = from_point(src[2]); |
reed | ce6acc9 | 2015-03-20 13:46:08 -0700 | [diff] [blame] | 206 | Sk2s tt(t); |
mtklein | c9adb05 | 2015-03-30 10:50:27 -0700 | [diff] [blame] | 207 | |
reed | 40b7dd5 | 2015-03-20 06:01:08 -0700 | [diff] [blame] | 208 | Sk2s p01 = interp(p0, p1, tt); |
| 209 | Sk2s p12 = interp(p1, p2, tt); |
| 210 | |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 211 | dst[0] = to_point(p0); |
| 212 | dst[1] = to_point(p01); |
| 213 | dst[2] = to_point(interp(p01, p12, tt)); |
| 214 | dst[3] = to_point(p12); |
| 215 | dst[4] = to_point(p2); |
reed | 40b7dd5 | 2015-03-20 06:01:08 -0700 | [diff] [blame] | 216 | } |
| 217 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 218 | void SkChopQuadAtHalf(const SkPoint src[3], SkPoint dst[5]) { |
reed | c08330f | 2015-03-26 07:26:08 -0700 | [diff] [blame] | 219 | SkChopQuadAt(src, dst, 0.5f); return; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 220 | } |
| 221 | |
| 222 | /** Quad'(t) = At + B, where |
| 223 | A = 2(a - 2b + c) |
| 224 | B = 2(b - a) |
| 225 | Solve for t, only if it fits between 0 < t < 1 |
| 226 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 227 | int SkFindQuadExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar tValue[1]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 228 | /* At + B == 0 |
| 229 | t = -B / A |
| 230 | */ |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 231 | return valid_unit_divide(a - b, a - b - b + c, tValue); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 232 | } |
| 233 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 234 | static inline void flatten_double_quad_extrema(SkScalar coords[14]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 235 | coords[2] = coords[6] = coords[4]; |
| 236 | } |
| 237 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 238 | /* Returns 0 for 1 quad, and 1 for two quads, either way the answer is |
reed@android.com | 77f0ef7 | 2009-11-17 18:47:52 +0000 | [diff] [blame] | 239 | stored in dst[]. Guarantees that the 1/2 quads will be monotonic. |
| 240 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 241 | int SkChopQuadAtYExtrema(const SkPoint src[3], SkPoint dst[5]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 242 | SkASSERT(src); |
| 243 | SkASSERT(dst); |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 244 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 245 | SkScalar a = src[0].fY; |
| 246 | SkScalar b = src[1].fY; |
| 247 | SkScalar c = src[2].fY; |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 248 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 249 | if (is_not_monotonic(a, b, c)) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 250 | SkScalar tValue; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 251 | if (valid_unit_divide(a - b, a - b - b + c, &tValue)) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 252 | SkChopQuadAt(src, dst, tValue); |
| 253 | flatten_double_quad_extrema(&dst[0].fY); |
| 254 | return 1; |
| 255 | } |
| 256 | // if we get here, we need to force dst to be monotonic, even though |
| 257 | // we couldn't compute a unit_divide value (probably underflow). |
| 258 | b = SkScalarAbs(a - b) < SkScalarAbs(b - c) ? a : c; |
| 259 | } |
| 260 | dst[0].set(src[0].fX, a); |
| 261 | dst[1].set(src[1].fX, b); |
| 262 | dst[2].set(src[2].fX, c); |
| 263 | return 0; |
| 264 | } |
| 265 | |
reed@android.com | 77f0ef7 | 2009-11-17 18:47:52 +0000 | [diff] [blame] | 266 | /* Returns 0 for 1 quad, and 1 for two quads, either way the answer is |
| 267 | stored in dst[]. Guarantees that the 1/2 quads will be monotonic. |
| 268 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 269 | int SkChopQuadAtXExtrema(const SkPoint src[3], SkPoint dst[5]) { |
reed@android.com | 77f0ef7 | 2009-11-17 18:47:52 +0000 | [diff] [blame] | 270 | SkASSERT(src); |
| 271 | SkASSERT(dst); |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 272 | |
reed@android.com | 77f0ef7 | 2009-11-17 18:47:52 +0000 | [diff] [blame] | 273 | SkScalar a = src[0].fX; |
| 274 | SkScalar b = src[1].fX; |
| 275 | SkScalar c = src[2].fX; |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 276 | |
reed@android.com | 77f0ef7 | 2009-11-17 18:47:52 +0000 | [diff] [blame] | 277 | if (is_not_monotonic(a, b, c)) { |
| 278 | SkScalar tValue; |
| 279 | if (valid_unit_divide(a - b, a - b - b + c, &tValue)) { |
| 280 | SkChopQuadAt(src, dst, tValue); |
| 281 | flatten_double_quad_extrema(&dst[0].fX); |
| 282 | return 1; |
| 283 | } |
| 284 | // if we get here, we need to force dst to be monotonic, even though |
| 285 | // we couldn't compute a unit_divide value (probably underflow). |
| 286 | b = SkScalarAbs(a - b) < SkScalarAbs(b - c) ? a : c; |
| 287 | } |
| 288 | dst[0].set(a, src[0].fY); |
| 289 | dst[1].set(b, src[1].fY); |
| 290 | dst[2].set(c, src[2].fY); |
| 291 | return 0; |
| 292 | } |
| 293 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 294 | // F(t) = a (1 - t) ^ 2 + 2 b t (1 - t) + c t ^ 2 |
| 295 | // F'(t) = 2 (b - a) + 2 (a - 2b + c) t |
| 296 | // F''(t) = 2 (a - 2b + c) |
| 297 | // |
| 298 | // A = 2 (b - a) |
| 299 | // B = 2 (a - 2b + c) |
| 300 | // |
| 301 | // Maximum curvature for a quadratic means solving |
| 302 | // Fx' Fx'' + Fy' Fy'' = 0 |
| 303 | // |
| 304 | // t = - (Ax Bx + Ay By) / (Bx ^ 2 + By ^ 2) |
| 305 | // |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 306 | SkScalar SkFindQuadMaxCurvature(const SkPoint src[3]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 307 | SkScalar Ax = src[1].fX - src[0].fX; |
| 308 | SkScalar Ay = src[1].fY - src[0].fY; |
| 309 | SkScalar Bx = src[0].fX - src[1].fX - src[1].fX + src[2].fX; |
| 310 | SkScalar By = src[0].fY - src[1].fY - src[1].fY + src[2].fY; |
| 311 | SkScalar t = 0; // 0 means don't chop |
| 312 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 313 | (void)valid_unit_divide(-(Ax * Bx + Ay * By), Bx * Bx + By * By, &t); |
egdaniel@google.com | 5383a75 | 2013-07-12 20:15:34 +0000 | [diff] [blame] | 314 | return t; |
| 315 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 316 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 317 | int SkChopQuadAtMaxCurvature(const SkPoint src[3], SkPoint dst[5]) { |
egdaniel@google.com | 5383a75 | 2013-07-12 20:15:34 +0000 | [diff] [blame] | 318 | SkScalar t = SkFindQuadMaxCurvature(src); |
| 319 | if (t == 0) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 320 | memcpy(dst, src, 3 * sizeof(SkPoint)); |
| 321 | return 1; |
egdaniel@google.com | 5383a75 | 2013-07-12 20:15:34 +0000 | [diff] [blame] | 322 | } else { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 323 | SkChopQuadAt(src, dst, t); |
| 324 | return 2; |
| 325 | } |
| 326 | } |
| 327 | |
reed@google.com | 6fc321a | 2011-07-27 13:54:36 +0000 | [diff] [blame] | 328 | void SkConvertQuadToCubic(const SkPoint src[3], SkPoint dst[4]) { |
reed | daee7ea | 2015-03-26 20:22:33 -0700 | [diff] [blame] | 329 | Sk2s scale(SkDoubleToScalar(2.0 / 3.0)); |
| 330 | Sk2s s0 = from_point(src[0]); |
| 331 | Sk2s s1 = from_point(src[1]); |
| 332 | Sk2s s2 = from_point(src[2]); |
| 333 | |
reed@google.com | 6fc321a | 2011-07-27 13:54:36 +0000 | [diff] [blame] | 334 | dst[0] = src[0]; |
reed | daee7ea | 2015-03-26 20:22:33 -0700 | [diff] [blame] | 335 | dst[1] = to_point(s0 + (s1 - s0) * scale); |
| 336 | dst[2] = to_point(s2 + (s1 - s2) * scale); |
reed@google.com | 6fc321a | 2011-07-27 13:54:36 +0000 | [diff] [blame] | 337 | dst[3] = src[2]; |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 338 | } |
| 339 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 340 | ////////////////////////////////////////////////////////////////////////////// |
| 341 | ///// CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS ///// |
| 342 | ////////////////////////////////////////////////////////////////////////////// |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 343 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 344 | static SkScalar eval_cubic(const SkScalar src[], SkScalar t) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 345 | SkASSERT(src); |
| 346 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
| 347 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 348 | if (t == 0) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 349 | return src[0]; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 350 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 351 | |
| 352 | #ifdef DIRECT_EVAL_OF_POLYNOMIALS |
| 353 | SkScalar D = src[0]; |
| 354 | SkScalar A = src[6] + 3*(src[2] - src[4]) - D; |
| 355 | SkScalar B = 3*(src[4] - src[2] - src[2] + D); |
| 356 | SkScalar C = 3*(src[2] - D); |
| 357 | |
| 358 | return SkScalarMulAdd(SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C), t, D); |
| 359 | #else |
| 360 | SkScalar ab = SkScalarInterp(src[0], src[2], t); |
| 361 | SkScalar bc = SkScalarInterp(src[2], src[4], t); |
| 362 | SkScalar cd = SkScalarInterp(src[4], src[6], t); |
| 363 | SkScalar abc = SkScalarInterp(ab, bc, t); |
