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" |
| 10 | |
kbr@chromium.org | 2e08619 | 2010-07-07 22:20:35 +0000 | [diff] [blame] | 11 | bool SkXRayCrossesLine(const SkXRay& pt, const SkPoint pts[2], bool* ambiguous) { |
| 12 | if (ambiguous) { |
| 13 | *ambiguous = false; |
| 14 | } |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 15 | // Determine quick discards. |
| 16 | // Consider query line going exactly through point 0 to not |
| 17 | // intersect, for symmetry with SkXRayCrossesMonotonicCubic. |
kbr@chromium.org | 2e08619 | 2010-07-07 22:20:35 +0000 | [diff] [blame] | 18 | if (pt.fY == pts[0].fY) { |
| 19 | if (ambiguous) { |
| 20 | *ambiguous = true; |
| 21 | } |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 22 | return false; |
kbr@chromium.org | 2e08619 | 2010-07-07 22:20:35 +0000 | [diff] [blame] | 23 | } |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 24 | if (pt.fY < pts[0].fY && pt.fY < pts[1].fY) |
| 25 | return false; |
| 26 | if (pt.fY > pts[0].fY && pt.fY > pts[1].fY) |
| 27 | return false; |
| 28 | if (pt.fX > pts[0].fX && pt.fX > pts[1].fX) |
| 29 | return false; |
| 30 | // Determine degenerate cases |
| 31 | if (SkScalarNearlyZero(pts[0].fY - pts[1].fY)) |
| 32 | return false; |
kbr@chromium.org | 2e08619 | 2010-07-07 22:20:35 +0000 | [diff] [blame] | 33 | if (SkScalarNearlyZero(pts[0].fX - pts[1].fX)) { |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 34 | // We've already determined the query point lies within the |
| 35 | // vertical range of the line segment. |
kbr@chromium.org | 2e08619 | 2010-07-07 22:20:35 +0000 | [diff] [blame] | 36 | if (pt.fX <= pts[0].fX) { |
| 37 | if (ambiguous) { |
| 38 | *ambiguous = (pt.fY == pts[1].fY); |
| 39 | } |
| 40 | return true; |
| 41 | } |
| 42 | return false; |
| 43 | } |
| 44 | // Ambiguity check |
| 45 | if (pt.fY == pts[1].fY) { |
| 46 | if (pt.fX <= pts[1].fX) { |
| 47 | if (ambiguous) { |
| 48 | *ambiguous = true; |
| 49 | } |
| 50 | return true; |
| 51 | } |
| 52 | return false; |
| 53 | } |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 54 | // Full line segment evaluation |
| 55 | SkScalar delta_y = pts[1].fY - pts[0].fY; |
| 56 | SkScalar delta_x = pts[1].fX - pts[0].fX; |
| 57 | SkScalar slope = SkScalarDiv(delta_y, delta_x); |
| 58 | SkScalar b = pts[0].fY - SkScalarMul(slope, pts[0].fX); |
| 59 | // Solve for x coordinate at y = pt.fY |
| 60 | SkScalar x = SkScalarDiv(pt.fY - b, slope); |
| 61 | return pt.fX <= x; |
| 62 | } |
| 63 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 64 | /** If defined, this makes eval_quad and eval_cubic do more setup (sometimes |
| 65 | involving integer multiplies by 2 or 3, but fewer calls to SkScalarMul. |
| 66 | May also introduce overflow of fixed when we compute our setup. |
| 67 | */ |
reed@google.com | 8f4d230 | 2013-12-17 16:44:46 +0000 | [diff] [blame] | 68 | // #define DIRECT_EVAL_OF_POLYNOMIALS |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 69 | |
| 70 | //////////////////////////////////////////////////////////////////////// |
| 71 | |
reed@google.com | 8f4d230 | 2013-12-17 16:44:46 +0000 | [diff] [blame] | 72 | static int is_not_monotonic(float a, float b, float c) { |
| 73 | float ab = a - b; |
| 74 | float bc = b - c; |
| 75 | if (ab < 0) { |
| 76 | bc = -bc; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 77 | } |
reed@google.com | 8f4d230 | 2013-12-17 16:44:46 +0000 | [diff] [blame] | 78 | return ab == 0 || bc < 0; |
| 79 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 80 | |
| 81 | //////////////////////////////////////////////////////////////////////// |
| 82 | |
| 83 | static bool is_unit_interval(SkScalar x) |
| 84 | { |
| 85 | return x > 0 && x < SK_Scalar1; |
| 86 | } |
| 87 | |
| 88 | static int valid_unit_divide(SkScalar numer, SkScalar denom, SkScalar* ratio) |
| 89 | { |
| 90 | SkASSERT(ratio); |
| 91 | |
| 92 | if (numer < 0) |
| 93 | { |
| 94 | numer = -numer; |
| 95 | denom = -denom; |
| 96 | } |
| 97 | |
| 98 | if (denom == 0 || numer == 0 || numer >= denom) |
| 99 | return 0; |
| 100 | |
| 101 | SkScalar r = SkScalarDiv(numer, denom); |
reed@android.com | 1516162 | 2010-03-08 17:44:42 +0000 | [diff] [blame] | 102 | if (SkScalarIsNaN(r)) { |
| 103 | return 0; |
| 104 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 105 | SkASSERT(r >= 0 && r < SK_Scalar1); |
| 106 | if (r == 0) // catch underflow if numer <<<< denom |
| 107 | return 0; |
| 108 | *ratio = r; |
| 109 | return 1; |
| 110 | } |
| 111 | |
| 112 | /** From Numerical Recipes in C. |
| 113 | |
| 114 | Q = -1/2 (B + sign(B) sqrt[B*B - 4*A*C]) |
| 115 | x1 = Q / A |
| 116 | x2 = C / Q |
| 117 | */ |
| 118 | int SkFindUnitQuadRoots(SkScalar A, SkScalar B, SkScalar C, SkScalar roots[2]) |
| 119 | { |
| 120 | SkASSERT(roots); |
| 121 | |
| 122 | if (A == 0) |
| 123 | return valid_unit_divide(-C, B, roots); |
| 124 | |
| 125 | SkScalar* r = roots; |
| 126 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 127 | float R = B*B - 4*A*C; |
reed@android.com | 1516162 | 2010-03-08 17:44:42 +0000 | [diff] [blame] | 128 | if (R < 0 || SkScalarIsNaN(R)) { // complex roots |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 129 | return 0; |
reed@android.com | 1516162 | 2010-03-08 17:44:42 +0000 | [diff] [blame] | 130 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 131 | R = sk_float_sqrt(R); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 132 | |
| 133 | SkScalar Q = (B < 0) ? -(B-R)/2 : -(B+R)/2; |
| 134 | r += valid_unit_divide(Q, A, r); |
| 135 | r += valid_unit_divide(C, Q, r); |
| 136 | if (r - roots == 2) |
| 137 | { |
| 138 | if (roots[0] > roots[1]) |
| 139 | SkTSwap<SkScalar>(roots[0], roots[1]); |
| 140 | else if (roots[0] == roots[1]) // nearly-equal? |
| 141 | r -= 1; // skip the double root |
| 142 | } |
| 143 | return (int)(r - roots); |
| 144 | } |
| 145 | |
reed@google.com | 8f4d230 | 2013-12-17 16:44:46 +0000 | [diff] [blame] | 146 | /////////////////////////////////////////////////////////////////////////////// |
| 147 | /////////////////////////////////////////////////////////////////////////////// |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 148 | |
| 149 | static SkScalar eval_quad(const SkScalar src[], SkScalar t) |
| 150 | { |
| 151 | SkASSERT(src); |
| 152 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
| 153 | |
| 154 | #ifdef DIRECT_EVAL_OF_POLYNOMIALS |
| 155 | SkScalar C = src[0]; |
| 156 | SkScalar A = src[4] - 2 * src[2] + C; |
| 157 | SkScalar B = 2 * (src[2] - C); |
| 158 | return SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C); |
| 159 | #else |
| 160 | SkScalar ab = SkScalarInterp(src[0], src[2], t); |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 161 | SkScalar bc = SkScalarInterp(src[2], src[4], t); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 162 | return SkScalarInterp(ab, bc, t); |
| 163 | #endif |
| 164 | } |
| 165 | |
| 166 | static SkScalar eval_quad_derivative(const SkScalar src[], SkScalar t) |
| 167 | { |
| 168 | SkScalar A = src[4] - 2 * src[2] + src[0]; |
| 169 | SkScalar B = src[2] - src[0]; |
| 170 | |
| 171 | return 2 * SkScalarMulAdd(A, t, B); |
| 172 | } |
| 173 | |
| 174 | static SkScalar eval_quad_derivative_at_half(const SkScalar src[]) |
| 175 | { |
| 176 | SkScalar A = src[4] - 2 * src[2] + src[0]; |
| 177 | SkScalar B = src[2] - src[0]; |
| 178 | return A + 2 * B; |
| 179 | } |
| 180 | |
| 181 | void SkEvalQuadAt(const SkPoint src[3], SkScalar t, SkPoint* pt, SkVector* tangent) |
| 182 | { |
| 183 | SkASSERT(src); |
| 184 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
| 185 | |
| 186 | if (pt) |
| 187 | pt->set(eval_quad(&src[0].fX, t), eval_quad(&src[0].fY, t)); |
| 188 | if (tangent) |
| 189 | tangent->set(eval_quad_derivative(&src[0].fX, t), |
| 190 | eval_quad_derivative(&src[0].fY, t)); |
| 191 | } |
| 192 | |
| 193 | void SkEvalQuadAtHalf(const SkPoint src[3], SkPoint* pt, SkVector* tangent) |
| 194 | { |
| 195 | SkASSERT(src); |
| 196 | |
| 197 | if (pt) |
| 198 | { |
| 199 | SkScalar x01 = SkScalarAve(src[0].fX, src[1].fX); |
| 200 | SkScalar y01 = SkScalarAve(src[0].fY, src[1].fY); |
| 201 | SkScalar x12 = SkScalarAve(src[1].fX, src[2].fX); |
| 202 | SkScalar y12 = SkScalarAve(src[1].fY, src[2].fY); |
| 203 | pt->set(SkScalarAve(x01, x12), SkScalarAve(y01, y12)); |
| 204 | } |
| 205 | if (tangent) |
| 206 | tangent->set(eval_quad_derivative_at_half(&src[0].fX), |
| 207 | eval_quad_derivative_at_half(&src[0].fY)); |
| 208 | } |
| 209 | |
| 210 | static void interp_quad_coords(const SkScalar* src, SkScalar* dst, SkScalar t) |
| 211 | { |
| 212 | SkScalar ab = SkScalarInterp(src[0], src[2], t); |
| 213 | SkScalar bc = SkScalarInterp(src[2], src[4], t); |
| 214 | |
| 215 | dst[0] = src[0]; |
