SkGeometry.cpp revision 8f4d2306fa866a26f9448048ff63f692b2ba43aa
1ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com 2ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com/* 3ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com * Copyright 2006 The Android Open Source Project 4ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com * 5ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com * Use of this source code is governed by a BSD-style license that can be 6ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com * found in the LICENSE file. 7ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com */ 8ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com 98a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#include "SkGeometry.h" 118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#include "Sk64.h" 128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#include "SkMatrix.h" 138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 142e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.orgbool SkXRayCrossesLine(const SkXRay& pt, const SkPoint pts[2], bool* ambiguous) { 152e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (ambiguous) { 162e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org *ambiguous = false; 172e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org } 18945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // Determine quick discards. 19945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // Consider query line going exactly through point 0 to not 20945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // intersect, for symmetry with SkXRayCrossesMonotonicCubic. 212e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (pt.fY == pts[0].fY) { 222e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (ambiguous) { 232e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org *ambiguous = true; 242e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org } 25945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com return false; 262e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org } 27945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com if (pt.fY < pts[0].fY && pt.fY < pts[1].fY) 28945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com return false; 29945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com if (pt.fY > pts[0].fY && pt.fY > pts[1].fY) 30945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com return false; 31945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com if (pt.fX > pts[0].fX && pt.fX > pts[1].fX) 32945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com return false; 33945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // Determine degenerate cases 34945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com if (SkScalarNearlyZero(pts[0].fY - pts[1].fY)) 35945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com return false; 362e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (SkScalarNearlyZero(pts[0].fX - pts[1].fX)) { 37945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // We've already determined the query point lies within the 38945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // vertical range of the line segment. 392e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (pt.fX <= pts[0].fX) { 402e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (ambiguous) { 412e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org *ambiguous = (pt.fY == pts[1].fY); 422e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org } 432e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org return true; 442e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org } 452e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org return false; 462e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org } 472e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org // Ambiguity check 482e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (pt.fY == pts[1].fY) { 492e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (pt.fX <= pts[1].fX) { 502e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (ambiguous) { 512e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org *ambiguous = true; 522e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org } 532e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org return true; 542e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org } 552e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org return false; 562e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org } 57945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // Full line segment evaluation 58945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkScalar delta_y = pts[1].fY - pts[0].fY; 59945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkScalar delta_x = pts[1].fX - pts[0].fX; 60945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkScalar slope = SkScalarDiv(delta_y, delta_x); 61945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkScalar b = pts[0].fY - SkScalarMul(slope, pts[0].fX); 62945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // Solve for x coordinate at y = pt.fY 63945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkScalar x = SkScalarDiv(pt.fY - b, slope); 64945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com return pt.fX <= x; 65945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com} 66945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com 678a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/** If defined, this makes eval_quad and eval_cubic do more setup (sometimes 688a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com involving integer multiplies by 2 or 3, but fewer calls to SkScalarMul. 698a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com May also introduce overflow of fixed when we compute our setup. 708a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 718f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.com// #define DIRECT_EVAL_OF_POLYNOMIALS 728a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 738a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com//////////////////////////////////////////////////////////////////////// 748a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 758f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.comstatic int is_not_monotonic(float a, float b, float c) { 768f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.com float ab = a - b; 778f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.com float bc = b - c; 788f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.com if (ab < 0) { 798f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.com bc = -bc; 808a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 818f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.com return ab == 0 || bc < 0; 828f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.com} 838a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 848a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com//////////////////////////////////////////////////////////////////////// 858a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 868a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic bool is_unit_interval(SkScalar x) 878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 888a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return x > 0 && x < SK_Scalar1; 898a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 908a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 918a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic int valid_unit_divide(SkScalar numer, SkScalar denom, SkScalar* ratio) 928a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 938a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(ratio); 948a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (numer < 0) 968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com numer = -numer; 988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com denom = -denom; 998a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 1008a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (denom == 0 || numer == 0 || numer >= denom) 1028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return 0; 1038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar r = SkScalarDiv(numer, denom); 10515161620bee33efcb706685486c9ce0fb51a72bbreed@android.com if (SkScalarIsNaN(r)) { 10615161620bee33efcb706685486c9ce0fb51a72bbreed@android.com return 0; 10715161620bee33efcb706685486c9ce0fb51a72bbreed@android.com } 1088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(r >= 0 && r < SK_Scalar1); 1098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (r == 0) // catch underflow if numer <<<< denom 1108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return 0; 1118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com *ratio = r; 1128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return 1; 1138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 1148a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1158a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/** From Numerical Recipes in C. 1168a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1178a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com Q = -1/2 (B + sign(B) sqrt[B*B - 4*A*C]) 1188a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com x1 = Q / A 1198a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com x2 = C / Q 1208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 1218a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comint SkFindUnitQuadRoots(SkScalar A, SkScalar B, SkScalar C, SkScalar roots[2]) 1228a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 1238a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(roots); 1248a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1258a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (A == 0) 1268a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return valid_unit_divide(-C, B, roots); 1278a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1288a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar* r = roots; 1298a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1308a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com float R = B*B - 4*A*C; 13115161620bee33efcb706685486c9ce0fb51a72bbreed@android.com if (R < 0 || SkScalarIsNaN(R)) { // complex roots 1328a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return 0; 13315161620bee33efcb706685486c9ce0fb51a72bbreed@android.com } 1348a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com R = sk_float_sqrt(R); 1358a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1368a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar Q = (B < 0) ? -(B-R)/2 : -(B+R)/2; 1378a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com r += valid_unit_divide(Q, A, r); 1388a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com r += valid_unit_divide(C, Q, r); 1398a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (r - roots == 2) 1408a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 1418a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (roots[0] > roots[1]) 1428a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkTSwap<SkScalar>(roots[0], roots[1]); 1438a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com else if (roots[0] == roots[1]) // nearly-equal? 