| 364 | SkScalar bcd = SkScalarInterp(bc, cd, t); |
| 365 | return SkScalarInterp(abc, bcd, t); |
| 366 | #endif |
| 367 | } |
| 368 | |
| 369 | /** return At^2 + Bt + C |
| 370 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 371 | static SkScalar eval_quadratic(SkScalar A, SkScalar B, SkScalar C, SkScalar t) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 372 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
| 373 | |
| 374 | return SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C); |
| 375 | } |
| 376 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 377 | static SkScalar eval_cubic_derivative(const SkScalar src[], SkScalar t) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 378 | SkScalar A = src[6] + 3*(src[2] - src[4]) - src[0]; |
| 379 | SkScalar B = 2*(src[4] - 2 * src[2] + src[0]); |
| 380 | SkScalar C = src[2] - src[0]; |
| 381 | |
| 382 | return eval_quadratic(A, B, C, t); |
| 383 | } |
| 384 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 385 | static SkScalar eval_cubic_2ndDerivative(const SkScalar src[], SkScalar t) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 386 | SkScalar A = src[6] + 3*(src[2] - src[4]) - src[0]; |
| 387 | SkScalar B = src[4] - 2 * src[2] + src[0]; |
| 388 | |
| 389 | return SkScalarMulAdd(A, t, B); |
| 390 | } |
| 391 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 392 | void SkEvalCubicAt(const SkPoint src[4], SkScalar t, SkPoint* loc, |
| 393 | SkVector* tangent, SkVector* curvature) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 394 | SkASSERT(src); |
| 395 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
| 396 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 397 | if (loc) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 398 | loc->set(eval_cubic(&src[0].fX, t), eval_cubic(&src[0].fY, t)); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 399 | } |
| 400 | if (tangent) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 401 | tangent->set(eval_cubic_derivative(&src[0].fX, t), |
| 402 | eval_cubic_derivative(&src[0].fY, t)); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 403 | } |
| 404 | if (curvature) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 405 | curvature->set(eval_cubic_2ndDerivative(&src[0].fX, t), |
| 406 | eval_cubic_2ndDerivative(&src[0].fY, t)); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 407 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 408 | } |
| 409 | |
| 410 | /** Cubic'(t) = At^2 + Bt + C, where |
| 411 | A = 3(-a + 3(b - c) + d) |
| 412 | B = 6(a - 2b + c) |
| 413 | C = 3(b - a) |
| 414 | Solve for t, keeping only those that fit betwee 0 < t < 1 |
| 415 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 416 | int SkFindCubicExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar d, |
| 417 | SkScalar tValues[2]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 418 | // we divide A,B,C by 3 to simplify |
| 419 | SkScalar A = d - a + 3*(b - c); |
| 420 | SkScalar B = 2*(a - b - b + c); |
| 421 | SkScalar C = b - a; |
| 422 | |
| 423 | return SkFindUnitQuadRoots(A, B, C, tValues); |
| 424 | } |
| 425 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 426 | void SkChopCubicAt(const SkPoint src[4], SkPoint dst[7], SkScalar t) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 427 | SkASSERT(t > 0 && t < SK_Scalar1); |
| 428 | |
reed | 6b9ef90 | 2015-03-24 19:24:34 -0700 | [diff] [blame] | 429 | Sk2s p0 = from_point(src[0]); |
| 430 | Sk2s p1 = from_point(src[1]); |
| 431 | Sk2s p2 = from_point(src[2]); |
| 432 | Sk2s p3 = from_point(src[3]); |
| 433 | Sk2s tt(t); |
| 434 | |
| 435 | Sk2s ab = interp(p0, p1, tt); |
| 436 | Sk2s bc = interp(p1, p2, tt); |
| 437 | Sk2s cd = interp(p2, p3, tt); |
| 438 | Sk2s abc = interp(ab, bc, tt); |
| 439 | Sk2s bcd = interp(bc, cd, tt); |
| 440 | Sk2s abcd = interp(abc, bcd, tt); |
mtklein | c9adb05 | 2015-03-30 10:50:27 -0700 | [diff] [blame] | 441 | |
reed | 6b9ef90 | 2015-03-24 19:24:34 -0700 | [diff] [blame] | 442 | dst[0] = src[0]; |
| 443 | dst[1] = to_point(ab); |
| 444 | dst[2] = to_point(abc); |
| 445 | dst[3] = to_point(abcd); |
| 446 | dst[4] = to_point(bcd); |
| 447 | dst[5] = to_point(cd); |
| 448 | dst[6] = src[3]; |
| 449 | } |
| 450 | |
reed | 6983f66 | 2015-04-15 18:23:03 -0700 | [diff] [blame] | 451 | void SkCubicToCoeff(const SkPoint pts[4], SkPoint coeff[4]) { |
| 452 | Sk2s p0 = from_point(pts[0]); |
| 453 | Sk2s p1 = from_point(pts[1]); |
| 454 | Sk2s p2 = from_point(pts[2]); |
| 455 | Sk2s p3 = from_point(pts[3]); |
| 456 | |
| 457 | const Sk2s three(3); |
| 458 | Sk2s p1minusp2 = p1 - p2; |
| 459 | |
| 460 | Sk2s D = p0; |
| 461 | Sk2s A = p3 + three * p1minusp2 - D; |
| 462 | Sk2s B = three * (D - p1minusp2 - p1); |
| 463 | Sk2s C = three * (p1 - D); |
| 464 | |
| 465 | coeff[0] = to_point(A); |
| 466 | coeff[1] = to_point(B); |
| 467 | coeff[2] = to_point(C); |
| 468 | coeff[3] = to_point(D); |
| 469 | } |
| 470 | |
reed@android.com | a964028 | 2009-08-28 20:06:54 +0000 | [diff] [blame] | 471 | /* http://code.google.com/p/skia/issues/detail?id=32 |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 472 | |
reed@android.com | a964028 | 2009-08-28 20:06:54 +0000 | [diff] [blame] | 473 | This test code would fail when we didn't check the return result of |
| 474 | valid_unit_divide in SkChopCubicAt(... tValues[], int roots). The reason is |
| 475 | that after the first chop, the parameters to valid_unit_divide are equal |
| 476 | (thanks to finite float precision and rounding in the subtracts). Thus |
| 477 | even though the 2nd tValue looks < 1.0, after we renormalize it, we end |
| 478 | up with 1.0, hence the need to check and just return the last cubic as |
| 479 | a degenerate clump of 4 points in the sampe place. |
| 480 | |
| 481 | static void test_cubic() { |
| 482 | SkPoint src[4] = { |
| 483 | { 556.25000, 523.03003 }, |
| 484 | { 556.23999, 522.96002 }, |
| 485 | { 556.21997, 522.89001 }, |
| 486 | { 556.21997, 522.82001 } |
| 487 | }; |
| 488 | SkPoint dst[10]; |
| 489 | SkScalar tval[] = { 0.33333334f, 0.99999994f }; |
| 490 | SkChopCubicAt(src, dst, tval, 2); |
| 491 | } |
| 492 | */ |
| 493 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 494 | void SkChopCubicAt(const SkPoint src[4], SkPoint dst[], |
| 495 | const SkScalar tValues[], int roots) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 496 | #ifdef SK_DEBUG |
| 497 | { |
| 498 | for (int i = 0; i < roots - 1; i++) |
| 499 | { |
| 500 | SkASSERT(is_unit_interval(tValues[i])); |
| 501 | SkASSERT(is_unit_interval(tValues[i+1])); |
| 502 | SkASSERT(tValues[i] < tValues[i+1]); |
| 503 | } |
| 504 | } |
| 505 | #endif |
| 506 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 507 | if (dst) { |
| 508 | if (roots == 0) { // nothing to chop |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 509 | memcpy(dst, src, 4*sizeof(SkPoint)); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 510 | } else { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 511 | SkScalar t = tValues[0]; |
| 512 | SkPoint tmp[4]; |
| 513 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 514 | for (int i = 0; i < roots; i++) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 515 | SkChopCubicAt(src, dst, t); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 516 | if (i == roots - 1) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 517 | break; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 518 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 519 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 520 | dst += 3; |
reed@android.com | a964028 | 2009-08-28 20:06:54 +0000 | [diff] [blame] | 521 | // have src point to the remaining cubic (after the chop) |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 522 | memcpy(tmp, dst, 4 * sizeof(SkPoint)); |
| 523 | src = tmp; |
reed@android.com | a964028 | 2009-08-28 20:06:54 +0000 | [diff] [blame] | 524 | |
| 525 | // watch out in case the renormalized t isn't in range |
| 526 | if (!valid_unit_divide(tValues[i+1] - tValues[i], |
| 527 | SK_Scalar1 - tValues[i], &t)) { |
| 528 | // if we can't, just create a degenerate cubic |
| 529 | dst[4] = dst[5] = dst[6] = src[3]; |
| 530 | break; |
| 531 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 532 | } |
| 533 | } |
| 534 | } |
| 535 | } |
| 536 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 537 | void SkChopCubicAtHalf(const SkPoint src[4], SkPoint dst[7]) { |
reed | c08330f | 2015-03-26 07:26:08 -0700 | [diff] [blame] | 538 | SkChopCubicAt(src, dst, 0.5f); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 539 | } |
| 540 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 541 | static void flatten_double_cubic_extrema(SkScalar coords[14]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 542 | coords[4] = coords[8] = coords[6]; |
| 543 | } |
| 544 | |
| 545 | /** Given 4 points on a cubic bezier, chop it into 1, 2, 3 beziers such that |
commit-bot@chromium.org | def6468 | 2014-02-21 19:49:10 +0000 | [diff] [blame] | 546 | the resulting beziers are monotonic in Y. This is called by the scan |