| 216 | dst[2] = ab; |
| 217 | dst[4] = SkScalarInterp(ab, bc, t); |
| 218 | dst[6] = bc; |
| 219 | dst[8] = src[4]; |
| 220 | } |
| 221 | |
| 222 | void SkChopQuadAt(const SkPoint src[3], SkPoint dst[5], SkScalar t) |
| 223 | { |
| 224 | SkASSERT(t > 0 && t < SK_Scalar1); |
| 225 | |
| 226 | interp_quad_coords(&src[0].fX, &dst[0].fX, t); |
| 227 | interp_quad_coords(&src[0].fY, &dst[0].fY, t); |
| 228 | } |
| 229 | |
| 230 | void SkChopQuadAtHalf(const SkPoint src[3], SkPoint dst[5]) |
| 231 | { |
| 232 | SkScalar x01 = SkScalarAve(src[0].fX, src[1].fX); |
| 233 | SkScalar y01 = SkScalarAve(src[0].fY, src[1].fY); |
| 234 | SkScalar x12 = SkScalarAve(src[1].fX, src[2].fX); |
| 235 | SkScalar y12 = SkScalarAve(src[1].fY, src[2].fY); |
| 236 | |
| 237 | dst[0] = src[0]; |
| 238 | dst[1].set(x01, y01); |
| 239 | dst[2].set(SkScalarAve(x01, x12), SkScalarAve(y01, y12)); |
| 240 | dst[3].set(x12, y12); |
| 241 | dst[4] = src[2]; |
| 242 | } |
| 243 | |
| 244 | /** Quad'(t) = At + B, where |
| 245 | A = 2(a - 2b + c) |
| 246 | B = 2(b - a) |
| 247 | Solve for t, only if it fits between 0 < t < 1 |
| 248 | */ |
| 249 | int SkFindQuadExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar tValue[1]) |
| 250 | { |
| 251 | /* At + B == 0 |
| 252 | t = -B / A |
| 253 | */ |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 254 | return valid_unit_divide(a - b, a - b - b + c, tValue); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 255 | } |
| 256 | |
reed@android.com | fc25abd | 2009-01-15 14:38:33 +0000 | [diff] [blame] | 257 | static inline void flatten_double_quad_extrema(SkScalar coords[14]) |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 258 | { |
| 259 | coords[2] = coords[6] = coords[4]; |
| 260 | } |
| 261 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 262 | /* 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] | 263 | stored in dst[]. Guarantees that the 1/2 quads will be monotonic. |
| 264 | */ |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 265 | int SkChopQuadAtYExtrema(const SkPoint src[3], SkPoint dst[5]) |
| 266 | { |
| 267 | SkASSERT(src); |
| 268 | SkASSERT(dst); |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 269 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 270 | #if 0 |
| 271 | static bool once = true; |
| 272 | if (once) |
| 273 | { |
| 274 | once = false; |
| 275 | SkPoint s[3] = { 0, 26398, 0, 26331, 0, 20621428 }; |
| 276 | SkPoint d[6]; |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 277 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 278 | int n = SkChopQuadAtYExtrema(s, d); |
| 279 | SkDebugf("chop=%d, Y=[%x %x %x %x %x %x]\n", n, d[0].fY, d[1].fY, d[2].fY, d[3].fY, d[4].fY, d[5].fY); |
| 280 | } |
| 281 | #endif |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 282 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 283 | SkScalar a = src[0].fY; |
| 284 | SkScalar b = src[1].fY; |
| 285 | SkScalar c = src[2].fY; |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 286 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 287 | if (is_not_monotonic(a, b, c)) |
| 288 | { |
| 289 | SkScalar tValue; |
| 290 | if (valid_unit_divide(a - b, a - b - b + c, &tValue)) |
| 291 | { |
| 292 | SkChopQuadAt(src, dst, tValue); |
| 293 | flatten_double_quad_extrema(&dst[0].fY); |
| 294 | return 1; |
| 295 | } |
| 296 | // if we get here, we need to force dst to be monotonic, even though |
| 297 | // we couldn't compute a unit_divide value (probably underflow). |
| 298 | b = SkScalarAbs(a - b) < SkScalarAbs(b - c) ? a : c; |
| 299 | } |
| 300 | dst[0].set(src[0].fX, a); |
| 301 | dst[1].set(src[1].fX, b); |
| 302 | dst[2].set(src[2].fX, c); |
| 303 | return 0; |
| 304 | } |
| 305 | |
reed@android.com | 77f0ef7 | 2009-11-17 18:47:52 +0000 | [diff] [blame] | 306 | /* Returns 0 for 1 quad, and 1 for two quads, either way the answer is |
| 307 | stored in dst[]. Guarantees that the 1/2 quads will be monotonic. |
| 308 | */ |
| 309 | int SkChopQuadAtXExtrema(const SkPoint src[3], SkPoint dst[5]) |
| 310 | { |
| 311 | SkASSERT(src); |
| 312 | SkASSERT(dst); |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 313 | |
reed@android.com | 77f0ef7 | 2009-11-17 18:47:52 +0000 | [diff] [blame] | 314 | SkScalar a = src[0].fX; |
| 315 | SkScalar b = src[1].fX; |
| 316 | SkScalar c = src[2].fX; |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 317 | |
reed@android.com | 77f0ef7 | 2009-11-17 18:47:52 +0000 | [diff] [blame] | 318 | if (is_not_monotonic(a, b, c)) { |
| 319 | SkScalar tValue; |
| 320 | if (valid_unit_divide(a - b, a - b - b + c, &tValue)) { |
| 321 | SkChopQuadAt(src, dst, tValue); |
| 322 | flatten_double_quad_extrema(&dst[0].fX); |
| 323 | return 1; |
| 324 | } |
| 325 | // if we get here, we need to force dst to be monotonic, even though |
| 326 | // we couldn't compute a unit_divide value (probably underflow). |
| 327 | b = SkScalarAbs(a - b) < SkScalarAbs(b - c) ? a : c; |
| 328 | } |
| 329 | dst[0].set(a, src[0].fY); |
| 330 | dst[1].set(b, src[1].fY); |
| 331 | dst[2].set(c, src[2].fY); |
| 332 | return 0; |
| 333 | } |
| 334 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 335 | // F(t) = a (1 - t) ^ 2 + 2 b t (1 - t) + c t ^ 2 |
| 336 | // F'(t) = 2 (b - a) + 2 (a - 2b + c) t |
| 337 | // F''(t) = 2 (a - 2b + c) |
| 338 | // |
| 339 | // A = 2 (b - a) |
| 340 | // B = 2 (a - 2b + c) |
| 341 | // |
| 342 | // Maximum curvature for a quadratic means solving |
| 343 | // Fx' Fx'' + Fy' Fy'' = 0 |
| 344 | // |
| 345 | // t = - (Ax Bx + Ay By) / (Bx ^ 2 + By ^ 2) |
| 346 | // |
egdaniel@google.com | 5383a75 | 2013-07-12 20:15:34 +0000 | [diff] [blame] | 347 | float SkFindQuadMaxCurvature(const SkPoint src[3]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 348 | SkScalar Ax = src[1].fX - src[0].fX; |
| 349 | SkScalar Ay = src[1].fY - src[0].fY; |
| 350 | SkScalar Bx = src[0].fX - src[1].fX - src[1].fX + src[2].fX; |
| 351 | SkScalar By = src[0].fY - src[1].fY - src[1].fY + src[2].fY; |
| 352 | SkScalar t = 0; // 0 means don't chop |
| 353 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 354 | (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] | 355 | return t; |
| 356 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 357 | |
egdaniel@google.com | 5383a75 | 2013-07-12 20:15:34 +0000 | [diff] [blame] | 358 | int SkChopQuadAtMaxCurvature(const SkPoint src[3], SkPoint dst[5]) |
| 359 | { |
| 360 | SkScalar t = SkFindQuadMaxCurvature(src); |
| 361 | if (t == 0) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 362 | memcpy(dst, src, 3 * sizeof(SkPoint)); |
| 363 | return 1; |
egdaniel@google.com | 5383a75 | 2013-07-12 20:15:34 +0000 | [diff] [blame] | 364 | } else { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 365 | SkChopQuadAt(src, dst, t); |
| 366 | return 2; |
| 367 | } |
| 368 | } |
| 369 | |
reed@google.com | 8f4d230 | 2013-12-17 16:44:46 +0000 | [diff] [blame] | 370 | #define SK_ScalarTwoThirds (0.666666666f) |
reed@google.com | 6fc321a | 2011-07-27 13:54:36 +0000 | [diff] [blame] | 371 | |
| 372 | void SkConvertQuadToCubic(const SkPoint src[3], SkPoint dst[4]) { |
| 373 | const SkScalar scale = SK_ScalarTwoThirds; |
| 374 | dst[0] = src[0]; |
| 375 | dst[1].set(src[0].fX + SkScalarMul(src[1].fX - src[0].fX, scale), |
| 376 | src[0].fY + SkScalarMul(src[1].fY - src[0].fY, scale)); |
| 377 | dst[2].set(src[2].fX + SkScalarMul(src[1].fX - src[2].fX, scale), |
| 378 | src[2].fY + SkScalarMul(src[1].fY - src[2].fY, scale)); |
| 379 | dst[3] = src[2]; |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 380 | } |
| 381 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 382 | //////////////////////////////////////////////////////////////////////////////////////// |
| 383 | ///// CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS ///// |
| 384 | //////////////////////////////////////////////////////////////////////////////////////// |
| 385 | |
| 386 | static void get_cubic_coeff(const SkScalar pt[], SkScalar coeff[4]) |
| 387 | { |
| 388 | coeff[0] = pt[6] + 3*(pt[2] - pt[4]) - pt[0]; |
| 389 | coeff[1] = 3*(pt[4] - pt[2] - pt[2] + pt[0]); |
| 390 | coeff[2] = 3*(pt[2] - pt[0]); |
| 391 | coeff[3] = pt[0]; |
| 392 | } |
| 393 | |
| 394 | void SkGetCubicCoeff(const SkPoint pts[4], SkScalar cx[4], SkScalar cy[4]) |
| 395 | { |
| 396 | SkASSERT(pts); |
| 397 | |
| 398 | if (cx) |
| 399 | get_cubic_coeff(&pts[0].fX, cx); |
| 400 | if (cy) |
| 401 | get_cubic_coeff(&pts[0].fY, cy); |
| 402 | } |
| 403 | |
| 404 | static SkScalar eval_cubic(const SkScalar src[], SkScalar t) |
| 405 | { |
| 406 | SkASSERT(src); |
| 407 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
| 408 | |
| 409 | if (t == 0) |
| 410 | return src[0]; |
| 411 | |
| 412 | #ifdef DIRECT_EVAL_OF_POLYNOMIALS |