1448a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com r -= 1; // skip the double root 1458a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 1468a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return (int)(r - roots); 1478a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 1488a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1498f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.com/////////////////////////////////////////////////////////////////////////////// 1508f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.com/////////////////////////////////////////////////////////////////////////////// 1518a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1528a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic SkScalar eval_quad(const SkScalar src[], SkScalar t) 1538a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 1548a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(src); 1558a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(t >= 0 && t <= SK_Scalar1); 1568a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1578a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#ifdef DIRECT_EVAL_OF_POLYNOMIALS 1588a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar C = src[0]; 1598a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar A = src[4] - 2 * src[2] + C; 1608a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar B = 2 * (src[2] - C); 1618a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C); 1628a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#else 1638a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar ab = SkScalarInterp(src[0], src[2], t); 164fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com SkScalar bc = SkScalarInterp(src[2], src[4], t); 1658a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return SkScalarInterp(ab, bc, t); 1668a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#endif 1678a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 1688a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1698a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic SkScalar eval_quad_derivative(const SkScalar src[], SkScalar t) 1708a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 1718a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar A = src[4] - 2 * src[2] + src[0]; 1728a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar B = src[2] - src[0]; 1738a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1748a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return 2 * SkScalarMulAdd(A, t, B); 1758a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 1768a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1778a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic SkScalar eval_quad_derivative_at_half(const SkScalar src[]) 1788a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 1798a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar A = src[4] - 2 * src[2] + src[0]; 1808a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar B = src[2] - src[0]; 1818a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return A + 2 * B; 1828a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 1838a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1848a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comvoid SkEvalQuadAt(const SkPoint src[3], SkScalar t, SkPoint* pt, SkVector* tangent) 1858a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 1868a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(src); 1878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(t >= 0 && t <= SK_Scalar1); 1888a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1898a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (pt) 1908a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com pt->set(eval_quad(&src[0].fX, t), eval_quad(&src[0].fY, t)); 1918a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (tangent) 1928a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com tangent->set(eval_quad_derivative(&src[0].fX, t), 1938a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com eval_quad_derivative(&src[0].fY, t)); 1948a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 1958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comvoid SkEvalQuadAtHalf(const SkPoint src[3], SkPoint* pt, SkVector* tangent) 1978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 1988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(src); 1998a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 2008a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (pt) 2018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 2028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar x01 = SkScalarAve(src[0].fX, src[1].fX); 2038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar y01 = SkScalarAve(src[0].fY, src[1].fY); 2048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar x12 = SkScalarAve(src[1].fX, src[2].fX); 2058a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar y12 = SkScalarAve(src[1].fY, src[2].fY); 2068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com pt->set(SkScalarAve(x01, x12), SkScalarAve(y01, y12)); 2078a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 2088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (tangent) 2098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com tangent->set(eval_quad_derivative_at_half(&src[0].fX), 2108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com eval_quad_derivative_at_half(&src[0].fY)); 2118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 2128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 2138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic void interp_quad_coords(const SkScalar* src, SkScalar* dst, SkScalar t) 2148a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 2158a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar ab = SkScalarInterp(src[0], src[2], t); 2168a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar bc = SkScalarInterp(src[2], src[4], t); 2178a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 2188a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[0] = src[0]; 2198a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[2] = ab; 2208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[4] = SkScalarInterp(ab, bc, t); 2218a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[6] = bc; 2228a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[8] = src[4]; 2238a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 2248a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 2258a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comvoid SkChopQuadAt(const SkPoint src[3], SkPoint dst[5], SkScalar t) 2268a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 2278a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(t > 0 && t < SK_Scalar1); 2288a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 2298a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com interp_quad_coords(&src[0].fX, &dst[0].fX, t); 2308a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com interp_quad_coords(&src[0].fY, &dst[0].fY, t); 2318a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 2328a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 2338a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comvoid SkChopQuadAtHalf(const SkPoint src[3], SkPoint dst[5]) 2348a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 2358a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar x01 = SkScalarAve(src[0].fX, src[1].fX); 2368a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar y01 = SkScalarAve(src[0].fY, src[1].fY); 2378a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar x12 = SkScalarAve(src[1].fX, src[2].fX); 2388a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar y12 = SkScalarAve(src[1].fY, src[2].fY); 2398a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 2408a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[0] = src[0]; 2418a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[1].set(x01, y01); 2428a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[2].set(SkScalarAve(x01, x12), SkScalarAve(y01, y12)); 2438a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[3].set(x12, y12); 2448a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[4] = src[2]; 2458a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 2468a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 