| 547 | converter. Depending on what is returned, dst[] is treated as follows: |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 548 | 0 dst[0..3] is the original cubic |
| 549 | 1 dst[0..3] and dst[3..6] are the two new cubics |
| 550 | 2 dst[0..3], dst[3..6], dst[6..9] are the three new cubics |
| 551 | If dst == null, it is ignored and only the count is returned. |
| 552 | */ |
reed@android.com | bb13586 | 2009-11-18 13:47:40 +0000 | [diff] [blame] | 553 | int SkChopCubicAtYExtrema(const SkPoint src[4], SkPoint dst[10]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 554 | SkScalar tValues[2]; |
reed@android.com | bb13586 | 2009-11-18 13:47:40 +0000 | [diff] [blame] | 555 | int roots = SkFindCubicExtrema(src[0].fY, src[1].fY, src[2].fY, |
| 556 | src[3].fY, tValues); |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 557 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 558 | SkChopCubicAt(src, dst, tValues, roots); |
reed@android.com | bb13586 | 2009-11-18 13:47:40 +0000 | [diff] [blame] | 559 | if (dst && roots > 0) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 560 | // we do some cleanup to ensure our Y extrema are flat |
| 561 | flatten_double_cubic_extrema(&dst[0].fY); |
reed@android.com | bb13586 | 2009-11-18 13:47:40 +0000 | [diff] [blame] | 562 | if (roots == 2) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 563 | flatten_double_cubic_extrema(&dst[3].fY); |
reed@android.com | bb13586 | 2009-11-18 13:47:40 +0000 | [diff] [blame] | 564 | } |
| 565 | } |
| 566 | return roots; |
| 567 | } |
| 568 | |
| 569 | int SkChopCubicAtXExtrema(const SkPoint src[4], SkPoint dst[10]) { |
| 570 | SkScalar tValues[2]; |
| 571 | int roots = SkFindCubicExtrema(src[0].fX, src[1].fX, src[2].fX, |
| 572 | src[3].fX, tValues); |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 573 | |
reed@android.com | bb13586 | 2009-11-18 13:47:40 +0000 | [diff] [blame] | 574 | SkChopCubicAt(src, dst, tValues, roots); |
| 575 | if (dst && roots > 0) { |
| 576 | // we do some cleanup to ensure our Y extrema are flat |
| 577 | flatten_double_cubic_extrema(&dst[0].fX); |
| 578 | if (roots == 2) { |
| 579 | flatten_double_cubic_extrema(&dst[3].fX); |
| 580 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 581 | } |
| 582 | return roots; |
| 583 | } |
| 584 | |
| 585 | /** http://www.faculty.idc.ac.il/arik/quality/appendixA.html |
| 586 | |
| 587 | Inflection means that curvature is zero. |
| 588 | Curvature is [F' x F''] / [F'^3] |
| 589 | So we solve F'x X F''y - F'y X F''y == 0 |
| 590 | After some canceling of the cubic term, we get |
| 591 | A = b - a |
| 592 | B = c - 2b + a |
| 593 | C = d - 3c + 3b - a |
| 594 | (BxCy - ByCx)t^2 + (AxCy - AyCx)t + AxBy - AyBx == 0 |
| 595 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 596 | int SkFindCubicInflections(const SkPoint src[4], SkScalar tValues[]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 597 | SkScalar Ax = src[1].fX - src[0].fX; |
| 598 | SkScalar Ay = src[1].fY - src[0].fY; |
| 599 | SkScalar Bx = src[2].fX - 2 * src[1].fX + src[0].fX; |
| 600 | SkScalar By = src[2].fY - 2 * src[1].fY + src[0].fY; |
| 601 | SkScalar Cx = src[3].fX + 3 * (src[1].fX - src[2].fX) - src[0].fX; |
| 602 | SkScalar Cy = src[3].fY + 3 * (src[1].fY - src[2].fY) - src[0].fY; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 603 | |
commit-bot@chromium.org | def6468 | 2014-02-21 19:49:10 +0000 | [diff] [blame] | 604 | return SkFindUnitQuadRoots(Bx*Cy - By*Cx, |
| 605 | Ax*Cy - Ay*Cx, |
| 606 | Ax*By - Ay*Bx, |
| 607 | tValues); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 608 | } |
| 609 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 610 | int SkChopCubicAtInflections(const SkPoint src[], SkPoint dst[10]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 611 | SkScalar tValues[2]; |
| 612 | int count = SkFindCubicInflections(src, tValues); |
| 613 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 614 | if (dst) { |
| 615 | if (count == 0) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 616 | memcpy(dst, src, 4 * sizeof(SkPoint)); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 617 | } else { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 618 | SkChopCubicAt(src, dst, tValues, count); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 619 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 620 | } |
| 621 | return count + 1; |
| 622 | } |
| 623 | |
caryclark | 8dd31cf | 2014-12-12 09:11:23 -0800 | [diff] [blame] | 624 | // See http://http.developer.nvidia.com/GPUGems3/gpugems3_ch25.html (from the book GPU Gems 3) |
| 625 | // discr(I) = d0^2 * (3*d1^2 - 4*d0*d2) |
| 626 | // Classification: |
| 627 | // discr(I) > 0 Serpentine |
| 628 | // discr(I) = 0 Cusp |
| 629 | // discr(I) < 0 Loop |
| 630 | // d0 = d1 = 0 Quadratic |
| 631 | // d0 = d1 = d2 = 0 Line |
| 632 | // p0 = p1 = p2 = p3 Point |
| 633 | static SkCubicType classify_cubic(const SkPoint p[4], const SkScalar d[3]) { |
| 634 | if (p[0] == p[1] && p[0] == p[2] && p[0] == p[3]) { |
| 635 | return kPoint_SkCubicType; |
| 636 | } |
| 637 | const SkScalar discr = d[0] * d[0] * (3.f * d[1] * d[1] - 4.f * d[0] * d[2]); |
| 638 | if (discr > SK_ScalarNearlyZero) { |
| 639 | return kSerpentine_SkCubicType; |
| 640 | } else if (discr < -SK_ScalarNearlyZero) { |
| 641 | return kLoop_SkCubicType; |
| 642 | } else { |
| 643 | if (0.f == d[0] && 0.f == d[1]) { |
| 644 | return (0.f == d[2] ? kLine_SkCubicType : kQuadratic_SkCubicType); |
| 645 | } else { |
| 646 | return kCusp_SkCubicType; |
| 647 | } |
| 648 | } |
| 649 | } |
| 650 | |
| 651 | // Assumes the third component of points is 1. |
| 652 | // Calcs p0 . (p1 x p2) |
| 653 | static SkScalar calc_dot_cross_cubic(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2) { |
| 654 | const SkScalar xComp = p0.fX * (p1.fY - p2.fY); |
| 655 | const SkScalar yComp = p0.fY * (p2.fX - p1.fX); |
| 656 | const SkScalar wComp = p1.fX * p2.fY - p1.fY * p2.fX; |
| 657 | return (xComp + yComp + wComp); |
| 658 | } |
| 659 | |
| 660 | // Calc coefficients of I(s,t) where roots of I are inflection points of curve |
| 661 | // I(s,t) = t*(3*d0*s^2 - 3*d1*s*t + d2*t^2) |
| 662 | // d0 = a1 - 2*a2+3*a3 |
| 663 | // d1 = -a2 + 3*a3 |
| 664 | // d2 = 3*a3 |
| 665 | // a1 = p0 . (p3 x p2) |
| 666 | // a2 = p1 . (p0 x p3) |
| 667 | // a3 = p2 . (p1 x p0) |
| 668 | // Places the values of d1, d2, d3 in array d passed in |
| 669 | static void calc_cubic_inflection_func(const SkPoint p[4], SkScalar d[3]) { |
| 670 | SkScalar a1 = calc_dot_cross_cubic(p[0], p[3], p[2]); |
| 671 | SkScalar a2 = calc_dot_cross_cubic(p[1], p[0], p[3]); |
| 672 | SkScalar a3 = calc_dot_cross_cubic(p[2], p[1], p[0]); |
| 673 | |
| 674 | // need to scale a's or values in later calculations will grow to high |
| 675 | SkScalar max = SkScalarAbs(a1); |
| 676 | max = SkMaxScalar(max, SkScalarAbs(a2)); |
| 677 | max = SkMaxScalar(max, SkScalarAbs(a3)); |
| 678 | max = 1.f/max; |
| 679 | a1 = a1 * max; |
| 680 | a2 = a2 * max; |
| 681 | a3 = a3 * max; |
| 682 | |
| 683 | d[2] = 3.f * a3; |
| 684 | d[1] = d[2] - a2; |
| 685 | d[0] = d[1] - a2 + a1; |
| 686 | } |
| 687 | |
| 688 | SkCubicType SkClassifyCubic(const SkPoint src[4], SkScalar d[3]) { |
| 689 | calc_cubic_inflection_func(src, d); |
| 690 | return classify_cubic(src, d); |
| 691 | } |
| 692 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 693 | template <typename T> void bubble_sort(T array[], int count) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 694 | for (int i = count - 1; i > 0; --i) |
| 695 | for (int j = i; j > 0; --j) |
| 696 | if (array[j] < array[j-1]) |
| 697 | { |
| 698 | T tmp(array[j]); |
| 699 | array[j] = array[j-1]; |
| 700 | array[j-1] = tmp; |
| 701 | } |
| 702 | } |
| 703 | |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 704 | /** |
| 705 | * Given an array and count, remove all pair-wise duplicates from the array, |
| 706 | * keeping the existing sorting, and return the new count |
| 707 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 708 | static int collaps_duplicates(SkScalar array[], int count) { |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 709 | for (int n = count; n > 1; --n) { |
| 710 | if (array[0] == array[1]) { |
| 711 | for (int i = 1; i < n; ++i) { |
| 712 | array[i - 1] = array[i]; |
| 713 | } |
| 714 | count -= 1; |
| 715 | } else { |
| 716 | array += 1; |
| 717 | } |
| 718 | } |
| 719 | return count; |
| 720 | } |
| 721 | |
| 722 | #ifdef SK_DEBUG |
| 723 | |
| 724 | #define TEST_COLLAPS_ENTRY(array) array, SK_ARRAY_COUNT(array) |
| 725 | |
| 726 | static void test_collaps_duplicates() { |
| 727 | static bool gOnce; |
| 728 | if (gOnce) { return; } |
| 729 | gOnce = true; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 730 | const SkScalar src0[] = { 0 }; |
| 731 | const SkScalar src1[] = { 0, 0 }; |
| 732 | const SkScalar src2[] = { 0, 1 }; |
| 733 | const SkScalar src3[] = { 0, 0, 0 }; |