| 413 | SkScalar D = src[0]; |
| 414 | SkScalar A = src[6] + 3*(src[2] - src[4]) - D; |
| 415 | SkScalar B = 3*(src[4] - src[2] - src[2] + D); |
| 416 | SkScalar C = 3*(src[2] - D); |
| 417 | |
| 418 | return SkScalarMulAdd(SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C), t, D); |
| 419 | #else |
| 420 | SkScalar ab = SkScalarInterp(src[0], src[2], t); |
| 421 | SkScalar bc = SkScalarInterp(src[2], src[4], t); |
| 422 | SkScalar cd = SkScalarInterp(src[4], src[6], t); |
| 423 | SkScalar abc = SkScalarInterp(ab, bc, t); |
| 424 | SkScalar bcd = SkScalarInterp(bc, cd, t); |
| 425 | return SkScalarInterp(abc, bcd, t); |
| 426 | #endif |
| 427 | } |
| 428 | |
| 429 | /** return At^2 + Bt + C |
| 430 | */ |
| 431 | static SkScalar eval_quadratic(SkScalar A, SkScalar B, SkScalar C, SkScalar t) |
| 432 | { |
| 433 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
| 434 | |
| 435 | return SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C); |
| 436 | } |
| 437 | |
| 438 | static SkScalar eval_cubic_derivative(const SkScalar src[], SkScalar t) |
| 439 | { |
| 440 | SkScalar A = src[6] + 3*(src[2] - src[4]) - src[0]; |
| 441 | SkScalar B = 2*(src[4] - 2 * src[2] + src[0]); |
| 442 | SkScalar C = src[2] - src[0]; |
| 443 | |
| 444 | return eval_quadratic(A, B, C, t); |
| 445 | } |
| 446 | |
| 447 | static SkScalar eval_cubic_2ndDerivative(const SkScalar src[], SkScalar t) |
| 448 | { |
| 449 | SkScalar A = src[6] + 3*(src[2] - src[4]) - src[0]; |
| 450 | SkScalar B = src[4] - 2 * src[2] + src[0]; |
| 451 | |
| 452 | return SkScalarMulAdd(A, t, B); |
| 453 | } |
| 454 | |
| 455 | void SkEvalCubicAt(const SkPoint src[4], SkScalar t, SkPoint* loc, SkVector* tangent, SkVector* curvature) |
| 456 | { |
| 457 | SkASSERT(src); |
| 458 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
| 459 | |
| 460 | if (loc) |
| 461 | loc->set(eval_cubic(&src[0].fX, t), eval_cubic(&src[0].fY, t)); |
| 462 | if (tangent) |
| 463 | tangent->set(eval_cubic_derivative(&src[0].fX, t), |
| 464 | eval_cubic_derivative(&src[0].fY, t)); |
| 465 | if (curvature) |
| 466 | curvature->set(eval_cubic_2ndDerivative(&src[0].fX, t), |
| 467 | eval_cubic_2ndDerivative(&src[0].fY, t)); |
| 468 | } |
| 469 | |
| 470 | /** Cubic'(t) = At^2 + Bt + C, where |
| 471 | A = 3(-a + 3(b - c) + d) |
| 472 | B = 6(a - 2b + c) |
| 473 | C = 3(b - a) |
| 474 | Solve for t, keeping only those that fit betwee 0 < t < 1 |
| 475 | */ |
| 476 | int SkFindCubicExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar d, SkScalar tValues[2]) |
| 477 | { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 478 | // we divide A,B,C by 3 to simplify |
| 479 | SkScalar A = d - a + 3*(b - c); |
| 480 | SkScalar B = 2*(a - b - b + c); |
| 481 | SkScalar C = b - a; |
| 482 | |
| 483 | return SkFindUnitQuadRoots(A, B, C, tValues); |
| 484 | } |
| 485 | |
| 486 | static void interp_cubic_coords(const SkScalar* src, SkScalar* dst, SkScalar t) |
| 487 | { |
| 488 | SkScalar ab = SkScalarInterp(src[0], src[2], t); |
| 489 | SkScalar bc = SkScalarInterp(src[2], src[4], t); |
| 490 | SkScalar cd = SkScalarInterp(src[4], src[6], t); |
| 491 | SkScalar abc = SkScalarInterp(ab, bc, t); |
| 492 | SkScalar bcd = SkScalarInterp(bc, cd, t); |
| 493 | SkScalar abcd = SkScalarInterp(abc, bcd, t); |
| 494 | |
| 495 | dst[0] = src[0]; |
| 496 | dst[2] = ab; |
| 497 | dst[4] = abc; |
| 498 | dst[6] = abcd; |
| 499 | dst[8] = bcd; |
| 500 | dst[10] = cd; |
| 501 | dst[12] = src[6]; |
| 502 | } |
| 503 | |
| 504 | void SkChopCubicAt(const SkPoint src[4], SkPoint dst[7], SkScalar t) |
| 505 | { |
| 506 | SkASSERT(t > 0 && t < SK_Scalar1); |
| 507 | |
| 508 | interp_cubic_coords(&src[0].fX, &dst[0].fX, t); |
| 509 | interp_cubic_coords(&src[0].fY, &dst[0].fY, t); |
| 510 | } |
| 511 | |
reed@android.com | a964028 | 2009-08-28 20:06:54 +0000 | [diff] [blame] | 512 | /* http://code.google.com/p/skia/issues/detail?id=32 |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 513 | |
reed@android.com | a964028 | 2009-08-28 20:06:54 +0000 | [diff] [blame] | 514 | This test code would fail when we didn't check the return result of |
| 515 | valid_unit_divide in SkChopCubicAt(... tValues[], int roots). The reason is |
| 516 | that after the first chop, the parameters to valid_unit_divide are equal |
| 517 | (thanks to finite float precision and rounding in the subtracts). Thus |
| 518 | even though the 2nd tValue looks < 1.0, after we renormalize it, we end |
| 519 | up with 1.0, hence the need to check and just return the last cubic as |
| 520 | a degenerate clump of 4 points in the sampe place. |
| 521 | |
| 522 | static void test_cubic() { |
| 523 | SkPoint src[4] = { |
| 524 | { 556.25000, 523.03003 }, |
| 525 | { 556.23999, 522.96002 }, |
| 526 | { 556.21997, 522.89001 }, |
| 527 | { 556.21997, 522.82001 } |
| 528 | }; |
| 529 | SkPoint dst[10]; |
| 530 | SkScalar tval[] = { 0.33333334f, 0.99999994f }; |
| 531 | SkChopCubicAt(src, dst, tval, 2); |
| 532 | } |
| 533 | */ |
| 534 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 535 | void SkChopCubicAt(const SkPoint src[4], SkPoint dst[], const SkScalar tValues[], int roots) |
| 536 | { |
| 537 | #ifdef SK_DEBUG |
| 538 | { |
| 539 | for (int i = 0; i < roots - 1; i++) |
| 540 | { |
| 541 | SkASSERT(is_unit_interval(tValues[i])); |
| 542 | SkASSERT(is_unit_interval(tValues[i+1])); |
| 543 | SkASSERT(tValues[i] < tValues[i+1]); |
| 544 | } |
| 545 | } |
| 546 | #endif |
| 547 | |
| 548 | if (dst) |
| 549 | { |
| 550 | if (roots == 0) // nothing to chop |
| 551 | memcpy(dst, src, 4*sizeof(SkPoint)); |
| 552 | else |
| 553 | { |
| 554 | SkScalar t = tValues[0]; |
| 555 | SkPoint tmp[4]; |
| 556 | |
| 557 | for (int i = 0; i < roots; i++) |
| 558 | { |
| 559 | SkChopCubicAt(src, dst, t); |
| 560 | if (i == roots - 1) |
| 561 | break; |
| 562 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 563 | dst += 3; |
reed@android.com | a964028 | 2009-08-28 20:06:54 +0000 | [diff] [blame] | 564 | // have src point to the remaining cubic (after the chop) |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 565 | memcpy(tmp, dst, 4 * sizeof(SkPoint)); |
| 566 | src = tmp; |
reed@android.com | a964028 | 2009-08-28 20:06:54 +0000 | [diff] [blame] | 567 | |
| 568 | // watch out in case the renormalized t isn't in range |
| 569 | if (!valid_unit_divide(tValues[i+1] - tValues[i], |
| 570 | SK_Scalar1 - tValues[i], &t)) { |
| 571 | // if we can't, just create a degenerate cubic |
| 572 | dst[4] = dst[5] = dst[6] = src[3]; |
| 573 | break; |
| 574 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 575 | } |
| 576 | } |
| 577 | } |
| 578 | } |
| 579 | |
| 580 | void SkChopCubicAtHalf(const SkPoint src[4], SkPoint dst[7]) |
| 581 | { |
| 582 | SkScalar x01 = SkScalarAve(src[0].fX, src[1].fX); |
| 583 | SkScalar y01 = SkScalarAve(src[0].fY, src[1].fY); |
| 584 | SkScalar x12 = SkScalarAve(src[1].fX, src[2].fX); |
| 585 | SkScalar y12 = SkScalarAve(src[1].fY, src[2].fY); |
| 586 | SkScalar x23 = SkScalarAve(src[2].fX, src[3].fX); |
| 587 | SkScalar y23 = SkScalarAve(src[2].fY, src[3].fY); |
| 588 | |
| 589 | SkScalar x012 = SkScalarAve(x01, x12); |
| 590 | SkScalar y012 = SkScalarAve(y01, y12); |
| 591 | SkScalar x123 = SkScalarAve(x12, x23); |
| 592 | SkScalar y123 = SkScalarAve(y12, y23); |
| 593 | |
| 594 | dst[0] = src[0]; |
| 595 | dst[1].set(x01, y01); |
| 596 | dst[2].set(x012, y012); |
| 597 | dst[3].set(SkScalarAve(x012, x123), SkScalarAve(y012, y123)); |
| 598 | dst[4].set(x123, y123); |
| 599 | dst[5].set(x23, y23); |
| 600 | dst[6] = src[3]; |
| 601 | } |
| 602 | |
| 603 | static void flatten_double_cubic_extrema(SkScalar coords[14]) |
| 604 | { |
| 605 | coords[4] = coords[8] = coords[6]; |
| 606 | } |
| 607 | |
| 608 | /** Given 4 points on a cubic bezier, chop it into 1, 2, 3 beziers such that |
| 609 | the resulting beziers are monotonic in Y. This is called by the scan converter. |
| 610 | Depending on what is returned, dst[] is treated as follows |
| 611 | 0 dst[0..3] is the original cubic |
| 612 | 1 dst[0..3] and dst[3..6] are the two new cubics |
| 613 | 2 dst[0..3], dst[3..6], dst[6..9] are the three new cubics |
| 614 | If dst == null, it is ignored and only the count is returned. |
| 615 | */ |
reed@android.com | bb13586 | 2009-11-18 13:47:40 +0000 | [diff] [blame] | 616 | int SkChopCubicAtYExtrema(const SkPoint src[4], SkPoint dst[10]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 617 | SkScalar tValues[2]; |
reed@android.com | bb13586 | 2009-11-18 13:47:40 +0000 | [diff] [blame] | 618 | int roots = SkFindCubicExtrema(src[0].fY, src[1].fY, src[2].fY, |
| 619 | src[3].fY, tValues); |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 620 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 621 | SkChopCubicAt(src, dst, tValues, roots); |