2478a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/** Quad'(t) = At + B, where 2488a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com A = 2(a - 2b + c) 2498a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com B = 2(b - a) 2508a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com Solve for t, only if it fits between 0 < t < 1 2518a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 2528a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comint SkFindQuadExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar tValue[1]) 2538a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 2548a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com /* At + B == 0 2558a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com t = -B / A 2568a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com */ 2578a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return valid_unit_divide(a - b, a - b - b + c, tValue); 2588a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 2598a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 260fc25abdabff76f913fb9d4f373418c10a1eca92breed@android.comstatic inline void flatten_double_quad_extrema(SkScalar coords[14]) 2618a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 2628a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com coords[2] = coords[6] = coords[4]; 2638a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 2648a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 2658a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/* Returns 0 for 1 quad, and 1 for two quads, either way the answer is 26677f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com stored in dst[]. Guarantees that the 1/2 quads will be monotonic. 26777f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com */ 2688a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comint SkChopQuadAtYExtrema(const SkPoint src[3], SkPoint dst[5]) 2698a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 2708a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(src); 2718a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(dst); 272fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 2738a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#if 0 2748a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com static bool once = true; 2758a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (once) 2768a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 2778a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com once = false; 2788a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkPoint s[3] = { 0, 26398, 0, 26331, 0, 20621428 }; 2798a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkPoint d[6]; 280fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 2818a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com int n = SkChopQuadAtYExtrema(s, d); 2828a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 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); 2838a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 2848a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#endif 285fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 2868a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar a = src[0].fY; 2878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar b = src[1].fY; 2888a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar c = src[2].fY; 289fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 2908a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (is_not_monotonic(a, b, c)) 2918a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 2928a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar tValue; 2938a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (valid_unit_divide(a - b, a - b - b + c, &tValue)) 2948a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 2958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkChopQuadAt(src, dst, tValue); 2968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com flatten_double_quad_extrema(&dst[0].fY); 2978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return 1; 2988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 2998a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // if we get here, we need to force dst to be monotonic, even though 3008a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // we couldn't compute a unit_divide value (probably underflow). 3018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com b = SkScalarAbs(a - b) < SkScalarAbs(b - c) ? a : c; 3028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 3038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[0].set(src[0].fX, a); 3048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[1].set(src[1].fX, b); 3058a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[2].set(src[2].fX, c); 3068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return 0; 3078a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 3088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 30977f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com/* Returns 0 for 1 quad, and 1 for two quads, either way the answer is 31077f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com stored in dst[]. Guarantees that the 1/2 quads will be monotonic. 31177f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com */ 31277f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.comint SkChopQuadAtXExtrema(const SkPoint src[3], SkPoint dst[5]) 31377f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com{ 31477f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com SkASSERT(src); 31577f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com SkASSERT(dst); 316fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 31777f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com SkScalar a = src[0].fX; 31877f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com SkScalar b = src[1].fX; 31977f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com SkScalar c = src[2].fX; 320fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 32177f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com if (is_not_monotonic(a, b, c)) { 32277f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com SkScalar tValue; 32377f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com if (valid_unit_divide(a - b, a - b - b + c, &tValue)) { 32477f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com SkChopQuadAt(src, dst, tValue); 32577f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com flatten_double_quad_extrema(&dst[0].fX); 32677f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com return 1; 32777f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com } 32877f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com // if we get here, we need to force dst to be monotonic, even though 32977f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com // we couldn't compute a unit_divide value (probably underflow). 33077f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com b = SkScalarAbs(a - b) < SkScalarAbs(b - c) ? a : c; 33177f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com } 33277f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com dst[0].set(a, src[0].fY); 33377f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com dst[1].set(b, src[1].fY); 33477f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com dst[2].set(c, src[2].fY); 33577f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com return 0; 33677f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com} 33777f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com 3388a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// F(t) = a (1 - t) ^ 2 + 2 b t (1 - t) + c t ^ 2 3398a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// F'(t) = 2 (b - a) + 2 (a - 2b + c) t 3408a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// F''(t) = 2 (a - 2b + c) 3418a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// 3428a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// A = 2 (b - a) 3438a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// B = 2 (a - 2b + c) 3448a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// 3458a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// Maximum curvature for a quadratic means solving 3468a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// Fx' Fx'' + Fy' Fy'' = 0 3478a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// 3488a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// t = - (Ax Bx + Ay By) / (Bx ^ 2 + By ^ 2) 3498a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// 3505383a7525355dec72efa2083aeadffdd09a962b9egdaniel@google.comfloat SkFindQuadMaxCurvature(const SkPoint src[3]) { 3518a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar Ax = src[1].fX - src[0].fX; 3528a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar Ay = src[1].fY - src[0].fY; 3538a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar Bx = src[0].fX - src[1].fX - src[1].fX + src[2].fX; 3548a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar By = src[0].fY - src[1].fY - src[1].fY + src[2].fY; 3558a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar t = 0; // 0 means don't chop 3568a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 3578a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com (void)valid_unit_divide(-(Ax * Bx + Ay * By), Bx * Bx + By * By, &t); 3585383a7525355dec72efa2083aeadffdd09a962b9egdaniel@google.com return t; 3595383a7525355dec72efa2083aeadffdd09a962b9egdaniel@google.com} 3608a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 3615383a7525355dec72efa2083aeadffdd09a962b9egdaniel@google.comint SkChopQuadAtMaxCurvature(const SkPoint src[3], SkPoint dst[5]) 3625383a7525355dec72efa2083aeadffdd09a962b9egdaniel@google.com{ 3635383a7525355dec72efa2083aeadffdd09a962b9egdaniel@google.com SkScalar t = SkFindQuadMaxCurvature(src); 3645383a7525355dec72efa2083aeadffdd09a962b9egdaniel@google.com