| 734 | const SkScalar src4[] = { 0, 0, 1 }; |
| 735 | const SkScalar src5[] = { 0, 1, 1 }; |
| 736 | const SkScalar src6[] = { 0, 1, 2 }; |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 737 | const struct { |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 738 | const SkScalar* fData; |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 739 | int fCount; |
| 740 | int fCollapsedCount; |
| 741 | } data[] = { |
| 742 | { TEST_COLLAPS_ENTRY(src0), 1 }, |
| 743 | { TEST_COLLAPS_ENTRY(src1), 1 }, |
| 744 | { TEST_COLLAPS_ENTRY(src2), 2 }, |
| 745 | { TEST_COLLAPS_ENTRY(src3), 1 }, |
| 746 | { TEST_COLLAPS_ENTRY(src4), 2 }, |
| 747 | { TEST_COLLAPS_ENTRY(src5), 2 }, |
| 748 | { TEST_COLLAPS_ENTRY(src6), 3 }, |
| 749 | }; |
| 750 | for (size_t i = 0; i < SK_ARRAY_COUNT(data); ++i) { |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 751 | SkScalar dst[3]; |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 752 | memcpy(dst, data[i].fData, data[i].fCount * sizeof(dst[0])); |
| 753 | int count = collaps_duplicates(dst, data[i].fCount); |
| 754 | SkASSERT(data[i].fCollapsedCount == count); |
| 755 | for (int j = 1; j < count; ++j) { |
| 756 | SkASSERT(dst[j-1] < dst[j]); |
| 757 | } |
| 758 | } |
| 759 | } |
| 760 | #endif |
| 761 | |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 762 | static SkScalar SkScalarCubeRoot(SkScalar x) { |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 763 | return SkScalarPow(x, 0.3333333f); |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 764 | } |
| 765 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 766 | /* Solve coeff(t) == 0, returning the number of roots that |
| 767 | lie withing 0 < t < 1. |
| 768 | coeff[0]t^3 + coeff[1]t^2 + coeff[2]t + coeff[3] |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 769 | |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 770 | Eliminates repeated roots (so that all tValues are distinct, and are always |
| 771 | in increasing order. |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 772 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 773 | static int solve_cubic_poly(const SkScalar coeff[4], SkScalar tValues[3]) { |
| 774 | if (SkScalarNearlyZero(coeff[0])) { // we're just a quadratic |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 775 | return SkFindUnitQuadRoots(coeff[1], coeff[2], coeff[3], tValues); |
| 776 | } |
| 777 | |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 778 | SkScalar a, b, c, Q, R; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 779 | |
| 780 | { |
| 781 | SkASSERT(coeff[0] != 0); |
| 782 | |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 783 | SkScalar inva = SkScalarInvert(coeff[0]); |
| 784 | a = coeff[1] * inva; |
| 785 | b = coeff[2] * inva; |
| 786 | c = coeff[3] * inva; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 787 | } |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 788 | Q = (a*a - b*3) / 9; |
| 789 | R = (2*a*a*a - 9*a*b + 27*c) / 54; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 790 | |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 791 | SkScalar Q3 = Q * Q * Q; |
| 792 | SkScalar R2MinusQ3 = R * R - Q3; |
| 793 | SkScalar adiv3 = a / 3; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 794 | |
| 795 | SkScalar* roots = tValues; |
| 796 | SkScalar r; |
| 797 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 798 | if (R2MinusQ3 < 0) { // we have 3 real roots |
| 799 | SkScalar theta = SkScalarACos(R / SkScalarSqrt(Q3)); |
| 800 | SkScalar neg2RootQ = -2 * SkScalarSqrt(Q); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 801 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 802 | r = neg2RootQ * SkScalarCos(theta/3) - adiv3; |
| 803 | if (is_unit_interval(r)) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 804 | *roots++ = r; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 805 | } |
| 806 | r = neg2RootQ * SkScalarCos((theta + 2*SK_ScalarPI)/3) - adiv3; |
| 807 | if (is_unit_interval(r)) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 808 | *roots++ = r; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 809 | } |
| 810 | r = neg2RootQ * SkScalarCos((theta - 2*SK_ScalarPI)/3) - adiv3; |
| 811 | if (is_unit_interval(r)) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 812 | *roots++ = r; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 813 | } |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 814 | SkDEBUGCODE(test_collaps_duplicates();) |
| 815 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 816 | // now sort the roots |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 817 | int count = (int)(roots - tValues); |
| 818 | SkASSERT((unsigned)count <= 3); |
| 819 | bubble_sort(tValues, count); |
| 820 | count = collaps_duplicates(tValues, count); |
| 821 | roots = tValues + count; // so we compute the proper count below |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 822 | } else { // we have 1 real root |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 823 | SkScalar A = SkScalarAbs(R) + SkScalarSqrt(R2MinusQ3); |
| 824 | A = SkScalarCubeRoot(A); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 825 | if (R > 0) { |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 826 | A = -A; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 827 | } |
| 828 | if (A != 0) { |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 829 | A += Q / A; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 830 | } |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 831 | r = A - adiv3; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 832 | if (is_unit_interval(r)) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 833 | *roots++ = r; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 834 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 835 | } |
| 836 | |
| 837 | return (int)(roots - tValues); |
| 838 | } |
| 839 | |
| 840 | /* Looking for F' dot F'' == 0 |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 841 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 842 | A = b - a |
| 843 | B = c - 2b + a |
| 844 | C = d - 3c + 3b - a |
| 845 | |
| 846 | F' = 3Ct^2 + 6Bt + 3A |
| 847 | F'' = 6Ct + 6B |
| 848 | |
| 849 | F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB |
| 850 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 851 | static void formulate_F1DotF2(const SkScalar src[], SkScalar coeff[4]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 852 | SkScalar a = src[2] - src[0]; |
| 853 | SkScalar b = src[4] - 2 * src[2] + src[0]; |
| 854 | SkScalar c = src[6] + 3 * (src[2] - src[4]) - src[0]; |
| 855 | |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 856 | coeff[0] = c * c; |
| 857 | coeff[1] = 3 * b * c; |
| 858 | coeff[2] = 2 * b * b + c * a; |
| 859 | coeff[3] = a * b; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 860 | } |
| 861 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 862 | /* Looking for F' dot F'' == 0 |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 863 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 864 | A = b - a |
| 865 | B = c - 2b + a |
| 866 | C = d - 3c + 3b - a |
| 867 | |
| 868 | F' = 3Ct^2 + 6Bt + 3A |
| 869 | F'' = 6Ct + 6B |
| 870 | |
| 871 | F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB |
| 872 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 873 | int SkFindCubicMaxCurvature(const SkPoint src[4], SkScalar tValues[3]) { |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 874 | SkScalar coeffX[4], coeffY[4]; |
| 875 | int i; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 876 | |
| 877 | formulate_F1DotF2(&src[0].fX, coeffX); |
| 878 | formulate_F1DotF2(&src[0].fY, coeffY); |
| 879 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 880 | for (i = 0; i < 4; i++) { |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 881 | coeffX[i] += coeffY[i]; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 882 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 883 | |
| 884 | SkScalar t[3]; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 885 | int count = solve_cubic_poly(coeffX, t); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 886 | int maxCount = 0; |
| 887 | |
| 888 | // now remove extrema where the curvature is zero (mins) |
| 889 | // !!!! need a test for this !!!! |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 890 | for (i = 0; i < count; i++) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 891 | // if (not_min_curvature()) |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 892 | if (t[i] > 0 && t[i] < SK_Scalar1) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 893 | tValues[maxCount++] = t[i]; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 894 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 895 | } |
| 896 | return maxCount; |
| 897 | } |
| 898 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 899 | int SkChopCubicAtMaxCurvature(const SkPoint src[4], SkPoint dst[13], |
| 900 | SkScalar tValues[3]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 901 | SkScalar t_storage[3]; |