reed@android.com | bb13586 | 2009-11-18 13:47:40 +0000 | [diff] [blame] | 622 | if (dst && roots > 0) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 623 | // we do some cleanup to ensure our Y extrema are flat |
| 624 | flatten_double_cubic_extrema(&dst[0].fY); |
reed@android.com | bb13586 | 2009-11-18 13:47:40 +0000 | [diff] [blame] | 625 | if (roots == 2) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 626 | flatten_double_cubic_extrema(&dst[3].fY); |
reed@android.com | bb13586 | 2009-11-18 13:47:40 +0000 | [diff] [blame] | 627 | } |
| 628 | } |
| 629 | return roots; |
| 630 | } |
| 631 | |
| 632 | int SkChopCubicAtXExtrema(const SkPoint src[4], SkPoint dst[10]) { |
| 633 | SkScalar tValues[2]; |
| 634 | int roots = SkFindCubicExtrema(src[0].fX, src[1].fX, src[2].fX, |
| 635 | src[3].fX, tValues); |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 636 | |
reed@android.com | bb13586 | 2009-11-18 13:47:40 +0000 | [diff] [blame] | 637 | SkChopCubicAt(src, dst, tValues, roots); |
| 638 | if (dst && roots > 0) { |
| 639 | // we do some cleanup to ensure our Y extrema are flat |
| 640 | flatten_double_cubic_extrema(&dst[0].fX); |
| 641 | if (roots == 2) { |
| 642 | flatten_double_cubic_extrema(&dst[3].fX); |
| 643 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 644 | } |
| 645 | return roots; |
| 646 | } |
| 647 | |
| 648 | /** http://www.faculty.idc.ac.il/arik/quality/appendixA.html |
| 649 | |
| 650 | Inflection means that curvature is zero. |
| 651 | Curvature is [F' x F''] / [F'^3] |
| 652 | So we solve F'x X F''y - F'y X F''y == 0 |
| 653 | After some canceling of the cubic term, we get |
| 654 | A = b - a |
| 655 | B = c - 2b + a |
| 656 | C = d - 3c + 3b - a |
| 657 | (BxCy - ByCx)t^2 + (AxCy - AyCx)t + AxBy - AyBx == 0 |
| 658 | */ |
| 659 | int SkFindCubicInflections(const SkPoint src[4], SkScalar tValues[]) |
| 660 | { |
| 661 | SkScalar Ax = src[1].fX - src[0].fX; |
| 662 | SkScalar Ay = src[1].fY - src[0].fY; |
| 663 | SkScalar Bx = src[2].fX - 2 * src[1].fX + src[0].fX; |
| 664 | SkScalar By = src[2].fY - 2 * src[1].fY + src[0].fY; |
| 665 | SkScalar Cx = src[3].fX + 3 * (src[1].fX - src[2].fX) - src[0].fX; |
| 666 | 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] | 667 | |
reed@google.com | 8f4d230 | 2013-12-17 16:44:46 +0000 | [diff] [blame] | 668 | return SkFindUnitQuadRoots(Bx*Cy - By*Cx, Ax*Cy - Ay*Cx, Ax*By - Ay*Bx, tValues); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 669 | } |
| 670 | |
| 671 | int SkChopCubicAtInflections(const SkPoint src[], SkPoint dst[10]) |
| 672 | { |
| 673 | SkScalar tValues[2]; |
| 674 | int count = SkFindCubicInflections(src, tValues); |
| 675 | |
| 676 | if (dst) |
| 677 | { |
| 678 | if (count == 0) |
| 679 | memcpy(dst, src, 4 * sizeof(SkPoint)); |
| 680 | else |
| 681 | SkChopCubicAt(src, dst, tValues, count); |
| 682 | } |
| 683 | return count + 1; |
| 684 | } |
| 685 | |
| 686 | template <typename T> void bubble_sort(T array[], int count) |
| 687 | { |
| 688 | for (int i = count - 1; i > 0; --i) |
| 689 | for (int j = i; j > 0; --j) |
| 690 | if (array[j] < array[j-1]) |
| 691 | { |
| 692 | T tmp(array[j]); |
| 693 | array[j] = array[j-1]; |
| 694 | array[j-1] = tmp; |
| 695 | } |
| 696 | } |
| 697 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 698 | // newton refinement |
| 699 | #if 0 |
| 700 | static SkScalar refine_cubic_root(const SkFP coeff[4], SkScalar root) |
| 701 | { |
| 702 | // x1 = x0 - f(t) / f'(t) |
| 703 | |
| 704 | SkFP T = SkScalarToFloat(root); |
| 705 | SkFP N, D; |
| 706 | |
| 707 | // f' = 3*coeff[0]*T^2 + 2*coeff[1]*T + coeff[2] |
| 708 | D = SkFPMul(SkFPMul(coeff[0], SkFPMul(T,T)), 3); |
| 709 | D = SkFPAdd(D, SkFPMulInt(SkFPMul(coeff[1], T), 2)); |
| 710 | D = SkFPAdd(D, coeff[2]); |
| 711 | |
| 712 | if (D == 0) |
| 713 | return root; |
| 714 | |
| 715 | // f = coeff[0]*T^3 + coeff[1]*T^2 + coeff[2]*T + coeff[3] |
| 716 | N = SkFPMul(SkFPMul(SkFPMul(T, T), T), coeff[0]); |
| 717 | N = SkFPAdd(N, SkFPMul(SkFPMul(T, T), coeff[1])); |
| 718 | N = SkFPAdd(N, SkFPMul(T, coeff[2])); |
| 719 | N = SkFPAdd(N, coeff[3]); |
| 720 | |
| 721 | if (N) |
| 722 | { |
| 723 | SkScalar delta = SkFPToScalar(SkFPDiv(N, D)); |
| 724 | |
| 725 | if (delta) |
| 726 | root -= delta; |
| 727 | } |
| 728 | return root; |
| 729 | } |
| 730 | #endif |
| 731 | |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 732 | /** |
| 733 | * Given an array and count, remove all pair-wise duplicates from the array, |
| 734 | * keeping the existing sorting, and return the new count |
| 735 | */ |
| 736 | static int collaps_duplicates(float array[], int count) { |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 737 | for (int n = count; n > 1; --n) { |
| 738 | if (array[0] == array[1]) { |
| 739 | for (int i = 1; i < n; ++i) { |
| 740 | array[i - 1] = array[i]; |
| 741 | } |
| 742 | count -= 1; |
| 743 | } else { |
| 744 | array += 1; |
| 745 | } |
| 746 | } |
| 747 | return count; |
| 748 | } |
| 749 | |
| 750 | #ifdef SK_DEBUG |
| 751 | |
| 752 | #define TEST_COLLAPS_ENTRY(array) array, SK_ARRAY_COUNT(array) |
| 753 | |
| 754 | static void test_collaps_duplicates() { |
| 755 | static bool gOnce; |
| 756 | if (gOnce) { return; } |
| 757 | gOnce = true; |
| 758 | const float src0[] = { 0 }; |
| 759 | const float src1[] = { 0, 0 }; |
| 760 | const float src2[] = { 0, 1 }; |
| 761 | const float src3[] = { 0, 0, 0 }; |
| 762 | const float src4[] = { 0, 0, 1 }; |
| 763 | const float src5[] = { 0, 1, 1 }; |
| 764 | const float src6[] = { 0, 1, 2 }; |
| 765 | const struct { |
| 766 | const float* fData; |
| 767 | int fCount; |
| 768 | int fCollapsedCount; |
| 769 | } data[] = { |
| 770 | { TEST_COLLAPS_ENTRY(src0), 1 }, |
| 771 | { TEST_COLLAPS_ENTRY(src1), 1 }, |
| 772 | { TEST_COLLAPS_ENTRY(src2), 2 }, |
| 773 | { TEST_COLLAPS_ENTRY(src3), 1 }, |
| 774 | { TEST_COLLAPS_ENTRY(src4), 2 }, |
| 775 | { TEST_COLLAPS_ENTRY(src5), 2 }, |
| 776 | { TEST_COLLAPS_ENTRY(src6), 3 }, |
| 777 | }; |
| 778 | for (size_t i = 0; i < SK_ARRAY_COUNT(data); ++i) { |
| 779 | float dst[3]; |
| 780 | memcpy(dst, data[i].fData, data[i].fCount * sizeof(dst[0])); |
| 781 | int count = collaps_duplicates(dst, data[i].fCount); |
| 782 | SkASSERT(data[i].fCollapsedCount == count); |
| 783 | for (int j = 1; j < count; ++j) { |
| 784 | SkASSERT(dst[j-1] < dst[j]); |
| 785 | } |
| 786 | } |
| 787 | } |
| 788 | #endif |
| 789 | |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 790 | static SkScalar SkScalarCubeRoot(SkScalar x) { |
| 791 | return sk_float_pow(x, 0.3333333f); |
| 792 | } |
| 793 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 794 | /* Solve coeff(t) == 0, returning the number of roots that |
| 795 | lie withing 0 < t < 1. |
| 796 | 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] | 797 | |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 798 | Eliminates repeated roots (so that all tValues are distinct, and are always |
| 799 | in increasing order. |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 800 | */ |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 801 | static int solve_cubic_polynomial(const SkScalar coeff[4], SkScalar tValues[3]) |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 802 | { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 803 | if (SkScalarNearlyZero(coeff[0])) // we're just a quadratic |
| 804 | { |
| 805 | return SkFindUnitQuadRoots(coeff[1], coeff[2], coeff[3], tValues); |
| 806 | } |
| 807 | |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 808 | SkScalar a, b, c, Q, R; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 809 | |
| 810 | { |
| 811 | SkASSERT(coeff[0] != 0); |
| 812 | |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 813 | SkScalar inva = SkScalarInvert(coeff[0]); |
| 814 | a = coeff[1] * inva; |
| 815 | b = coeff[2] * inva; |
| 816 | c = coeff[3] * inva; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 817 | } |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 818 | Q = (a*a - b*3) / 9; |
| 819 | R = (2*a*a*a - 9*a*b + 27*c) / 54; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 820 | |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 821 | SkScalar Q3 = Q * Q * Q; |
| 822 | SkScalar R2MinusQ3 = R * R - Q3; |
| 823 | SkScalar adiv3 = a / 3; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 824 | |
| 825 | SkScalar* roots = tValues; |
| 826 | SkScalar r; |
| 827 | |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 828 | if (R2MinusQ3 < 0) // we have 3 real roots |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 829 | { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 830 | float theta = sk_float_acos(R / sk_float_sqrt(Q3)); |