if (t == 0) { 3658a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com memcpy(dst, src, 3 * sizeof(SkPoint)); 3668a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return 1; 3675383a7525355dec72efa2083aeadffdd09a962b9egdaniel@google.com } else { 3688a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkChopQuadAt(src, dst, t); 3698a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return 2; 3708a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 3718a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 3728a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 3738f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.com#define SK_ScalarTwoThirds (0.666666666f) 3746fc321a18acc8c6437735007240eefe7054e83b0reed@google.com 3756fc321a18acc8c6437735007240eefe7054e83b0reed@google.comvoid SkConvertQuadToCubic(const SkPoint src[3], SkPoint dst[4]) { 3766fc321a18acc8c6437735007240eefe7054e83b0reed@google.com const SkScalar scale = SK_ScalarTwoThirds; 3776fc321a18acc8c6437735007240eefe7054e83b0reed@google.com dst[0] = src[0]; 3786fc321a18acc8c6437735007240eefe7054e83b0reed@google.com dst[1].set(src[0].fX + SkScalarMul(src[1].fX - src[0].fX, scale), 3796fc321a18acc8c6437735007240eefe7054e83b0reed@google.com src[0].fY + SkScalarMul(src[1].fY - src[0].fY, scale)); 3806fc321a18acc8c6437735007240eefe7054e83b0reed@google.com dst[2].set(src[2].fX + SkScalarMul(src[1].fX - src[2].fX, scale), 3816fc321a18acc8c6437735007240eefe7054e83b0reed@google.com src[2].fY + SkScalarMul(src[1].fY - src[2].fY, scale)); 3826fc321a18acc8c6437735007240eefe7054e83b0reed@google.com dst[3] = src[2]; 383945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com} 384945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com 3858a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com//////////////////////////////////////////////////////////////////////////////////////// 3868a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com///// CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS ///// 3878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com//////////////////////////////////////////////////////////////////////////////////////// 3888a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 3898a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic void get_cubic_coeff(const SkScalar pt[], SkScalar coeff[4]) 3908a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 3918a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com coeff[0] = pt[6] + 3*(pt[2] - pt[4]) - pt[0]; 3928a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com coeff[1] = 3*(pt[4] - pt[2] - pt[2] + pt[0]); 3938a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com coeff[2] = 3*(pt[2] - pt[0]); 3948a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com coeff[3] = pt[0]; 3958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 3968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 3978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comvoid SkGetCubicCoeff(const SkPoint pts[4], SkScalar cx[4], SkScalar cy[4]) 3988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 3998a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(pts); 4008a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (cx) 4028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com get_cubic_coeff(&pts[0].fX, cx); 4038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (cy) 4048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com get_cubic_coeff(&pts[0].fY, cy); 4058a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 4068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4078a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic SkScalar eval_cubic(const SkScalar src[], SkScalar t) 4088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 4098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(src); 4108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(t >= 0 && t <= SK_Scalar1); 4118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (t == 0) 4138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return src[0]; 4148a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4158a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#ifdef DIRECT_EVAL_OF_POLYNOMIALS 4168a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar D = src[0]; 4178a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar A = src[6] + 3*(src[2] - src[4]) - D; 4188a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar B = 3*(src[4] - src[2] - src[2] + D); 4198a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar C = 3*(src[2] - D); 4208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4218a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return SkScalarMulAdd(SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C), t, D); 4228a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#else 4238a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar ab = SkScalarInterp(src[0], src[2], t); 4248a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar bc = SkScalarInterp(src[2], src[4], t); 4258a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar cd = SkScalarInterp(src[4], src[6], t); 4268a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar abc = SkScalarInterp(ab, bc, t); 4278a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar bcd = SkScalarInterp(bc, cd, t); 4288a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return SkScalarInterp(abc, bcd, t); 4298a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#endif 4308a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 4318a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4328a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/** return At^2 + Bt + C 4338a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 4348a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic SkScalar eval_quadratic(SkScalar A, SkScalar B, SkScalar C, SkScalar t) 4358a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 4368a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(t >= 0 && t <= SK_Scalar1); 4378a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4388a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C); 4398a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 4408a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4418a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic SkScalar eval_cubic_derivative(const SkScalar src[], SkScalar t) 4428a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 4438a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar A = src[6] + 3*(src[2] - src[4]) - src[0]; 4448a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar B = 2*(src[4] - 2 * src[2] + src[0]); 4458a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar C = src[2] - src[0]; 4468a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4478a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return eval_quadratic(A, B, C, t); 4488a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 4498a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4508a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic SkScalar eval_cubic_2ndDerivative(const SkScalar src[], SkScalar t) 4518a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 4528a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar A = src[6] + 3*(src[2] - src[4]) - src[0]; 4538a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar B = src[4] - 2 * src[2] + src[0]; 4548a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4558a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return SkScalarMulAdd(A, t, B); 4568a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 4578a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4588a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comvoid SkEvalCubicAt(const SkPoint src[4], SkScalar t, SkPoint* loc, SkVector* tangent, SkVector* curvature) 4598a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 4608a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(src); 4618a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(t >= 0 && t <= SK_Scalar1); 4628a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4638a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (loc) 4648a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com loc->set(eval_cubic(&src[0].fX, t), eval_cubic(&src[0].fY, t)); 4658a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (tangent) 4668a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com tangent->set(eval_cubic_derivative(&src[0].fX, t), 4678a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com eval_cubic_derivative(&src[0].fY, t)); 4688a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (curvature) 4698a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com curvature->set(eval_cubic_2ndDerivative(&src[0].fX, t), 4708a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com eval_cubic_2ndDerivative(&src[0].fY, t)); 4718a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 4728a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4738a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/** Cubic'(t) = At^2 + Bt + C, where 4748a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com A = 3(-a + 3(b - c) + d) 4758a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com B = 6(a - 2b + c) 4768a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com C = 3(b - a) 4778a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com Solve for t, keeping only those that fit betwee 0 < t < 1 4788a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 4798a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comint SkFindCubicExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar d, SkScalar tValues[2]) 4808a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 4818a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // we divide A,B,C by 3 to simplify 4828a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar A = d - a + 3*(b - c); 4838a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar B = 2*(a - b - b + c); 4848a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar C = b - a; 4858a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4868a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return SkFindUnitQuadRoots(A, B, C, tValues); 4878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 4888a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4898a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic void interp_cubic_coords(const SkScalar* src, SkScalar* dst, SkScalar t) 4908a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 4918a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar ab = SkScalarInterp(src[0], src[2], t); 4928a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar bc = SkScalarInterp(src[2], src[4], t); 4938a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar cd = SkScalarInterp(src[4], src[6], t); 4948a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar abc = SkScalarInterp(ab, bc, t); 4958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar bcd = SkScalarInterp(bc, cd, t); 4968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar abcd = SkScalarInterp(abc, bcd, t); 4978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[0] = src[0]; 4998a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[2] = ab; 5008a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[4] = abc; 5018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[6] = abcd; 5028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[8] = bcd; 5038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[10] = cd; 5048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[12] = src[6]; 5058a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 5068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 5078a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comvoid SkChopCubicAt(const SkPoint src[4], SkPoint dst[7], SkScalar t) 5088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 5098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(t > 0 && t < SK_Scalar1); 5108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 5118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com interp_cubic_coords(&src[0].fX, &dst[0].fX, t); 5128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com interp_cubic_coords(&src[0].fY, &dst[0].fY, t); 5138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 5148a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 515a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com/* http://code.google.com/p/skia/issues/detail?id=32 516fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 517a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com This test code would fail when we didn't check the return result of 518a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com valid_unit_divide in SkChopCubicAt(... tValues[], int roots). The reason is 519a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com that after the first chop, the parameters to valid_unit_divide are equal 520a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com (thanks to finite float precision and rounding in the subtracts). Thus 521a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com even though the 2nd tValue looks < 1.0, after we renormalize it, we end 522a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com up with 1.0, hence the need to check and just return the last cubic as 523a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com a degenerate clump of 4 points in the sampe place. 524a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com 525a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com static void test_cubic() { 526a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com SkPoint src[4] = { 527a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com { 556.25000, 523.03003 }, 528a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com { 556.23999, 522.96002 }, 529a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com { 556.21997, 522.89001 }, 530a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com { 556.21997, 522.82001 } 531a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com }; 532a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com SkPoint dst[10]; 533a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com SkScalar tval[] = { 0.33333334f, 0.99999994f }; 534a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com SkChopCubicAt(src, dst, tval, 2); 535a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com } 536a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com */ 537a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com 5388a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comvoid SkChopCubicAt(const SkPoint src[4], SkPoint dst[], const SkScalar tValues[], int roots) 5398a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 5408a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#ifdef SK_DEBUG 5418a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 5428a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com for (int i = 0; i < roots - 1; i++) 5438a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 5448a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(is_unit_interval(tValues[i])); 5458a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(is_unit_interval(tValues[i+1])); 5468a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(tValues[i] < tValues[i+1]); 5478a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 5488a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 5498a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#endif 5508a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 5518a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (dst) 5528a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 5538a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (roots == 0) // nothing to chop 5548a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com memcpy(dst, src, 4*sizeof(SkPoint)); 5558a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com else 5568a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 5578a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar t = tValues[0]; 5588a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkPoint tmp[4]; 5598a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 5608a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com for (int i = 0; i < roots; i++) 5618a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 5628a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkChopCubicAt(src, dst, t); 5638a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (i == roots - 1) 5648a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com break; 5658a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 5668a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst += 3; 567a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com // have src point to the remaining cubic (after the chop) 5688a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com memcpy(tmp, dst, 4 * sizeof(SkPoint)); 5698a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com src = tmp; 570a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com 571a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com // watch out in case the renormalized t isn't in range 572a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com if (!valid_unit_divide(tValues[i+1] - tValues[i], 573a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com SK_Scalar1 - tValues[i], &t)) { 574a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com // if we can't, just create a degenerate cubic 575a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com dst[4] = dst[5] = dst[6] = src[3]; 576a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com break; 577a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com } 5788a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 5798a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 5808a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 5818a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 5828a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 5838a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comvoid SkChopCubicAtHalf(const SkPoint src[4], SkPoint dst[7]) 5848a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 5858a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar x01 = SkScalarAve(src[0].fX, src[1].fX); 5868a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar y01 = SkScalarAve(src[0].fY, src[1].fY); 5878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar x12 = SkScalarAve(src[1].fX, src[2].fX); 5888a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar y12 = SkScalarAve(src[1].fY, src[2].fY); 5898a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar x23 = SkScalarAve(src[2].fX, src[3].fX); 5908a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar y23 = SkScalarAve(src[2].fY, src[3].fY); 5918a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 5928a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar x012 = SkScalarAve(x01, x12); 5938a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar y012 = SkScalarAve(y01, y12); 5948a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar x123 = SkScalarAve(x12, x23); 5958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar y123 = SkScalarAve(y12, y23); 5968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 5978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[0] = src[0]; 5988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[1].set(x01, y01); 5998a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[2].set(x012, y012); 6008a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[3].set(SkScalarAve(x012, x123), SkScalarAve(y012, y123)); 6018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[4].set(x123, y123); 6028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[5].set(x23, y23); 6038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[6] = src[3]; 6048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 6058a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 6068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic void flatten_double_cubic_extrema(SkScalar coords[14]) 6078a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 6088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com coords[4] = coords[8] = coords[6]; 6098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 6108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 6118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/** Given 4 points on a cubic bezier, chop it into 1, 2, 3 beziers such that 6128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com the resulting beziers are monotonic in Y. This is called by the scan converter. 