| 902 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 903 | if (tValues == NULL) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 904 | tValues = t_storage; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 905 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 906 | |
| 907 | int count = SkFindCubicMaxCurvature(src, tValues); |
| 908 | |
egdaniel@google.com | 5383a75 | 2013-07-12 20:15:34 +0000 | [diff] [blame] | 909 | if (dst) { |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 910 | if (count == 0) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 911 | memcpy(dst, src, 4 * sizeof(SkPoint)); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 912 | } else { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 913 | SkChopCubicAt(src, dst, tValues, count); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 914 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 915 | } |
| 916 | return count + 1; |
| 917 | } |
| 918 | |
reed | dc30885 | 2015-04-30 07:47:13 -0700 | [diff] [blame] | 919 | #include "../pathops/SkPathOpsCubic.h" |
| 920 | |
| 921 | typedef int (SkDCubic::*InterceptProc)(double intercept, double roots[3]) const; |
| 922 | |
| 923 | static bool cubic_dchop_at_intercept(const SkPoint src[4], SkScalar intercept, SkPoint dst[7], |
| 924 | InterceptProc method) { |
| 925 | SkDCubic cubic; |
| 926 | double roots[3]; |
| 927 | int count = (cubic.set(src).*method)(intercept, roots); |
| 928 | if (count > 0) { |
| 929 | SkDCubicPair pair = cubic.chopAt(roots[0]); |
| 930 | for (int i = 0; i < 7; ++i) { |
| 931 | dst[i] = pair.pts[i].asSkPoint(); |
| 932 | } |
| 933 | return true; |
| 934 | } |
| 935 | return false; |
| 936 | } |
| 937 | |
| 938 | bool SkChopMonoCubicAtY(SkPoint src[4], SkScalar y, SkPoint dst[7]) { |
| 939 | return cubic_dchop_at_intercept(src, y, dst, &SkDCubic::horizontalIntersect); |
| 940 | } |
| 941 | |
| 942 | bool SkChopMonoCubicAtX(SkPoint src[4], SkScalar x, SkPoint dst[7]) { |
| 943 | return cubic_dchop_at_intercept(src, x, dst, &SkDCubic::verticalIntersect); |
| 944 | } |
| 945 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 946 | /////////////////////////////////////////////////////////////////////////////// |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 947 | |
| 948 | /* Find t value for quadratic [a, b, c] = d. |
| 949 | Return 0 if there is no solution within [0, 1) |
| 950 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 951 | static SkScalar quad_solve(SkScalar a, SkScalar b, SkScalar c, SkScalar d) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 952 | // At^2 + Bt + C = d |
| 953 | SkScalar A = a - 2 * b + c; |
| 954 | SkScalar B = 2 * (b - a); |
| 955 | SkScalar C = a - d; |
| 956 | |
| 957 | SkScalar roots[2]; |
| 958 | int count = SkFindUnitQuadRoots(A, B, C, roots); |
| 959 | |
| 960 | SkASSERT(count <= 1); |
| 961 | return count == 1 ? roots[0] : 0; |
| 962 | } |
| 963 | |
robertphillips@google.com | e1b75b4 | 2013-07-09 15:03:59 +0000 | [diff] [blame] | 964 | /* given a quad-curve and a point (x,y), chop the quad at that point and place |
skia.committer@gmail.com | 50df4d0 | 2013-09-28 07:01:33 +0000 | [diff] [blame] | 965 | the new off-curve point and endpoint into 'dest'. |
skia.committer@gmail.com | 9e1ec1a | 2013-07-10 07:00:58 +0000 | [diff] [blame] | 966 | Should only return false if the computed pos is the start of the curve |
robertphillips@google.com | e1b75b4 | 2013-07-09 15:03:59 +0000 | [diff] [blame] | 967 | (i.e. root == 0) |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 968 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 969 | static bool truncate_last_curve(const SkPoint quad[3], SkScalar x, SkScalar y, |
| 970 | SkPoint* dest) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 971 | const SkScalar* base; |
| 972 | SkScalar value; |
| 973 | |
| 974 | if (SkScalarAbs(x) < SkScalarAbs(y)) { |
| 975 | base = &quad[0].fX; |
| 976 | value = x; |
| 977 | } else { |
| 978 | base = &quad[0].fY; |
| 979 | value = y; |
| 980 | } |
| 981 | |
| 982 | // note: this returns 0 if it thinks value is out of range, meaning the |
| 983 | // root might return something outside of [0, 1) |
| 984 | SkScalar t = quad_solve(base[0], base[2], base[4], value); |
| 985 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 986 | if (t > 0) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 987 | SkPoint tmp[5]; |
| 988 | SkChopQuadAt(quad, tmp, t); |
robertphillips@google.com | e1b75b4 | 2013-07-09 15:03:59 +0000 | [diff] [blame] | 989 | dest[0] = tmp[1]; |
robertphillips@google.com | b0889a5 | 2013-09-27 17:05:59 +0000 | [diff] [blame] | 990 | dest[1].set(x, y); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 991 | return true; |
| 992 | } else { |
| 993 | /* t == 0 means either the value triggered a root outside of [0, 1) |
| 994 | For our purposes, we can ignore the <= 0 roots, but we want to |
| 995 | catch the >= 1 roots (which given our caller, will basically mean |
| 996 | a root of 1, give-or-take numerical instability). If we are in the |
| 997 | >= 1 case, return the existing offCurve point. |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 998 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 999 | The test below checks to see if we are close to the "end" of the |
| 1000 | curve (near base[4]). Rather than specifying a tolerance, I just |
| 1001 | check to see if value is on to the right/left of the middle point |
| 1002 | (depending on the direction/sign of the end points). |
| 1003 | */ |
| 1004 | if ((base[0] < base[4] && value > base[2]) || |
| 1005 | (base[0] > base[4] && value < base[2])) // should root have been 1 |
| 1006 | { |
robertphillips@google.com | e1b75b4 | 2013-07-09 15:03:59 +0000 | [diff] [blame] | 1007 | dest[0] = quad[1]; |
| 1008 | dest[1].set(x, y); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1009 | return true; |
| 1010 | } |
| 1011 | } |
| 1012 | return false; |
| 1013 | } |
| 1014 | |
| 1015 | static const SkPoint gQuadCirclePts[kSkBuildQuadArcStorage] = { |
commit-bot@chromium.org | f91aaec | 2013-11-01 15:24:55 +0000 | [diff] [blame] | 1016 | // The mid point of the quadratic arc approximation is half way between the two |
| 1017 | // control points. The float epsilon adjustment moves the on curve point out by |
commit-bot@chromium.org | def6468 | 2014-02-21 19:49:10 +0000 | [diff] [blame] | 1018 | // two bits, distributing the convex test error between the round rect |
| 1019 | // approximation and the convex cross product sign equality test. |
| 1020 | #define SK_MID_RRECT_OFFSET \ |
| 1021 | (SK_Scalar1 + SK_ScalarTanPIOver8 + FLT_EPSILON * 4) / 2 |
commit-bot@chromium.org | f91aaec | 2013-11-01 15:24:55 +0000 | [diff] [blame] | 1022 | { SK_Scalar1, 0 }, |
| 1023 | { SK_Scalar1, SK_ScalarTanPIOver8 }, |
| 1024 | { SK_MID_RRECT_OFFSET, SK_MID_RRECT_OFFSET }, |
| 1025 | { SK_ScalarTanPIOver8, SK_Scalar1 }, |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1026 | |
commit-bot@chromium.org | f91aaec | 2013-11-01 15:24:55 +0000 | [diff] [blame] | 1027 | { 0, SK_Scalar1 }, |
| 1028 | { -SK_ScalarTanPIOver8, SK_Scalar1 }, |
| 1029 | { -SK_MID_RRECT_OFFSET, SK_MID_RRECT_OFFSET }, |
| 1030 | { -SK_Scalar1, SK_ScalarTanPIOver8 }, |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1031 | |
commit-bot@chromium.org | f91aaec | 2013-11-01 15:24:55 +0000 | [diff] [blame] | 1032 | { -SK_Scalar1, 0 }, |
| 1033 | { -SK_Scalar1, -SK_ScalarTanPIOver8 }, |
| 1034 | { -SK_MID_RRECT_OFFSET, -SK_MID_RRECT_OFFSET }, |
| 1035 | { -SK_ScalarTanPIOver8, -SK_Scalar1 }, |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1036 | |
commit-bot@chromium.org | f91aaec | 2013-11-01 15:24:55 +0000 | [diff] [blame] | 1037 | { 0, -SK_Scalar1 }, |
| 1038 | { SK_ScalarTanPIOver8, -SK_Scalar1 }, |
| 1039 | { SK_MID_RRECT_OFFSET, -SK_MID_RRECT_OFFSET }, |
| 1040 | { SK_Scalar1, -SK_ScalarTanPIOver8 }, |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1041 | |
commit-bot@chromium.org | f91aaec | 2013-11-01 15:24:55 +0000 | [diff] [blame] | 1042 | { SK_Scalar1, 0 } |
| 1043 | #undef SK_MID_RRECT_OFFSET |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1044 | }; |
| 1045 | |
| 1046 | int SkBuildQuadArc(const SkVector& uStart, const SkVector& uStop, |
| 1047 | SkRotationDirection dir, const SkMatrix* userMatrix, |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 1048 | SkPoint quadPoints[]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1049 | // rotate by x,y so that uStart is (1.0) |
| 1050 | SkScalar x = SkPoint::DotProduct(uStart, uStop); |
| 1051 | SkScalar y = SkPoint::CrossProduct(uStart, uStop); |
| 1052 | |
| 1053 | SkScalar absX = SkScalarAbs(x); |
| 1054 | SkScalar absY = SkScalarAbs(y); |
| 1055 | |
| 1056 | int pointCount; |
| 1057 | |
| 1058 | // check for (effectively) coincident vectors |
| 1059 | // this can happen if our angle is nearly 0 or nearly 180 (y == 0) |
| 1060 | // ... we use the dot-prod to distinguish between 0 and 180 (x > 0) |