| 831 | float neg2RootQ = -2 * sk_float_sqrt(Q); |
| 832 | |
| 833 | r = neg2RootQ * sk_float_cos(theta/3) - adiv3; |
| 834 | if (is_unit_interval(r)) |
| 835 | *roots++ = r; |
| 836 | |
| 837 | r = neg2RootQ * sk_float_cos((theta + 2*SK_ScalarPI)/3) - adiv3; |
| 838 | if (is_unit_interval(r)) |
| 839 | *roots++ = r; |
| 840 | |
| 841 | r = neg2RootQ * sk_float_cos((theta - 2*SK_ScalarPI)/3) - adiv3; |
| 842 | if (is_unit_interval(r)) |
| 843 | *roots++ = r; |
| 844 | |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 845 | SkDEBUGCODE(test_collaps_duplicates();) |
| 846 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 847 | // now sort the roots |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 848 | int count = (int)(roots - tValues); |
| 849 | SkASSERT((unsigned)count <= 3); |
| 850 | bubble_sort(tValues, count); |
| 851 | count = collaps_duplicates(tValues, count); |
| 852 | roots = tValues + count; // so we compute the proper count below |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 853 | } |
| 854 | else // we have 1 real root |
| 855 | { |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 856 | SkScalar A = SkScalarAbs(R) + SkScalarSqrt(R2MinusQ3); |
| 857 | A = SkScalarCubeRoot(A); |
| 858 | if (R > 0) |
| 859 | A = -A; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 860 | |
| 861 | if (A != 0) |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 862 | A += Q / A; |
| 863 | r = A - adiv3; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 864 | if (is_unit_interval(r)) |
| 865 | *roots++ = r; |
| 866 | } |
| 867 | |
| 868 | return (int)(roots - tValues); |
| 869 | } |
| 870 | |
| 871 | /* Looking for F' dot F'' == 0 |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 872 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 873 | A = b - a |
| 874 | B = c - 2b + a |
| 875 | C = d - 3c + 3b - a |
| 876 | |
| 877 | F' = 3Ct^2 + 6Bt + 3A |
| 878 | F'' = 6Ct + 6B |
| 879 | |
| 880 | F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB |
| 881 | */ |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 882 | static void formulate_F1DotF2(const SkScalar src[], SkScalar coeff[4]) |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 883 | { |
| 884 | SkScalar a = src[2] - src[0]; |
| 885 | SkScalar b = src[4] - 2 * src[2] + src[0]; |
| 886 | SkScalar c = src[6] + 3 * (src[2] - src[4]) - src[0]; |
| 887 | |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 888 | coeff[0] = c * c; |
| 889 | coeff[1] = 3 * b * c; |
| 890 | coeff[2] = 2 * b * b + c * a; |
| 891 | coeff[3] = a * b; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 892 | } |
| 893 | |
| 894 | // EXPERIMENTAL: can set this to zero to accept all t-values 0 < t < 1 |
| 895 | //#define kMinTValueForChopping (SK_Scalar1 / 256) |
| 896 | #define kMinTValueForChopping 0 |
| 897 | |
| 898 | /* Looking for F' dot F'' == 0 |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 899 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 900 | A = b - a |
| 901 | B = c - 2b + a |
| 902 | C = d - 3c + 3b - a |
| 903 | |
| 904 | F' = 3Ct^2 + 6Bt + 3A |
| 905 | F'' = 6Ct + 6B |
| 906 | |
| 907 | F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB |
| 908 | */ |
| 909 | int SkFindCubicMaxCurvature(const SkPoint src[4], SkScalar tValues[3]) |
| 910 | { |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 911 | SkScalar coeffX[4], coeffY[4]; |
| 912 | int i; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 913 | |
| 914 | formulate_F1DotF2(&src[0].fX, coeffX); |
| 915 | formulate_F1DotF2(&src[0].fY, coeffY); |
| 916 | |
| 917 | for (i = 0; i < 4; i++) |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 918 | coeffX[i] += coeffY[i]; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 919 | |
| 920 | SkScalar t[3]; |
| 921 | int count = solve_cubic_polynomial(coeffX, t); |
| 922 | int maxCount = 0; |
| 923 | |
| 924 | // now remove extrema where the curvature is zero (mins) |
| 925 | // !!!! need a test for this !!!! |
| 926 | for (i = 0; i < count; i++) |
| 927 | { |
| 928 | // if (not_min_curvature()) |
| 929 | if (t[i] > kMinTValueForChopping && t[i] < SK_Scalar1 - kMinTValueForChopping) |
| 930 | tValues[maxCount++] = t[i]; |
| 931 | } |
| 932 | return maxCount; |
| 933 | } |
| 934 | |
| 935 | int SkChopCubicAtMaxCurvature(const SkPoint src[4], SkPoint dst[13], SkScalar tValues[3]) |
| 936 | { |
| 937 | SkScalar t_storage[3]; |
| 938 | |
| 939 | if (tValues == NULL) |
| 940 | tValues = t_storage; |
| 941 | |
| 942 | int count = SkFindCubicMaxCurvature(src, tValues); |
| 943 | |
egdaniel@google.com | 5383a75 | 2013-07-12 20:15:34 +0000 | [diff] [blame] | 944 | if (dst) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 945 | if (count == 0) |
| 946 | memcpy(dst, src, 4 * sizeof(SkPoint)); |
| 947 | else |
| 948 | SkChopCubicAt(src, dst, tValues, count); |
| 949 | } |
| 950 | return count + 1; |
| 951 | } |
| 952 | |
kbr@chromium.org | 2e08619 | 2010-07-07 22:20:35 +0000 | [diff] [blame] | 953 | bool SkXRayCrossesMonotonicCubic(const SkXRay& pt, const SkPoint cubic[4], bool* ambiguous) { |
| 954 | if (ambiguous) { |
| 955 | *ambiguous = false; |
| 956 | } |
| 957 | |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 958 | // Find the minimum and maximum y of the extrema, which are the |
| 959 | // first and last points since this cubic is monotonic |
| 960 | SkScalar min_y = SkMinScalar(cubic[0].fY, cubic[3].fY); |
| 961 | SkScalar max_y = SkMaxScalar(cubic[0].fY, cubic[3].fY); |
| 962 | |
| 963 | if (pt.fY == cubic[0].fY |
| 964 | || pt.fY < min_y |
| 965 | || pt.fY > max_y) { |
| 966 | // The query line definitely does not cross the curve |
kbr@chromium.org | 2e08619 | 2010-07-07 22:20:35 +0000 | [diff] [blame] | 967 | if (ambiguous) { |
| 968 | *ambiguous = (pt.fY == cubic[0].fY); |
| 969 | } |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 970 | return false; |
| 971 | } |
| 972 | |
kbr@chromium.org | 2e08619 | 2010-07-07 22:20:35 +0000 | [diff] [blame] | 973 | bool pt_at_extremum = (pt.fY == cubic[3].fY); |
| 974 | |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 975 | SkScalar min_x = |
| 976 | SkMinScalar( |
| 977 | SkMinScalar( |
| 978 | SkMinScalar(cubic[0].fX, cubic[1].fX), |
| 979 | cubic[2].fX), |
| 980 | cubic[3].fX); |
| 981 | if (pt.fX < min_x) { |
| 982 | // The query line definitely crosses the curve |
kbr@chromium.org | 2e08619 | 2010-07-07 22:20:35 +0000 | [diff] [blame] | 983 | if (ambiguous) { |
| 984 | *ambiguous = pt_at_extremum; |
| 985 | } |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 986 | return true; |
| 987 | } |
| 988 | |
| 989 | SkScalar max_x = |
| 990 | SkMaxScalar( |
| 991 | SkMaxScalar( |
| 992 | SkMaxScalar(cubic[0].fX, cubic[1].fX), |
| 993 | cubic[2].fX), |
| 994 | cubic[3].fX); |
| 995 | if (pt.fX > max_x) { |
| 996 | // The query line definitely does not cross the curve |
| 997 | return false; |
| 998 | } |
| 999 | |
| 1000 | // Do a binary search to find the parameter value which makes y as |
| 1001 | // close as possible to the query point. See whether the query |
| 1002 | // line's origin is to the left of the associated x coordinate. |
| 1003 | |
| 1004 | // kMaxIter is chosen as the number of mantissa bits for a float, |
| 1005 | // since there's no way we are going to get more precision by |
| 1006 | // iterating more times than that. |
| 1007 | const int kMaxIter = 23; |
| 1008 | SkPoint eval; |
| 1009 | int iter = 0; |
| 1010 | SkScalar upper_t; |
| 1011 | SkScalar lower_t; |
| 1012 | // Need to invert direction of t parameter if cubic goes up |
| 1013 | // instead of down |
| 1014 | if (cubic[3].fY > cubic[0].fY) { |
| 1015 | upper_t = SK_Scalar1; |
commit-bot@chromium.org | 4b413c8 | 2013-11-25 19:44:07 +0000 | [diff] [blame] | 1016 | lower_t = 0; |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 1017 | } else { |
commit-bot@chromium.org | 4b413c8 | 2013-11-25 19:44:07 +0000 | [diff] [blame] | 1018 | upper_t = 0; |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 1019 | lower_t = SK_Scalar1; |
| 1020 | } |
| 1021 | do { |
| 1022 | SkScalar t = SkScalarAve(upper_t, lower_t); |
| 1023 | SkEvalCubicAt(cubic, t, &eval, NULL, NULL); |
| 1024 | if (pt.fY > eval.fY) { |
| 1025 | lower_t = t; |
| 1026 | } else { |
| 1027 | upper_t = t; |
| 1028 | } |
| 1029 | } while (++iter < kMaxIter |
| 1030 | && !SkScalarNearlyZero(eval.fY - pt.fY)); |
| 1031 | if (pt.fX <= eval.fX) { |
kbr@chromium.org | 2e08619 | 2010-07-07 22:20:35 +0000 | [diff] [blame] | 1032 | if (ambiguous) { |
| 1033 | *ambiguous = pt_at_extremum; |
| 1034 | } |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 1035 | return true; |
| 1036 | } |
| 1037 | return false; |
| 1038 | } |
| 1039 | |