6138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com Depending on what is returned, dst[] is treated as follows 6148a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 0 dst[0..3] is the original cubic 6158a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1 dst[0..3] and dst[3..6] are the two new cubics 6168a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 2 dst[0..3], dst[3..6], dst[6..9] are the three new cubics 6178a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com If dst == null, it is ignored and only the count is returned. 6188a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 619bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.comint SkChopCubicAtYExtrema(const SkPoint src[4], SkPoint dst[10]) { 6208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar tValues[2]; 621bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com int roots = SkFindCubicExtrema(src[0].fY, src[1].fY, src[2].fY, 622bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com src[3].fY, tValues); 623fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 6248a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkChopCubicAt(src, dst, tValues, roots); 625bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com if (dst && roots > 0) { 6268a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // we do some cleanup to ensure our Y extrema are flat 6278a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com flatten_double_cubic_extrema(&dst[0].fY); 628bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com if (roots == 2) { 6298a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com flatten_double_cubic_extrema(&dst[3].fY); 630bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com } 631bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com } 632bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com return roots; 633bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com} 634bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com 635bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.comint SkChopCubicAtXExtrema(const SkPoint src[4], SkPoint dst[10]) { 636bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com SkScalar tValues[2]; 637bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com int roots = SkFindCubicExtrema(src[0].fX, src[1].fX, src[2].fX, 638bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com src[3].fX, tValues); 639fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 640bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com SkChopCubicAt(src, dst, tValues, roots); 641bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com if (dst && roots > 0) { 642bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com // we do some cleanup to ensure our Y extrema are flat 643bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com flatten_double_cubic_extrema(&dst[0].fX); 644bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com if (roots == 2) { 645bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com flatten_double_cubic_extrema(&dst[3].fX); 646bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com } 6478a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 6488a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return roots; 6498a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 6508a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 6518a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/** http://www.faculty.idc.ac.il/arik/quality/appendixA.html 6528a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 6538a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com Inflection means that curvature is zero. 6548a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com Curvature is [F' x F''] / [F'^3] 6558a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com So we solve F'x X F''y - F'y X F''y == 0 6568a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com After some canceling of the cubic term, we get 6578a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com A = b - a 6588a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com B = c - 2b + a 6598a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com C = d - 3c + 3b - a 6608a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com (BxCy - ByCx)t^2 + (AxCy - AyCx)t + AxBy - AyBx == 0 6618a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 6628a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comint SkFindCubicInflections(const SkPoint src[4], SkScalar tValues[]) 6638a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 6648a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar Ax = src[1].fX - src[0].fX; 6658a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar Ay = src[1].fY - src[0].fY; 6668a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar Bx = src[2].fX - 2 * src[1].fX + src[0].fX; 6678a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar By = src[2].fY - 2 * src[1].fY + src[0].fY; 6688a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar Cx = src[3].fX + 3 * (src[1].fX - src[2].fX) - src[0].fX; 6698a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar Cy = src[3].fY + 3 * (src[1].fY - src[2].fY) - src[0].fY; 6708a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 6718f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.com return SkFindUnitQuadRoots(Bx*Cy - By*Cx, Ax*Cy - Ay*Cx, Ax*By - Ay*Bx, tValues); 6728a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 6738a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 6748a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comint SkChopCubicAtInflections(const SkPoint src[], SkPoint dst[10]) 6758a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 6768a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar tValues[2]; 6778a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com int count = SkFindCubicInflections(src, tValues); 6788a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 6798a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (dst) 6808a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 6818a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (count == 0) 6828a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com memcpy(dst, src, 4 * sizeof(SkPoint)); 6838a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com else 6848a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkChopCubicAt(src, dst, tValues, count); 6858a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 6868a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return count + 1; 6878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 6888a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 6898a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comtemplate <typename T> void bubble_sort(T array[], int count) 6908a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 6918a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com for (int i = count - 1; i > 0; --i) 6928a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com for (int j = i; j > 0; --j) 6938a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (array[j] < array[j-1]) 6948a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 6958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com T tmp(array[j]); 6968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com array[j] = array[j-1]; 6978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com array[j-1] = tmp; 6988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 6998a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 7008a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 7018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// newton refinement 7028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#if 0 7038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic SkScalar refine_cubic_root(const SkFP coeff[4], SkScalar root) 7048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 7058a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // x1 = x0 - f(t) / f'(t) 7068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 7078a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkFP T = SkScalarToFloat(root); 7088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkFP N, D; 7098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 7108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // f' = 3*coeff[0]*T^2 + 2*coeff[1]*T + coeff[2] 7118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com D = SkFPMul(SkFPMul(coeff[0], SkFPMul(T,T)), 3); 7128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com D = SkFPAdd(D, SkFPMulInt(SkFPMul(coeff[1], T), 2)); 7138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com D = SkFPAdd(D, coeff[2]); 7148a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 7158a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (D == 0) 7168a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return root; 7178a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 