| 1061 | if (absY <= SK_ScalarNearlyZero && x > 0 && |
| 1062 | ((y >= 0 && kCW_SkRotationDirection == dir) || |
| 1063 | (y <= 0 && kCCW_SkRotationDirection == dir))) { |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 1064 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1065 | // just return the start-point |
| 1066 | quadPoints[0].set(SK_Scalar1, 0); |
| 1067 | pointCount = 1; |
| 1068 | } else { |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 1069 | if (dir == kCCW_SkRotationDirection) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1070 | y = -y; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 1071 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1072 | // what octant (quadratic curve) is [xy] in? |
| 1073 | int oct = 0; |
| 1074 | bool sameSign = true; |
| 1075 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 1076 | if (0 == y) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1077 | oct = 4; // 180 |
| 1078 | SkASSERT(SkScalarAbs(x + SK_Scalar1) <= SK_ScalarNearlyZero); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 1079 | } else if (0 == x) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1080 | SkASSERT(absY - SK_Scalar1 <= SK_ScalarNearlyZero); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 1081 | oct = y > 0 ? 2 : 6; // 90 : 270 |
| 1082 | } else { |
| 1083 | if (y < 0) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1084 | oct += 4; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 1085 | } |
| 1086 | if ((x < 0) != (y < 0)) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1087 | oct += 2; |
| 1088 | sameSign = false; |
| 1089 | } |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 1090 | if ((absX < absY) == sameSign) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1091 | oct += 1; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 1092 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1093 | } |
| 1094 | |
| 1095 | int wholeCount = oct << 1; |
| 1096 | memcpy(quadPoints, gQuadCirclePts, (wholeCount + 1) * sizeof(SkPoint)); |
| 1097 | |
| 1098 | const SkPoint* arc = &gQuadCirclePts[wholeCount]; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 1099 | if (truncate_last_curve(arc, x, y, &quadPoints[wholeCount + 1])) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1100 | wholeCount += 2; |
| 1101 | } |
| 1102 | pointCount = wholeCount + 1; |
| 1103 | } |
| 1104 | |
| 1105 | // now handle counter-clockwise and the initial unitStart rotation |
| 1106 | SkMatrix matrix; |
| 1107 | matrix.setSinCos(uStart.fY, uStart.fX); |
| 1108 | if (dir == kCCW_SkRotationDirection) { |
| 1109 | matrix.preScale(SK_Scalar1, -SK_Scalar1); |
| 1110 | } |
| 1111 | if (userMatrix) { |
| 1112 | matrix.postConcat(*userMatrix); |
| 1113 | } |
| 1114 | matrix.mapPoints(quadPoints, pointCount); |
| 1115 | return pointCount; |
| 1116 | } |
reed@google.com | c518710 | 2013-04-12 19:11:10 +0000 | [diff] [blame] | 1117 | |
reed@google.com | c518710 | 2013-04-12 19:11:10 +0000 | [diff] [blame] | 1118 | |
commit-bot@chromium.org | def6468 | 2014-02-21 19:49:10 +0000 | [diff] [blame] | 1119 | /////////////////////////////////////////////////////////////////////////////// |
| 1120 | // |
| 1121 | // NURB representation for conics. Helpful explanations at: |
| 1122 | // |
| 1123 | // http://citeseerx.ist.psu.edu/viewdoc/ |
| 1124 | // download?doi=10.1.1.44.5740&rep=rep1&type=ps |
| 1125 | // and |
| 1126 | // http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/NURBS/RB-conics.html |
| 1127 | // |
reed@google.com | 17a2c91 | 2013-04-16 21:07:27 +0000 | [diff] [blame] | 1128 | // F = (A (1 - t)^2 + C t^2 + 2 B (1 - t) t w) |
| 1129 | // ------------------------------------------ |
| 1130 | // ((1 - t)^2 + t^2 + 2 (1 - t) t w) |
| 1131 | // |
| 1132 | // = {t^2 (P0 + P2 - 2 P1 w), t (-2 P0 + 2 P1 w), P0} |
| 1133 | // ------------------------------------------------ |
| 1134 | // {t^2 (2 - 2 w), t (-2 + 2 w), 1} |
| 1135 | // |
reed@google.com | 17a2c91 | 2013-04-16 21:07:27 +0000 | [diff] [blame] | 1136 | |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1137 | static SkScalar conic_eval_pos(const SkScalar src[], SkScalar w, SkScalar t) { |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1138 | SkASSERT(src); |
| 1139 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
skia.committer@gmail.com | 45fb8b6 | 2013-04-17 07:00:56 +0000 | [diff] [blame] | 1140 | |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1141 | SkScalar src2w = SkScalarMul(src[2], w); |
| 1142 | SkScalar C = src[0]; |
| 1143 | SkScalar A = src[4] - 2 * src2w + C; |
| 1144 | SkScalar B = 2 * (src2w - C); |
| 1145 | SkScalar numer = SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C); |
skia.committer@gmail.com | 45fb8b6 | 2013-04-17 07:00:56 +0000 | [diff] [blame] | 1146 | |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1147 | B = 2 * (w - SK_Scalar1); |
| 1148 | C = SK_Scalar1; |
| 1149 | A = -B; |
| 1150 | SkScalar denom = SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C); |
skia.committer@gmail.com | 45fb8b6 | 2013-04-17 07:00:56 +0000 | [diff] [blame] | 1151 | |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1152 | return SkScalarDiv(numer, denom); |
| 1153 | } |
| 1154 | |
| 1155 | // F' = 2 (C t (1 + t (-1 + w)) - A (-1 + t) (t (-1 + w) - w) + B (1 - 2 t) w) |
| 1156 | // |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1157 | // t^2 : (2 P0 - 2 P2 - 2 P0 w + 2 P2 w) |
| 1158 | // t^1 : (-2 P0 + 2 P2 + 4 P0 w - 4 P1 w) |
| 1159 | // t^0 : -2 P0 w + 2 P1 w |
| 1160 | // |
| 1161 | // We disregard magnitude, so we can freely ignore the denominator of F', and |
| 1162 | // divide the numerator by 2 |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1163 | // |
reed@google.com | 17a2c91 | 2013-04-16 21:07:27 +0000 | [diff] [blame] | 1164 | // coeff[0] for t^2 |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1165 | // coeff[1] for t^1 |
| 1166 | // coeff[2] for t^0 |
reed@google.com | 17a2c91 | 2013-04-16 21:07:27 +0000 | [diff] [blame] | 1167 | // |
commit-bot@chromium.org | def6468 | 2014-02-21 19:49:10 +0000 | [diff] [blame] | 1168 | static void conic_deriv_coeff(const SkScalar src[], |
| 1169 | SkScalar w, |
| 1170 | SkScalar coeff[3]) { |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1171 | const SkScalar P20 = src[4] - src[0]; |
| 1172 | const SkScalar P10 = src[2] - src[0]; |
| 1173 | const SkScalar wP10 = w * P10; |
| 1174 | coeff[0] = w * P20 - P20; |
| 1175 | coeff[1] = P20 - 2 * wP10; |
| 1176 | coeff[2] = wP10; |
reed@google.com | 17a2c91 | 2013-04-16 21:07:27 +0000 | [diff] [blame] | 1177 | } |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1178 | |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1179 | static SkScalar conic_eval_tan(const SkScalar coord[], SkScalar w, SkScalar t) { |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1180 | SkScalar coeff[3]; |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1181 | conic_deriv_coeff(coord, w, coeff); |
| 1182 | return t * (t * coeff[0] + coeff[1]) + coeff[2]; |
| 1183 | } |
| 1184 | |
| 1185 | static bool conic_find_extrema(const SkScalar src[], SkScalar w, SkScalar* t) { |
| 1186 | SkScalar coeff[3]; |
| 1187 | conic_deriv_coeff(src, w, coeff); |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1188 | |
| 1189 | SkScalar tValues[2]; |
| 1190 | int roots = SkFindUnitQuadRoots(coeff[0], coeff[1], coeff[2], tValues); |
| 1191 | SkASSERT(0 == roots || 1 == roots); |
skia.committer@gmail.com | 45fb8b6 | 2013-04-17 07:00:56 +0000 | [diff] [blame] | 1192 | |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1193 | if (1 == roots) { |
| 1194 | *t = tValues[0]; |
| 1195 | return true; |
| 1196 | } |
| 1197 | return false; |
| 1198 | } |
reed@google.com | 17a2c91 | 2013-04-16 21:07:27 +0000 | [diff] [blame] | 1199 | |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 1200 | struct SkP3D { |
| 1201 | SkScalar fX, fY, fZ; |
skia.committer@gmail.com | 4bb50b2 | 2013-04-13 07:01:15 +0000 | [diff] [blame] | 1202 | |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 1203 | void set(SkScalar x, SkScalar y, SkScalar z) { |
| 1204 | fX = x; fY = y; fZ = z; |
| 1205 | } |
skia.committer@gmail.com | 4bb50b2 | 2013-04-13 07:01:15 +0000 | [diff] [blame] | 1206 | |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 1207 | void projectDown(SkPoint* dst) const { |
| 1208 | dst->set(fX / fZ, fY / fZ); |
| 1209 | } |
| 1210 | }; |
| 1211 | |
commit-bot@chromium.org | d50d87a | 2014-01-28 14:36:52 +0000 | [diff] [blame] | 1212 | // We only interpolate one dimension at a time (the first, at +0, +3, +6). |
| 1213 | static void p3d_interp(const SkScalar src[7], SkScalar dst[7], SkScalar t) { |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 1214 | SkScalar ab = SkScalarInterp(src[0], src[3], t); |
| 1215 | SkScalar bc = SkScalarInterp(src[3], src[6], t); |
| 1216 | dst[0] = ab; |
| 1217 | dst[3] = SkScalarInterp(ab, bc, t); |
| 1218 | dst[6] = bc; |
| 1219 | } |
| 1220 | |