kbr@chromium.org | 2e08619 | 2010-07-07 22:20:35 +0000 | [diff] [blame] | 1040 | int SkNumXRayCrossingsForCubic(const SkXRay& pt, const SkPoint cubic[4], bool* ambiguous) { |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 1041 | int num_crossings = 0; |
| 1042 | SkPoint monotonic_cubics[10]; |
| 1043 | int num_monotonic_cubics = SkChopCubicAtYExtrema(cubic, monotonic_cubics); |
kbr@chromium.org | 2e08619 | 2010-07-07 22:20:35 +0000 | [diff] [blame] | 1044 | if (ambiguous) { |
| 1045 | *ambiguous = false; |
| 1046 | } |
| 1047 | bool locally_ambiguous; |
| 1048 | if (SkXRayCrossesMonotonicCubic(pt, &monotonic_cubics[0], &locally_ambiguous)) |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 1049 | ++num_crossings; |
kbr@chromium.org | 2e08619 | 2010-07-07 22:20:35 +0000 | [diff] [blame] | 1050 | if (ambiguous) { |
| 1051 | *ambiguous |= locally_ambiguous; |
| 1052 | } |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 1053 | if (num_monotonic_cubics > 0) |
kbr@chromium.org | 2e08619 | 2010-07-07 22:20:35 +0000 | [diff] [blame] | 1054 | if (SkXRayCrossesMonotonicCubic(pt, &monotonic_cubics[3], &locally_ambiguous)) |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 1055 | ++num_crossings; |
kbr@chromium.org | 2e08619 | 2010-07-07 22:20:35 +0000 | [diff] [blame] | 1056 | if (ambiguous) { |
| 1057 | *ambiguous |= locally_ambiguous; |
| 1058 | } |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 1059 | if (num_monotonic_cubics > 1) |
kbr@chromium.org | 2e08619 | 2010-07-07 22:20:35 +0000 | [diff] [blame] | 1060 | if (SkXRayCrossesMonotonicCubic(pt, &monotonic_cubics[6], &locally_ambiguous)) |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 1061 | ++num_crossings; |
kbr@chromium.org | 2e08619 | 2010-07-07 22:20:35 +0000 | [diff] [blame] | 1062 | if (ambiguous) { |
| 1063 | *ambiguous |= locally_ambiguous; |
| 1064 | } |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 1065 | return num_crossings; |
| 1066 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1067 | //////////////////////////////////////////////////////////////////////////////// |
| 1068 | |
| 1069 | /* Find t value for quadratic [a, b, c] = d. |
| 1070 | Return 0 if there is no solution within [0, 1) |
| 1071 | */ |
| 1072 | static SkScalar quad_solve(SkScalar a, SkScalar b, SkScalar c, SkScalar d) |
| 1073 | { |
| 1074 | // At^2 + Bt + C = d |
| 1075 | SkScalar A = a - 2 * b + c; |
| 1076 | SkScalar B = 2 * (b - a); |
| 1077 | SkScalar C = a - d; |
| 1078 | |
| 1079 | SkScalar roots[2]; |
| 1080 | int count = SkFindUnitQuadRoots(A, B, C, roots); |
| 1081 | |
| 1082 | SkASSERT(count <= 1); |
| 1083 | return count == 1 ? roots[0] : 0; |
| 1084 | } |
| 1085 | |
robertphillips@google.com | e1b75b4 | 2013-07-09 15:03:59 +0000 | [diff] [blame] | 1086 | /* 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] | 1087 | the new off-curve point and endpoint into 'dest'. |
skia.committer@gmail.com | 9e1ec1a | 2013-07-10 07:00:58 +0000 | [diff] [blame] | 1088 | 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] | 1089 | (i.e. root == 0) |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1090 | */ |
robertphillips@google.com | e1b75b4 | 2013-07-09 15:03:59 +0000 | [diff] [blame] | 1091 | static bool truncate_last_curve(const SkPoint quad[3], SkScalar x, SkScalar y, SkPoint* dest) |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1092 | { |
| 1093 | const SkScalar* base; |
| 1094 | SkScalar value; |
| 1095 | |
| 1096 | if (SkScalarAbs(x) < SkScalarAbs(y)) { |
| 1097 | base = &quad[0].fX; |
| 1098 | value = x; |
| 1099 | } else { |
| 1100 | base = &quad[0].fY; |
| 1101 | value = y; |
| 1102 | } |
| 1103 | |
| 1104 | // note: this returns 0 if it thinks value is out of range, meaning the |
| 1105 | // root might return something outside of [0, 1) |
| 1106 | SkScalar t = quad_solve(base[0], base[2], base[4], value); |
| 1107 | |
| 1108 | if (t > 0) |
| 1109 | { |
| 1110 | SkPoint tmp[5]; |
| 1111 | SkChopQuadAt(quad, tmp, t); |
robertphillips@google.com | e1b75b4 | 2013-07-09 15:03:59 +0000 | [diff] [blame] | 1112 | dest[0] = tmp[1]; |
robertphillips@google.com | b0889a5 | 2013-09-27 17:05:59 +0000 | [diff] [blame] | 1113 | dest[1].set(x, y); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1114 | return true; |
| 1115 | } else { |
| 1116 | /* t == 0 means either the value triggered a root outside of [0, 1) |
| 1117 | For our purposes, we can ignore the <= 0 roots, but we want to |
| 1118 | catch the >= 1 roots (which given our caller, will basically mean |
| 1119 | a root of 1, give-or-take numerical instability). If we are in the |
| 1120 | >= 1 case, return the existing offCurve point. |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 1121 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1122 | The test below checks to see if we are close to the "end" of the |
| 1123 | curve (near base[4]). Rather than specifying a tolerance, I just |
| 1124 | check to see if value is on to the right/left of the middle point |
| 1125 | (depending on the direction/sign of the end points). |
| 1126 | */ |
| 1127 | if ((base[0] < base[4] && value > base[2]) || |
| 1128 | (base[0] > base[4] && value < base[2])) // should root have been 1 |
| 1129 | { |
robertphillips@google.com | e1b75b4 | 2013-07-09 15:03:59 +0000 | [diff] [blame] | 1130 | dest[0] = quad[1]; |
| 1131 | dest[1].set(x, y); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1132 | return true; |
| 1133 | } |
| 1134 | } |
| 1135 | return false; |
| 1136 | } |
| 1137 | |
| 1138 | static const SkPoint gQuadCirclePts[kSkBuildQuadArcStorage] = { |
commit-bot@chromium.org | f91aaec | 2013-11-01 15:24:55 +0000 | [diff] [blame] | 1139 | // The mid point of the quadratic arc approximation is half way between the two |
| 1140 | // control points. The float epsilon adjustment moves the on curve point out by |
| 1141 | // two bits, distributing the convex test error between the round rect approximation |
| 1142 | // and the convex cross product sign equality test. |
| 1143 | #define SK_MID_RRECT_OFFSET (SK_Scalar1 + SK_ScalarTanPIOver8 + FLT_EPSILON * 4) / 2 |
| 1144 | { SK_Scalar1, 0 }, |
| 1145 | { SK_Scalar1, SK_ScalarTanPIOver8 }, |
| 1146 | { SK_MID_RRECT_OFFSET, SK_MID_RRECT_OFFSET }, |
| 1147 | { SK_ScalarTanPIOver8, SK_Scalar1 }, |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1148 | |
commit-bot@chromium.org | f91aaec | 2013-11-01 15:24:55 +0000 | [diff] [blame] | 1149 | { 0, SK_Scalar1 }, |
| 1150 | { -SK_ScalarTanPIOver8, SK_Scalar1 }, |
| 1151 | { -SK_MID_RRECT_OFFSET, SK_MID_RRECT_OFFSET }, |
| 1152 | { -SK_Scalar1, SK_ScalarTanPIOver8 }, |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1153 | |
commit-bot@chromium.org | f91aaec | 2013-11-01 15:24:55 +0000 | [diff] [blame] | 1154 | { -SK_Scalar1, 0 }, |
| 1155 | { -SK_Scalar1, -SK_ScalarTanPIOver8 }, |
| 1156 | { -SK_MID_RRECT_OFFSET, -SK_MID_RRECT_OFFSET }, |
| 1157 | { -SK_ScalarTanPIOver8, -SK_Scalar1 }, |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1158 | |
commit-bot@chromium.org | f91aaec | 2013-11-01 15:24:55 +0000 | [diff] [blame] | 1159 | { 0, -SK_Scalar1 }, |
| 1160 | { SK_ScalarTanPIOver8, -SK_Scalar1 }, |
| 1161 | { SK_MID_RRECT_OFFSET, -SK_MID_RRECT_OFFSET }, |
| 1162 | { SK_Scalar1, -SK_ScalarTanPIOver8 }, |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1163 | |
commit-bot@chromium.org | f91aaec | 2013-11-01 15:24:55 +0000 | [diff] [blame] | 1164 | { SK_Scalar1, 0 } |
| 1165 | #undef SK_MID_RRECT_OFFSET |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1166 | }; |
| 1167 | |
| 1168 | int SkBuildQuadArc(const SkVector& uStart, const SkVector& uStop, |
| 1169 | SkRotationDirection dir, const SkMatrix* userMatrix, |
| 1170 | SkPoint quadPoints[]) |
| 1171 | { |
| 1172 | // rotate by x,y so that uStart is (1.0) |
| 1173 | SkScalar x = SkPoint::DotProduct(uStart, uStop); |
| 1174 | SkScalar y = SkPoint::CrossProduct(uStart, uStop); |
| 1175 | |
| 1176 | SkScalar absX = SkScalarAbs(x); |
| 1177 | SkScalar absY = SkScalarAbs(y); |
| 1178 | |
| 1179 | int pointCount; |
| 1180 | |
| 1181 | // check for (effectively) coincident vectors |
| 1182 | // this can happen if our angle is nearly 0 or nearly 180 (y == 0) |
| 1183 | // ... we use the dot-prod to distinguish between 0 and 180 (x > 0) |
| 1184 | if (absY <= SK_ScalarNearlyZero && x > 0 && |
| 1185 | ((y >= 0 && kCW_SkRotationDirection == dir) || |
| 1186 | (y <= 0 && kCCW_SkRotationDirection == dir))) { |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 1187 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1188 | // just return the start-point |
| 1189 | quadPoints[0].set(SK_Scalar1, 0); |
| 1190 | pointCount = 1; |
| 1191 | } else { |
| 1192 | if (dir == kCCW_SkRotationDirection) |
| 1193 | y = -y; |
| 1194 | |