7188a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // f = coeff[0]*T^3 + coeff[1]*T^2 + coeff[2]*T + coeff[3] 7198a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com N = SkFPMul(SkFPMul(SkFPMul(T, T), T), coeff[0]); 7208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com N = SkFPAdd(N, SkFPMul(SkFPMul(T, T), coeff[1])); 7218a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com N = SkFPAdd(N, SkFPMul(T, coeff[2])); 7228a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com N = SkFPAdd(N, coeff[3]); 7238a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 7248a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (N) 7258a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 7268a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar delta = SkFPToScalar(SkFPDiv(N, D)); 7278a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 7288a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (delta) 7298a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com root -= delta; 7308a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 7318a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return root; 7328a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 7338a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#endif 7348a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 735087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com/** 736087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com * Given an array and count, remove all pair-wise duplicates from the array, 737087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com * keeping the existing sorting, and return the new count 738087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com */ 739087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.comstatic int collaps_duplicates(float array[], int count) { 740087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com for (int n = count; n > 1; --n) { 741087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com if (array[0] == array[1]) { 742087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com for (int i = 1; i < n; ++i) { 743087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com array[i - 1] = array[i]; 744087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com } 745087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com count -= 1; 746087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com } else { 747087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com array += 1; 748087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com } 749087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com } 750087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com return count; 751087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com} 752087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com 753087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com#ifdef SK_DEBUG 754087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com 755087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com#define TEST_COLLAPS_ENTRY(array) array, SK_ARRAY_COUNT(array) 756087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com 757087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.comstatic void test_collaps_duplicates() { 758087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com static bool gOnce; 759087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com if (gOnce) { return; } 760087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com gOnce = true; 761087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com const float src0[] = { 0 }; 762087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com const float src1[] = { 0, 0 }; 763087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com const float src2[] = { 0, 1 }; 764087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com const float src3[] = { 0, 0, 0 }; 765087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com const float src4[] = { 0, 0, 1 }; 766087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com const float src5[] = { 0, 1, 1 }; 767087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com const float src6[] = { 0, 1, 2 }; 768087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com const struct { 769087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com const float* fData; 770087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com int fCount; 771087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com int fCollapsedCount; 772087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com } data[] = { 773087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com { TEST_COLLAPS_ENTRY(src0), 1 }, 774087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com { TEST_COLLAPS_ENTRY(src1), 1 }, 775087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com { TEST_COLLAPS_ENTRY(src2), 2 }, 776087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com { TEST_COLLAPS_ENTRY(src3), 1 }, 777087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com { TEST_COLLAPS_ENTRY(src4), 2 }, 778087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com { TEST_COLLAPS_ENTRY(src5), 2 }, 779087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com { TEST_COLLAPS_ENTRY(src6), 3 }, 780087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com }; 781087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com for (size_t i = 0; i < SK_ARRAY_COUNT(data); ++i) { 782087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com float dst[3]; 783087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com memcpy(dst, data[i].fData, data[i].fCount * sizeof(dst[0])); 784087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com int count = collaps_duplicates(dst, data[i].fCount); 785087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com SkASSERT(data[i].fCollapsedCount == count); 786087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com for (int j = 1; j < count; ++j) { 787087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com SkASSERT(dst[j-1] < dst[j]); 788087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com } 789087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com } 790087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com} 791087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com#endif 792087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com 7933c12840b234e614faf569e80f311a77ce65d9fe0reed@google.comstatic SkScalar SkScalarCubeRoot(SkScalar x) { 7943c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com return sk_float_pow(x, 0.3333333f); 7953c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com} 7963c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com 7978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/* Solve coeff(t) == 0, returning the number of roots that 7988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com lie withing 0 < t < 1. 7998a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com coeff[0]t^3 + coeff[1]t^2 + coeff[2]t + coeff[3] 800fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 801087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com Eliminates repeated roots (so that all tValues are distinct, and are always 802087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com in increasing order. 8038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 8043c12840b234e614faf569e80f311a77ce65d9fe0reed@google.comstatic int solve_cubic_polynomial(const SkScalar coeff[4], SkScalar tValues[3]) 8058a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 8068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (SkScalarNearlyZero(coeff[0])) // we're just a quadratic 8078a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 8088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return SkFindUnitQuadRoots(coeff[1], coeff[2], coeff[3], tValues); 8098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 8108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8113c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com SkScalar a, b, c, Q, R; 8128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 8148a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(coeff[0] != 0); 8158a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8163c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com SkScalar inva = SkScalarInvert(coeff[0]); 8173c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com a = coeff[1] * inva; 8183c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com b = coeff[2] * inva; 8193c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com c = coeff[3] * inva; 8208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 8213c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com Q = (a*a - b*3) / 9; 8223c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com R = (2*a*a*a - 9*a*b + 27*c) / 54; 8238a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8243c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com SkScalar Q3 = Q * Q * Q; 8253c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com SkScalar R2MinusQ3 = R * R - Q3; 8263c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com SkScalar adiv3 = a / 3; 8278a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8288a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar* roots = tValues; 8298a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar r; 8308a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8313c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com if (R2MinusQ3 < 0) // we have 3 real roots 8328a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 8338a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com float theta = sk_float_acos(R / sk_float_sqrt(Q3)); 8348a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com float neg2RootQ = -2 * sk_float_sqrt(Q); 