| 1221 | static void ratquad_mapTo3D(const SkPoint src[3], SkScalar w, SkP3D dst[]) { |
| 1222 | dst[0].set(src[0].fX * 1, src[0].fY * 1, 1); |
| 1223 | dst[1].set(src[1].fX * w, src[1].fY * w, w); |
| 1224 | dst[2].set(src[2].fX * 1, src[2].fY * 1, 1); |
| 1225 | } |
| 1226 | |
reed@google.com | 24bd210 | 2013-05-07 20:42:35 +0000 | [diff] [blame] | 1227 | void SkConic::evalAt(SkScalar t, SkPoint* pt, SkVector* tangent) const { |
reed@google.com | c518710 | 2013-04-12 19:11:10 +0000 | [diff] [blame] | 1228 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
skia.committer@gmail.com | 4bb50b2 | 2013-04-13 07:01:15 +0000 | [diff] [blame] | 1229 | |
reed@google.com | c518710 | 2013-04-12 19:11:10 +0000 | [diff] [blame] | 1230 | if (pt) { |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1231 | pt->set(conic_eval_pos(&fPts[0].fX, fW, t), |
| 1232 | conic_eval_pos(&fPts[0].fY, fW, t)); |
reed@google.com | c518710 | 2013-04-12 19:11:10 +0000 | [diff] [blame] | 1233 | } |
reed@google.com | 24bd210 | 2013-05-07 20:42:35 +0000 | [diff] [blame] | 1234 | if (tangent) { |
| 1235 | tangent->set(conic_eval_tan(&fPts[0].fX, fW, t), |
| 1236 | conic_eval_tan(&fPts[0].fY, fW, t)); |
| 1237 | } |
reed@google.com | c518710 | 2013-04-12 19:11:10 +0000 | [diff] [blame] | 1238 | } |
| 1239 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1240 | void SkConic::chopAt(SkScalar t, SkConic dst[2]) const { |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 1241 | SkP3D tmp[3], tmp2[3]; |
| 1242 | |
| 1243 | ratquad_mapTo3D(fPts, fW, tmp); |
skia.committer@gmail.com | 4bb50b2 | 2013-04-13 07:01:15 +0000 | [diff] [blame] | 1244 | |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 1245 | p3d_interp(&tmp[0].fX, &tmp2[0].fX, t); |
| 1246 | p3d_interp(&tmp[0].fY, &tmp2[0].fY, t); |
| 1247 | p3d_interp(&tmp[0].fZ, &tmp2[0].fZ, t); |
skia.committer@gmail.com | 4bb50b2 | 2013-04-13 07:01:15 +0000 | [diff] [blame] | 1248 | |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 1249 | dst[0].fPts[0] = fPts[0]; |
| 1250 | tmp2[0].projectDown(&dst[0].fPts[1]); |
| 1251 | tmp2[1].projectDown(&dst[0].fPts[2]); dst[1].fPts[0] = dst[0].fPts[2]; |
| 1252 | tmp2[2].projectDown(&dst[1].fPts[1]); |
| 1253 | dst[1].fPts[2] = fPts[2]; |
| 1254 | |
mike@reedtribe.org | 4af6280 | 2013-04-13 10:51:51 +0000 | [diff] [blame] | 1255 | // to put in "standard form", where w0 and w2 are both 1, we compute the |
| 1256 | // new w1 as sqrt(w1*w1/w0*w2) |
| 1257 | // or |
| 1258 | // w1 /= sqrt(w0*w2) |
| 1259 | // |
commit-bot@chromium.org | def6468 | 2014-02-21 19:49:10 +0000 | [diff] [blame] | 1260 | // However, in our case, we know that for dst[0]: |
| 1261 | // w0 == 1, and for dst[1], w2 == 1 |
mike@reedtribe.org | 4af6280 | 2013-04-13 10:51:51 +0000 | [diff] [blame] | 1262 | // |
| 1263 | SkScalar root = SkScalarSqrt(tmp2[1].fZ); |
| 1264 | dst[0].fW = tmp2[0].fZ / root; |
| 1265 | dst[1].fW = tmp2[2].fZ / root; |
reed@google.com | c518710 | 2013-04-12 19:11:10 +0000 | [diff] [blame] | 1266 | } |
mike@reedtribe.org | 8d55101 | 2013-04-14 02:40:50 +0000 | [diff] [blame] | 1267 | |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 1268 | static Sk2s times_2(const Sk2s& value) { |
| 1269 | return value + value; |
| 1270 | } |
| 1271 | |
| 1272 | SkPoint SkConic::evalAt(SkScalar t) const { |
| 1273 | Sk2s p0 = from_point(fPts[0]); |
| 1274 | Sk2s p1 = from_point(fPts[1]); |
| 1275 | Sk2s p2 = from_point(fPts[2]); |
reed | ce6acc9 | 2015-03-20 13:46:08 -0700 | [diff] [blame] | 1276 | Sk2s tt(t); |
| 1277 | Sk2s ww(fW); |
| 1278 | Sk2s one(1); |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 1279 | |
| 1280 | Sk2s p1w = p1 * ww; |
| 1281 | Sk2s C = p0; |
| 1282 | Sk2s A = p2 - times_2(p1w) + p0; |
| 1283 | Sk2s B = times_2(p1w - C); |
| 1284 | Sk2s numer = quad_poly_eval(A, B, C, tt); |
| 1285 | |
| 1286 | B = times_2(ww - one); |
| 1287 | A = -B; |
| 1288 | Sk2s denom = quad_poly_eval(A, B, one, tt); |
| 1289 | |
| 1290 | return to_point(numer / denom); |
| 1291 | } |
| 1292 | |
| 1293 | SkVector SkConic::evalTangentAt(SkScalar t) const { |
| 1294 | Sk2s p0 = from_point(fPts[0]); |
| 1295 | Sk2s p1 = from_point(fPts[1]); |
| 1296 | Sk2s p2 = from_point(fPts[2]); |
reed | ce6acc9 | 2015-03-20 13:46:08 -0700 | [diff] [blame] | 1297 | Sk2s ww(fW); |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 1298 | |
| 1299 | Sk2s p20 = p2 - p0; |
| 1300 | Sk2s p10 = p1 - p0; |
| 1301 | |
| 1302 | Sk2s C = ww * p10; |
| 1303 | Sk2s A = ww * p20 - p20; |
| 1304 | Sk2s B = p20 - C - C; |
| 1305 | |
| 1306 | return to_vector(quad_poly_eval(A, B, C, Sk2s(t))); |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 1307 | } |
| 1308 | |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1309 | static SkScalar subdivide_w_value(SkScalar w) { |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1310 | return SkScalarSqrt(SK_ScalarHalf + w * SK_ScalarHalf); |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1311 | } |
| 1312 | |
reed | 5501103 | 2015-03-26 09:10:22 -0700 | [diff] [blame] | 1313 | static Sk2s twice(const Sk2s& value) { |
| 1314 | return value + value; |
mike@reedtribe.org | 8d55101 | 2013-04-14 02:40:50 +0000 | [diff] [blame] | 1315 | } |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1316 | |
reed | 5501103 | 2015-03-26 09:10:22 -0700 | [diff] [blame] | 1317 | void SkConic::chop(SkConic * SK_RESTRICT dst) const { |
| 1318 | Sk2s scale = Sk2s(SkScalarInvert(SK_Scalar1 + fW)); |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 1319 | SkScalar newW = subdivide_w_value(fW); |
| 1320 | |
| 1321 | Sk2s p0 = from_point(fPts[0]); |
| 1322 | Sk2s p1 = from_point(fPts[1]); |
| 1323 | Sk2s p2 = from_point(fPts[2]); |
reed | ce6acc9 | 2015-03-20 13:46:08 -0700 | [diff] [blame] | 1324 | Sk2s ww(fW); |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 1325 | |
| 1326 | Sk2s wp1 = ww * p1; |
reed | 5501103 | 2015-03-26 09:10:22 -0700 | [diff] [blame] | 1327 | Sk2s m = (p0 + twice(wp1) + p2) * scale * Sk2s(0.5f); |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 1328 | |
| 1329 | dst[0].fPts[0] = fPts[0]; |
| 1330 | dst[0].fPts[1] = to_point((p0 + wp1) * scale); |
| 1331 | dst[0].fPts[2] = dst[1].fPts[0] = to_point(m); |
| 1332 | dst[1].fPts[1] = to_point((wp1 + p2) * scale); |
| 1333 | dst[1].fPts[2] = fPts[2]; |
| 1334 | |
| 1335 | dst[0].fW = dst[1].fW = newW; |
| 1336 | } |
| 1337 | |
mike@reedtribe.org | 97514f2 | 2013-04-27 18:23:16 +0000 | [diff] [blame] | 1338 | /* |
| 1339 | * "High order approximation of conic sections by quadratic splines" |
| 1340 | * by Michael Floater, 1993 |
| 1341 | */ |
mike@reedtribe.org | af5c506 | 2013-04-30 02:14:58 +0000 | [diff] [blame] | 1342 | #define AS_QUAD_ERROR_SETUP \ |
| 1343 | SkScalar a = fW - 1; \ |
| 1344 | SkScalar k = a / (4 * (2 + a)); \ |
| 1345 | SkScalar x = k * (fPts[0].fX - 2 * fPts[1].fX + fPts[2].fX); \ |
| 1346 | SkScalar y = k * (fPts[0].fY - 2 * fPts[1].fY + fPts[2].fY); |
| 1347 | |
| 1348 | void SkConic::computeAsQuadError(SkVector* err) const { |
| 1349 | AS_QUAD_ERROR_SETUP |
| 1350 | err->set(x, y); |
| 1351 | } |
| 1352 | |
| 1353 | bool SkConic::asQuadTol(SkScalar tol) const { |
| 1354 | AS_QUAD_ERROR_SETUP |
| 1355 | return (x * x + y * y) <= tol * tol; |
mike@reedtribe.org | 97514f2 | 2013-04-27 18:23:16 +0000 | [diff] [blame] | 1356 | } |
| 1357 | |
reed | f16c00e | 2015-02-12 17:56:21 -0800 | [diff] [blame] | 1358 | // Limit the number of suggested quads to approximate a conic |
| 1359 | #define kMaxConicToQuadPOW2 5 |
| 1360 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1361 | int SkConic::computeQuadPOW2(SkScalar tol) const { |
reed | f16c00e | 2015-02-12 17:56:21 -0800 | [diff] [blame] | 1362 | if (tol < 0 || !SkScalarIsFinite(tol)) { |
| 1363 | return 0; |
| 1364 | } |
| 1365 | |
mike@reedtribe.org | af5c506 | 2013-04-30 02:14:58 +0000 | [diff] [blame] | 1366 | AS_QUAD_ERROR_SETUP |
reed | f16c00e | 2015-02-12 17:56:21 -0800 | [diff] [blame] | 1367 | |
reed | f16c00e | 2015-02-12 17:56:21 -0800 | [diff] [blame] | 1368 | SkScalar error = SkScalarSqrt(x * x + y * y); |
| 1369 | int pow2; |
| 1370 | for (pow2 = 0; pow2 < kMaxConicToQuadPOW2; ++pow2) { |
| 1371 | if (error <= tol) { |
| 1372 | break; |
| 1373 | } |
| 1374 | error *= 0.25f; |
| 1375 | } |
| 1376 | // float version -- using ceil gives the same results as the above. |
| 1377 | if (false) { |
| 1378 | SkScalar err = SkScalarSqrt(x * x + y * y); |
| 1379 | if (err <= tol) { |
| 1380 | return 0; |
| 1381 | } |
| 1382 | SkScalar tol2 = tol * tol; |
| 1383 | if (tol2 == 0) { |
| 1384 | return kMaxConicToQuadPOW2; |
| 1385 | } |
| 1386 | SkScalar fpow2 = SkScalarLog2((x * x + y * y) / tol2) * 0.25f; |
| 1387 | int altPow2 = SkScalarCeilToInt(fpow2); |
| 1388 | if (altPow2 != pow2) { |
| 1389 | SkDebugf("pow2 %d altPow2 %d fbits %g err %g tol %g\n", pow2, altPow2, fpow2, err, tol); |
| 1390 | } |
| 1391 | pow2 = altPow2; |
| 1392 | } |
| 1393 | return pow2; |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1394 | } |