| 1195 | // what octant (quadratic curve) is [xy] in? |
| 1196 | int oct = 0; |
| 1197 | bool sameSign = true; |
| 1198 | |
| 1199 | if (0 == y) |
| 1200 | { |
| 1201 | oct = 4; // 180 |
| 1202 | SkASSERT(SkScalarAbs(x + SK_Scalar1) <= SK_ScalarNearlyZero); |
| 1203 | } |
| 1204 | else if (0 == x) |
| 1205 | { |
| 1206 | SkASSERT(absY - SK_Scalar1 <= SK_ScalarNearlyZero); |
| 1207 | if (y > 0) |
| 1208 | oct = 2; // 90 |
| 1209 | else |
| 1210 | oct = 6; // 270 |
| 1211 | } |
| 1212 | else |
| 1213 | { |
| 1214 | if (y < 0) |
| 1215 | oct += 4; |
| 1216 | if ((x < 0) != (y < 0)) |
| 1217 | { |
| 1218 | oct += 2; |
| 1219 | sameSign = false; |
| 1220 | } |
| 1221 | if ((absX < absY) == sameSign) |
| 1222 | oct += 1; |
| 1223 | } |
| 1224 | |
| 1225 | int wholeCount = oct << 1; |
| 1226 | memcpy(quadPoints, gQuadCirclePts, (wholeCount + 1) * sizeof(SkPoint)); |
| 1227 | |
| 1228 | const SkPoint* arc = &gQuadCirclePts[wholeCount]; |
robertphillips@google.com | e1b75b4 | 2013-07-09 15:03:59 +0000 | [diff] [blame] | 1229 | if (truncate_last_curve(arc, x, y, &quadPoints[wholeCount + 1])) |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1230 | { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 1231 | wholeCount += 2; |
| 1232 | } |
| 1233 | pointCount = wholeCount + 1; |
| 1234 | } |
| 1235 | |
| 1236 | // now handle counter-clockwise and the initial unitStart rotation |
| 1237 | SkMatrix matrix; |
| 1238 | matrix.setSinCos(uStart.fY, uStart.fX); |
| 1239 | if (dir == kCCW_SkRotationDirection) { |
| 1240 | matrix.preScale(SK_Scalar1, -SK_Scalar1); |
| 1241 | } |
| 1242 | if (userMatrix) { |
| 1243 | matrix.postConcat(*userMatrix); |
| 1244 | } |
| 1245 | matrix.mapPoints(quadPoints, pointCount); |
| 1246 | return pointCount; |
| 1247 | } |
reed@google.com | c518710 | 2013-04-12 19:11:10 +0000 | [diff] [blame] | 1248 | |
| 1249 | /////////////////////////////////////////////////////////////////////////////// |
| 1250 | |
reed@google.com | 17a2c91 | 2013-04-16 21:07:27 +0000 | [diff] [blame] | 1251 | // F = (A (1 - t)^2 + C t^2 + 2 B (1 - t) t w) |
| 1252 | // ------------------------------------------ |
| 1253 | // ((1 - t)^2 + t^2 + 2 (1 - t) t w) |
| 1254 | // |
| 1255 | // = {t^2 (P0 + P2 - 2 P1 w), t (-2 P0 + 2 P1 w), P0} |
| 1256 | // ------------------------------------------------ |
| 1257 | // {t^2 (2 - 2 w), t (-2 + 2 w), 1} |
| 1258 | // |
reed@google.com | 17a2c91 | 2013-04-16 21:07:27 +0000 | [diff] [blame] | 1259 | |
| 1260 | // Take the parametric specification for the conic (either X or Y) and return |
| 1261 | // in coeff[] the coefficients for the simple quadratic polynomial |
| 1262 | // coeff[0] for t^2 |
| 1263 | // coeff[1] for t |
| 1264 | // coeff[2] for constant term |
| 1265 | // |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1266 | 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] | 1267 | SkASSERT(src); |
| 1268 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
skia.committer@gmail.com | 45fb8b6 | 2013-04-17 07:00:56 +0000 | [diff] [blame] | 1269 | |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1270 | SkScalar src2w = SkScalarMul(src[2], w); |
| 1271 | SkScalar C = src[0]; |
| 1272 | SkScalar A = src[4] - 2 * src2w + C; |
| 1273 | SkScalar B = 2 * (src2w - C); |
| 1274 | SkScalar numer = SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C); |
skia.committer@gmail.com | 45fb8b6 | 2013-04-17 07:00:56 +0000 | [diff] [blame] | 1275 | |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1276 | B = 2 * (w - SK_Scalar1); |
| 1277 | C = SK_Scalar1; |
| 1278 | A = -B; |
| 1279 | SkScalar denom = SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C); |
skia.committer@gmail.com | 45fb8b6 | 2013-04-17 07:00:56 +0000 | [diff] [blame] | 1280 | |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1281 | return SkScalarDiv(numer, denom); |
| 1282 | } |
| 1283 | |
| 1284 | // F' = 2 (C t (1 + t (-1 + w)) - A (-1 + t) (t (-1 + w) - w) + B (1 - 2 t) w) |
| 1285 | // |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1286 | // t^2 : (2 P0 - 2 P2 - 2 P0 w + 2 P2 w) |
| 1287 | // t^1 : (-2 P0 + 2 P2 + 4 P0 w - 4 P1 w) |
| 1288 | // t^0 : -2 P0 w + 2 P1 w |
| 1289 | // |
| 1290 | // We disregard magnitude, so we can freely ignore the denominator of F', and |
| 1291 | // divide the numerator by 2 |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1292 | // |
reed@google.com | 17a2c91 | 2013-04-16 21:07:27 +0000 | [diff] [blame] | 1293 | // coeff[0] for t^2 |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1294 | // coeff[1] for t^1 |
| 1295 | // coeff[2] for t^0 |
reed@google.com | 17a2c91 | 2013-04-16 21:07:27 +0000 | [diff] [blame] | 1296 | // |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1297 | static void conic_deriv_coeff(const SkScalar src[], SkScalar w, SkScalar coeff[3]) { |
| 1298 | const SkScalar P20 = src[4] - src[0]; |
| 1299 | const SkScalar P10 = src[2] - src[0]; |
| 1300 | const SkScalar wP10 = w * P10; |
| 1301 | coeff[0] = w * P20 - P20; |
| 1302 | coeff[1] = P20 - 2 * wP10; |
| 1303 | coeff[2] = wP10; |
reed@google.com | 17a2c91 | 2013-04-16 21:07:27 +0000 | [diff] [blame] | 1304 | } |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1305 | |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1306 | 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] | 1307 | SkScalar coeff[3]; |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1308 | conic_deriv_coeff(coord, w, coeff); |
| 1309 | return t * (t * coeff[0] + coeff[1]) + coeff[2]; |
| 1310 | } |
| 1311 | |
| 1312 | static bool conic_find_extrema(const SkScalar src[], SkScalar w, SkScalar* t) { |
| 1313 | SkScalar coeff[3]; |
| 1314 | conic_deriv_coeff(src, w, coeff); |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1315 | |
| 1316 | SkScalar tValues[2]; |
| 1317 | int roots = SkFindUnitQuadRoots(coeff[0], coeff[1], coeff[2], tValues); |
| 1318 | SkASSERT(0 == roots || 1 == roots); |
skia.committer@gmail.com | 45fb8b6 | 2013-04-17 07:00:56 +0000 | [diff] [blame] | 1319 | |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1320 | if (1 == roots) { |
| 1321 | *t = tValues[0]; |
| 1322 | return true; |
| 1323 | } |
| 1324 | return false; |
| 1325 | } |
reed@google.com | 17a2c91 | 2013-04-16 21:07:27 +0000 | [diff] [blame] | 1326 | |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 1327 | struct SkP3D { |
| 1328 | SkScalar fX, fY, fZ; |
skia.committer@gmail.com | 4bb50b2 | 2013-04-13 07:01:15 +0000 | [diff] [blame] | 1329 | |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 1330 | void set(SkScalar x, SkScalar y, SkScalar z) { |
| 1331 | fX = x; fY = y; fZ = z; |
| 1332 | } |
skia.committer@gmail.com | 4bb50b2 | 2013-04-13 07:01:15 +0000 | [diff] [blame] | 1333 | |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 1334 | void projectDown(SkPoint* dst) const { |
| 1335 | dst->set(fX / fZ, fY / fZ); |
| 1336 | } |
| 1337 | }; |
| 1338 | |
| 1339 | // we just return the middle 3 points, since the first and last are dups of src |
| 1340 | // |
| 1341 | static void p3d_interp(const SkScalar src[3], SkScalar dst[3], SkScalar t) { |
| 1342 | SkScalar ab = SkScalarInterp(src[0], src[3], t); |
| 1343 | SkScalar bc = SkScalarInterp(src[3], src[6], t); |
| 1344 | dst[0] = ab; |
| 1345 | dst[3] = SkScalarInterp(ab, bc, t); |
| 1346 | dst[6] = bc; |
| 1347 | } |
| 1348 | |
| 1349 | static void ratquad_mapTo3D(const SkPoint src[3], SkScalar w, SkP3D dst[]) { |
| 1350 | dst[0].set(src[0].fX * 1, src[0].fY * 1, 1); |
| 1351 | dst[1].set(src[1].fX * w, src[1].fY * w, w); |
| 1352 | dst[2].set(src[2].fX * 1, src[2].fY * 1, 1); |
| 1353 | } |
| 1354 | |
reed@google.com | 24bd210 | 2013-05-07 20:42:35 +0000 | [diff] [blame] | 1355 | void SkConic::evalAt(SkScalar t, SkPoint* pt, SkVector* tangent) const { |
reed@google.com | c518710 | 2013-04-12 19:11:10 +0000 | [diff] [blame] | 1356 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
skia.committer@gmail.com | 4bb50b2 | 2013-04-13 07:01:15 +0000 | [diff] [blame] | 1357 | |
reed@google.com | c518710 | 2013-04-12 19:11:10 +0000 | [diff] [blame] | 1358 | if (pt) { |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1359 | pt->set(conic_eval_pos(&fPts[0].fX, fW, t), |
| 1360 | conic_eval_pos(&fPts[0].fY, fW, t)); |
reed@google.com | c518710 | 2013-04-12 19:11:10 +0000 | [diff] [blame] | 1361 | } |
reed@google.com | 24bd210 | 2013-05-07 20:42:35 +0000 | [diff] [blame] | 1362 | if (tangent) { |
| 1363 | tangent->set(conic_eval_tan(&fPts[0].fX, fW, t), |
| 1364 | conic_eval_tan(&fPts[0].fY, fW, t)); |
| 1365 | } |
reed@google.com | c518710 | 2013-04-12 19:11:10 +0000 | [diff] [blame] | 1366 | } |
| 1367 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1368 | void SkConic::chopAt(SkScalar t, SkConic dst[2]) const { |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 1369 | SkP3D tmp[3], tmp2[3]; |