| 1395 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1396 | static SkPoint* subdivide(const SkConic& src, SkPoint pts[], int level) { |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1397 | SkASSERT(level >= 0); |
mike@reedtribe.org | af5c506 | 2013-04-30 02:14:58 +0000 | [diff] [blame] | 1398 | |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1399 | if (0 == level) { |
| 1400 | memcpy(pts, &src.fPts[1], 2 * sizeof(SkPoint)); |
| 1401 | return pts + 2; |
| 1402 | } else { |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1403 | SkConic dst[2]; |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1404 | src.chop(dst); |
| 1405 | --level; |
| 1406 | pts = subdivide(dst[0], pts, level); |
| 1407 | return subdivide(dst[1], pts, level); |
| 1408 | } |
| 1409 | } |
| 1410 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1411 | int SkConic::chopIntoQuadsPOW2(SkPoint pts[], int pow2) const { |
mike@reedtribe.org | af5c506 | 2013-04-30 02:14:58 +0000 | [diff] [blame] | 1412 | SkASSERT(pow2 >= 0); |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1413 | *pts = fPts[0]; |
reed@google.com | aebfa7e | 2013-04-15 15:23:38 +0000 | [diff] [blame] | 1414 | SkDEBUGCODE(SkPoint* endPts =) subdivide(*this, pts + 1, pow2); |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1415 | SkASSERT(endPts - pts == (2 * (1 << pow2) + 1)); |
| 1416 | return 1 << pow2; |
| 1417 | } |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1418 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1419 | bool SkConic::findXExtrema(SkScalar* t) const { |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1420 | return conic_find_extrema(&fPts[0].fX, fW, t); |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1421 | } |
| 1422 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1423 | bool SkConic::findYExtrema(SkScalar* t) const { |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1424 | return conic_find_extrema(&fPts[0].fY, fW, t); |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1425 | } |
| 1426 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1427 | bool SkConic::chopAtXExtrema(SkConic dst[2]) const { |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1428 | SkScalar t; |
| 1429 | if (this->findXExtrema(&t)) { |
| 1430 | this->chopAt(t, dst); |
| 1431 | // now clean-up the middle, since we know t was meant to be at |
| 1432 | // an X-extrema |
| 1433 | SkScalar value = dst[0].fPts[2].fX; |
| 1434 | dst[0].fPts[1].fX = value; |
| 1435 | dst[1].fPts[0].fX = value; |
| 1436 | dst[1].fPts[1].fX = value; |
| 1437 | return true; |
| 1438 | } |
| 1439 | return false; |
| 1440 | } |
| 1441 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1442 | bool SkConic::chopAtYExtrema(SkConic dst[2]) const { |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1443 | SkScalar t; |
| 1444 | if (this->findYExtrema(&t)) { |
| 1445 | this->chopAt(t, dst); |
| 1446 | // now clean-up the middle, since we know t was meant to be at |
| 1447 | // an Y-extrema |
| 1448 | SkScalar value = dst[0].fPts[2].fY; |
| 1449 | dst[0].fPts[1].fY = value; |
| 1450 | dst[1].fPts[0].fY = value; |
| 1451 | dst[1].fPts[1].fY = value; |
| 1452 | return true; |
| 1453 | } |
| 1454 | return false; |
| 1455 | } |
| 1456 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1457 | void SkConic::computeTightBounds(SkRect* bounds) const { |
mike@reedtribe.org | 5c082a1 | 2013-04-17 02:25:33 +0000 | [diff] [blame] | 1458 | SkPoint pts[4]; |
| 1459 | pts[0] = fPts[0]; |
| 1460 | pts[1] = fPts[2]; |
| 1461 | int count = 2; |
| 1462 | |
| 1463 | SkScalar t; |
| 1464 | if (this->findXExtrema(&t)) { |
| 1465 | this->evalAt(t, &pts[count++]); |
| 1466 | } |
| 1467 | if (this->findYExtrema(&t)) { |
| 1468 | this->evalAt(t, &pts[count++]); |
| 1469 | } |
| 1470 | bounds->set(pts, count); |
| 1471 | } |
| 1472 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1473 | void SkConic::computeFastBounds(SkRect* bounds) const { |
mike@reedtribe.org | 5c082a1 | 2013-04-17 02:25:33 +0000 | [diff] [blame] | 1474 | bounds->set(fPts, 3); |
| 1475 | } |
commit-bot@chromium.org | def6468 | 2014-02-21 19:49:10 +0000 | [diff] [blame] | 1476 | |
| 1477 | bool SkConic::findMaxCurvature(SkScalar* t) const { |
| 1478 | // TODO: Implement me |
| 1479 | return false; |
| 1480 | } |
reed | 220f926 | 2014-12-17 08:21:04 -0800 | [diff] [blame] | 1481 | |
| 1482 | SkScalar SkConic::TransformW(const SkPoint pts[], SkScalar w, |
| 1483 | const SkMatrix& matrix) { |
| 1484 | if (!matrix.hasPerspective()) { |
| 1485 | return w; |
| 1486 | } |
| 1487 | |
| 1488 | SkP3D src[3], dst[3]; |
mtklein | 950e986 | 2015-03-19 12:03:29 -0700 | [diff] [blame] | 1489 | |
reed | 220f926 | 2014-12-17 08:21:04 -0800 | [diff] [blame] | 1490 | ratquad_mapTo3D(pts, w, src); |
| 1491 | |
| 1492 | matrix.mapHomogeneousPoints(&dst[0].fX, &src[0].fX, 3); |
| 1493 | |
| 1494 | // w' = sqrt(w1*w1/w0*w2) |
| 1495 | SkScalar w0 = dst[0].fZ; |
| 1496 | SkScalar w1 = dst[1].fZ; |
| 1497 | SkScalar w2 = dst[2].fZ; |
| 1498 | w = SkScalarSqrt((w1 * w1) / (w0 * w2)); |
| 1499 | return w; |
| 1500 | } |
reed | d5d27d9 | 2015-02-09 13:54:43 -0800 | [diff] [blame] | 1501 | |
| 1502 | int SkConic::BuildUnitArc(const SkVector& uStart, const SkVector& uStop, SkRotationDirection dir, |
| 1503 | const SkMatrix* userMatrix, SkConic dst[kMaxConicsForArc]) { |
| 1504 | // rotate by x,y so that uStart is (1.0) |
| 1505 | SkScalar x = SkPoint::DotProduct(uStart, uStop); |
| 1506 | SkScalar y = SkPoint::CrossProduct(uStart, uStop); |
| 1507 | |
| 1508 | SkScalar absY = SkScalarAbs(y); |
| 1509 | |
| 1510 | // check for (effectively) coincident vectors |
| 1511 | // this can happen if our angle is nearly 0 or nearly 180 (y == 0) |
| 1512 | // ... we use the dot-prod to distinguish between 0 and 180 (x > 0) |
| 1513 | if (absY <= SK_ScalarNearlyZero && x > 0 && ((y >= 0 && kCW_SkRotationDirection == dir) || |
| 1514 | (y <= 0 && kCCW_SkRotationDirection == dir))) { |
| 1515 | return 0; |
| 1516 | } |
| 1517 | |
| 1518 | if (dir == kCCW_SkRotationDirection) { |
| 1519 | y = -y; |
| 1520 | } |
| 1521 | |
| 1522 | // We decide to use 1-conic per quadrant of a circle. What quadrant does [xy] lie in? |
| 1523 | // 0 == [0 .. 90) |
| 1524 | // 1 == [90 ..180) |
| 1525 | // 2 == [180..270) |
| 1526 | // 3 == [270..360) |
| 1527 | // |
| 1528 | int quadrant = 0; |
| 1529 | if (0 == y) { |
| 1530 | quadrant = 2; // 180 |
| 1531 | SkASSERT(SkScalarAbs(x + SK_Scalar1) <= SK_ScalarNearlyZero); |
| 1532 | } else if (0 == x) { |
| 1533 | SkASSERT(absY - SK_Scalar1 <= SK_ScalarNearlyZero); |
| 1534 | quadrant = y > 0 ? 1 : 3; // 90 : 270 |
| 1535 | } else { |
| 1536 | if (y < 0) { |
| 1537 | quadrant += 2; |
| 1538 | } |
| 1539 | if ((x < 0) != (y < 0)) { |
| 1540 | quadrant += 1; |
| 1541 | } |
| 1542 | } |
| 1543 | |
| 1544 | const SkPoint quadrantPts[] = { |
| 1545 | { 1, 0 }, { 1, 1 }, { 0, 1 }, { -1, 1 }, { -1, 0 }, { -1, -1 }, { 0, -1 }, { 1, -1 } |
| 1546 | }; |
| 1547 | const SkScalar quadrantWeight = SK_ScalarRoot2Over2; |
| 1548 | |
| 1549 | int conicCount = quadrant; |
| 1550 | for (int i = 0; i < conicCount; ++i) { |
| 1551 | dst[i].set(&quadrantPts[i * 2], quadrantWeight); |
| 1552 | } |
| 1553 | |
| 1554 | // Now compute any remaing (sub-90-degree) arc for the last conic |
| 1555 | const SkPoint finalP = { x, y }; |
| 1556 | const SkPoint& lastQ = quadrantPts[quadrant * 2]; // will already be a unit-vector |
| 1557 | const SkScalar dot = SkVector::DotProduct(lastQ, finalP); |
reed | 88f0a99 | 2015-02-10 08:45:06 -0800 | [diff] [blame] | 1558 | SkASSERT(0 <= dot && dot <= SK_Scalar1 + SK_ScalarNearlyZero); |
reed | d5d27d9 | 2015-02-09 13:54:43 -0800 | [diff] [blame] | 1559 | |
caryclark | c6325cd | 2015-05-11 14:36:33 -0700 | [diff] [blame^] | 1560 | if (dot < 1) { |
reed | d5d27d9 | 2015-02-09 13:54:43 -0800 | [diff] [blame] | 1561 | SkVector offCurve = { lastQ.x() + x, lastQ.y() + y }; |
| 1562 | // compute the bisector vector, and then rescale to be the off-curve point. |
| 1563 | // we compute its length from cos(theta/2) = length / 1, using half-angle identity we get |
| 1564 | // length = sqrt(2 / (1 + cos(theta)). We already have cos() when to computed the dot. |
| 1565 | // This is nice, since our computed weight is cos(theta/2) as well! |
| 1566 | // |
| 1567 | const SkScalar cosThetaOver2 = SkScalarSqrt((1 + dot) / 2); |
| 1568 | offCurve.setLength(SkScalarInvert(cosThetaOver2)); |
| 1569 | dst[conicCount].set(lastQ, offCurve, finalP, cosThetaOver2); |
| 1570 | conicCount += 1; |
| 1571 | } |
| 1572 | |
| 1573 | // now handle counter-clockwise and the initial unitStart rotation |
| 1574 | SkMatrix matrix; |
| 1575 | matrix.setSinCos(uStart.fY, uStart.fX); |
| 1576 | if (dir == kCCW_SkRotationDirection) { |
| 1577 | matrix.preScale(SK_Scalar1, -SK_Scalar1); |
| 1578 | } |
| 1579 | if (userMatrix) { |
| 1580 | matrix.postConcat(*userMatrix); |
| 1581 | } |
| 1582 | for (int i = 0; i < conicCount; ++i) { |
| 1583 | matrix.mapPoints(dst[i].fPts, 3); |
| 1584 | } |
| 1585 | return conicCount; |
| 1586 | } |