| 1370 | |
| 1371 | ratquad_mapTo3D(fPts, fW, tmp); |
skia.committer@gmail.com | 4bb50b2 | 2013-04-13 07:01:15 +0000 | [diff] [blame] | 1372 | |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 1373 | p3d_interp(&tmp[0].fX, &tmp2[0].fX, t); |
| 1374 | p3d_interp(&tmp[0].fY, &tmp2[0].fY, t); |
| 1375 | p3d_interp(&tmp[0].fZ, &tmp2[0].fZ, t); |
skia.committer@gmail.com | 4bb50b2 | 2013-04-13 07:01:15 +0000 | [diff] [blame] | 1376 | |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 1377 | dst[0].fPts[0] = fPts[0]; |
| 1378 | tmp2[0].projectDown(&dst[0].fPts[1]); |
| 1379 | tmp2[1].projectDown(&dst[0].fPts[2]); dst[1].fPts[0] = dst[0].fPts[2]; |
| 1380 | tmp2[2].projectDown(&dst[1].fPts[1]); |
| 1381 | dst[1].fPts[2] = fPts[2]; |
| 1382 | |
mike@reedtribe.org | 4af6280 | 2013-04-13 10:51:51 +0000 | [diff] [blame] | 1383 | // to put in "standard form", where w0 and w2 are both 1, we compute the |
| 1384 | // new w1 as sqrt(w1*w1/w0*w2) |
| 1385 | // or |
| 1386 | // w1 /= sqrt(w0*w2) |
| 1387 | // |
| 1388 | // However, in our case, we know that for dst[0], w0 == 1, and for dst[1], w2 == 1 |
| 1389 | // |
| 1390 | SkScalar root = SkScalarSqrt(tmp2[1].fZ); |
| 1391 | dst[0].fW = tmp2[0].fZ / root; |
| 1392 | dst[1].fW = tmp2[2].fZ / root; |
reed@google.com | c518710 | 2013-04-12 19:11:10 +0000 | [diff] [blame] | 1393 | } |
mike@reedtribe.org | 8d55101 | 2013-04-14 02:40:50 +0000 | [diff] [blame] | 1394 | |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1395 | static SkScalar subdivide_w_value(SkScalar w) { |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1396 | return SkScalarSqrt(SK_ScalarHalf + w * SK_ScalarHalf); |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1397 | } |
| 1398 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1399 | void SkConic::chop(SkConic dst[2]) const { |
mike@reedtribe.org | 8d55101 | 2013-04-14 02:40:50 +0000 | [diff] [blame] | 1400 | SkScalar scale = SkScalarInvert(SK_Scalar1 + fW); |
| 1401 | SkScalar p1x = fW * fPts[1].fX; |
| 1402 | SkScalar p1y = fW * fPts[1].fY; |
| 1403 | SkScalar mx = (fPts[0].fX + 2 * p1x + fPts[2].fX) * scale * SK_ScalarHalf; |
| 1404 | SkScalar my = (fPts[0].fY + 2 * p1y + fPts[2].fY) * scale * SK_ScalarHalf; |
| 1405 | |
| 1406 | dst[0].fPts[0] = fPts[0]; |
| 1407 | dst[0].fPts[1].set((fPts[0].fX + p1x) * scale, |
| 1408 | (fPts[0].fY + p1y) * scale); |
| 1409 | dst[0].fPts[2].set(mx, my); |
| 1410 | |
| 1411 | dst[1].fPts[0].set(mx, my); |
| 1412 | dst[1].fPts[1].set((p1x + fPts[2].fX) * scale, |
| 1413 | (p1y + fPts[2].fY) * scale); |
| 1414 | dst[1].fPts[2] = fPts[2]; |
| 1415 | |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1416 | dst[0].fW = dst[1].fW = subdivide_w_value(fW); |
mike@reedtribe.org | 8d55101 | 2013-04-14 02:40:50 +0000 | [diff] [blame] | 1417 | } |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1418 | |
mike@reedtribe.org | 97514f2 | 2013-04-27 18:23:16 +0000 | [diff] [blame] | 1419 | /* |
| 1420 | * "High order approximation of conic sections by quadratic splines" |
| 1421 | * by Michael Floater, 1993 |
| 1422 | */ |
mike@reedtribe.org | af5c506 | 2013-04-30 02:14:58 +0000 | [diff] [blame] | 1423 | #define AS_QUAD_ERROR_SETUP \ |
| 1424 | SkScalar a = fW - 1; \ |
| 1425 | SkScalar k = a / (4 * (2 + a)); \ |
| 1426 | SkScalar x = k * (fPts[0].fX - 2 * fPts[1].fX + fPts[2].fX); \ |
| 1427 | SkScalar y = k * (fPts[0].fY - 2 * fPts[1].fY + fPts[2].fY); |
| 1428 | |
| 1429 | void SkConic::computeAsQuadError(SkVector* err) const { |
| 1430 | AS_QUAD_ERROR_SETUP |
| 1431 | err->set(x, y); |
| 1432 | } |
| 1433 | |
| 1434 | bool SkConic::asQuadTol(SkScalar tol) const { |
| 1435 | AS_QUAD_ERROR_SETUP |
| 1436 | return (x * x + y * y) <= tol * tol; |
mike@reedtribe.org | 97514f2 | 2013-04-27 18:23:16 +0000 | [diff] [blame] | 1437 | } |
| 1438 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1439 | int SkConic::computeQuadPOW2(SkScalar tol) const { |
mike@reedtribe.org | af5c506 | 2013-04-30 02:14:58 +0000 | [diff] [blame] | 1440 | AS_QUAD_ERROR_SETUP |
| 1441 | SkScalar error = SkScalarSqrt(x * x + y * y) - tol; |
| 1442 | |
| 1443 | if (error <= 0) { |
mike@reedtribe.org | 97514f2 | 2013-04-27 18:23:16 +0000 | [diff] [blame] | 1444 | return 0; |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1445 | } |
mike@reedtribe.org | 97514f2 | 2013-04-27 18:23:16 +0000 | [diff] [blame] | 1446 | uint32_t ierr = (uint32_t)error; |
mike@reedtribe.org | af5c506 | 2013-04-30 02:14:58 +0000 | [diff] [blame] | 1447 | return (34 - SkCLZ(ierr)) >> 1; |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1448 | } |
| 1449 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1450 | static SkPoint* subdivide(const SkConic& src, SkPoint pts[], int level) { |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1451 | SkASSERT(level >= 0); |
mike@reedtribe.org | af5c506 | 2013-04-30 02:14:58 +0000 | [diff] [blame] | 1452 | |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1453 | if (0 == level) { |
| 1454 | memcpy(pts, &src.fPts[1], 2 * sizeof(SkPoint)); |
| 1455 | return pts + 2; |
| 1456 | } else { |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1457 | SkConic dst[2]; |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1458 | src.chop(dst); |
| 1459 | --level; |
| 1460 | pts = subdivide(dst[0], pts, level); |
| 1461 | return subdivide(dst[1], pts, level); |
| 1462 | } |
| 1463 | } |
| 1464 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1465 | int SkConic::chopIntoQuadsPOW2(SkPoint pts[], int pow2) const { |
mike@reedtribe.org | af5c506 | 2013-04-30 02:14:58 +0000 | [diff] [blame] | 1466 | SkASSERT(pow2 >= 0); |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1467 | *pts = fPts[0]; |
reed@google.com | aebfa7e | 2013-04-15 15:23:38 +0000 | [diff] [blame] | 1468 | SkDEBUGCODE(SkPoint* endPts =) subdivide(*this, pts + 1, pow2); |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1469 | SkASSERT(endPts - pts == (2 * (1 << pow2) + 1)); |
| 1470 | return 1 << pow2; |
| 1471 | } |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1472 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1473 | bool SkConic::findXExtrema(SkScalar* t) const { |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1474 | return conic_find_extrema(&fPts[0].fX, fW, t); |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1475 | } |
| 1476 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1477 | bool SkConic::findYExtrema(SkScalar* t) const { |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1478 | return conic_find_extrema(&fPts[0].fY, fW, t); |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1479 | } |
| 1480 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1481 | bool SkConic::chopAtXExtrema(SkConic dst[2]) const { |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1482 | SkScalar t; |
| 1483 | if (this->findXExtrema(&t)) { |
| 1484 | this->chopAt(t, dst); |
| 1485 | // now clean-up the middle, since we know t was meant to be at |
| 1486 | // an X-extrema |
| 1487 | SkScalar value = dst[0].fPts[2].fX; |
| 1488 | dst[0].fPts[1].fX = value; |
| 1489 | dst[1].fPts[0].fX = value; |
| 1490 | dst[1].fPts[1].fX = value; |
| 1491 | return true; |
| 1492 | } |
| 1493 | return false; |
| 1494 | } |
| 1495 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1496 | bool SkConic::chopAtYExtrema(SkConic dst[2]) const { |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1497 | SkScalar t; |
| 1498 | if (this->findYExtrema(&t)) { |
| 1499 | this->chopAt(t, dst); |
| 1500 | // now clean-up the middle, since we know t was meant to be at |
| 1501 | // an Y-extrema |
| 1502 | SkScalar value = dst[0].fPts[2].fY; |
| 1503 | dst[0].fPts[1].fY = value; |
| 1504 | dst[1].fPts[0].fY = value; |
| 1505 | dst[1].fPts[1].fY = value; |
| 1506 | return true; |
| 1507 | } |
| 1508 | return false; |
| 1509 | } |
| 1510 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1511 | void SkConic::computeTightBounds(SkRect* bounds) const { |
mike@reedtribe.org | 5c082a1 | 2013-04-17 02:25:33 +0000 | [diff] [blame] | 1512 | SkPoint pts[4]; |
| 1513 | pts[0] = fPts[0]; |
| 1514 | pts[1] = fPts[2]; |
| 1515 | int count = 2; |
| 1516 | |
| 1517 | SkScalar t; |
| 1518 | if (this->findXExtrema(&t)) { |
| 1519 | this->evalAt(t, &pts[count++]); |
| 1520 | } |
| 1521 | if (this->findYExtrema(&t)) { |
| 1522 | this->evalAt(t, &pts[count++]); |
| 1523 | } |
| 1524 | bounds->set(pts, count); |
| 1525 | } |
| 1526 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1527 | void SkConic::computeFastBounds(SkRect* bounds) const { |
mike@reedtribe.org | 5c082a1 | 2013-04-17 02:25:33 +0000 | [diff] [blame] | 1528 | bounds->set(fPts, 3); |
| 1529 | } |