8358a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8368a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com r = neg2RootQ * sk_float_cos(theta/3) - adiv3; 8378a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (is_unit_interval(r)) 8388a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com *roots++ = r; 8398a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8408a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com r = neg2RootQ * sk_float_cos((theta + 2*SK_ScalarPI)/3) - adiv3; 8418a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (is_unit_interval(r)) 8428a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com *roots++ = r; 8438a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8448a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com r = neg2RootQ * sk_float_cos((theta - 2*SK_ScalarPI)/3) - adiv3; 8458a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (is_unit_interval(r)) 8468a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com *roots++ = r; 8478a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 848087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com SkDEBUGCODE(test_collaps_duplicates();) 849087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com 8508a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // now sort the roots 851087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com int count = (int)(roots - tValues); 852087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com SkASSERT((unsigned)count <= 3); 853087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com bubble_sort(tValues, count); 854087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com count = collaps_duplicates(tValues, count); 855087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com roots = tValues + count; // so we compute the proper count below 8568a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 8578a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com else // we have 1 real root 8588a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 8593c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com SkScalar A = SkScalarAbs(R) + SkScalarSqrt(R2MinusQ3); 8603c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com A = SkScalarCubeRoot(A); 8613c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com if (R > 0) 8623c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com A = -A; 8638a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8648a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (A != 0) 8653c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com A += Q / A; 8663c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com r = A - adiv3; 8678a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (is_unit_interval(r)) 8688a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com *roots++ = r; 8698a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 8708a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8718a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return (int)(roots - tValues); 8728a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 8738a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8748a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/* Looking for F' dot F'' == 0 875fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 8768a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com A = b - a 8778a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com B = c - 2b + a 8788a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com C = d - 3c + 3b - a 8798a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8808a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com F' = 3Ct^2 + 6Bt + 3A 8818a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com F'' = 6Ct + 6B 8828a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8838a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB 8848a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 8853c12840b234e614faf569e80f311a77ce65d9fe0reed@google.comstatic void formulate_F1DotF2(const SkScalar src[], SkScalar coeff[4]) 8868a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 8878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar a = src[2] - src[0]; 8888a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar b = src[4] - 2 * src[2] + src[0]; 8898a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar c = src[6] + 3 * (src[2] - src[4]) - src[0]; 8908a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8913c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com coeff[0] = c * c; 8923c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com coeff[1] = 3 * b * c; 8933c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com coeff[2] = 2 * b * b + c * a; 8943c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com coeff[3] = a * b; 8958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 8968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// EXPERIMENTAL: can set this to zero to accept all t-values 0 < t < 1 8988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com//#define kMinTValueForChopping (SK_Scalar1 / 256) 8998a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#define kMinTValueForChopping 0 9008a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/* Looking for F' dot F'' == 0 902fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 9038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com A = b - a 9048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com B = c - 2b + a 9058a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com C = d - 3c + 3b - a 9068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9078a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com F' = 3Ct^2 + 6Bt + 3A 9088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com F'' = 6Ct + 6B 9098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB 9118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 9128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comint SkFindCubicMaxCurvature(const SkPoint src[4], SkScalar tValues[3]) 9138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 9143c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com SkScalar coeffX[4], coeffY[4]; 9153c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com int i; 9168a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9178a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com formulate_F1DotF2(&src[0].fX, coeffX); 9188a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com formulate_F1DotF2(&src[0].fY, coeffY); 9198a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com for (i = 0; i < 4; i++) 9213c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com coeffX[i] += coeffY[i]; 9228a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9238a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar t[3]; 9248a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com int count = solve_cubic_polynomial(coeffX, t); 9258a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com int maxCount = 0; 9268a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9278a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // now remove extrema where the curvature is zero (mins) 9288a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // !!!! need a test for this !!!! 9298a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com for (i = 0; i < count; i++) 9308a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 9318a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // if (not_min_curvature()) 9328a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (t[i] > kMinTValueForChopping && t[i] < SK_Scalar1 - kMinTValueForChopping) 9338a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com tValues[maxCount++] = t[i]; 9348a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 9358a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return maxCount; 9368a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 9378a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9388a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comint SkChopCubicAtMaxCurvature(const SkPoint src[4], SkPoint dst[13], SkScalar tValues[3]) 9398a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 9408a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar t_storage[3]; 9418a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9428a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (tValues == NULL) 9438a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com tValues = t_storage; 9448a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9458a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com int count = SkFindCubicMaxCurvature(src, tValues); 9468a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9475383a7525355dec72efa2083aeadffdd09a962b9egdaniel@google.com if (dst) { 9488a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (count == 0) 9498a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com memcpy(dst, src, 4 * sizeof(SkPoint)); 9508a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com else 9518a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkChopCubicAt(src, dst, tValues, count); 9528a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 9538a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return count + 1; 9548a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 9558a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9562e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.orgbool SkXRayCrossesMonotonicCubic(const SkXRay& pt, const SkPoint cubic[4], bool* ambiguous) { 9572e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (ambiguous) { 9582e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org *ambiguous = false; 9592e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org } 9602e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org 961945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // Find the minimum and maximum y of the extrema, which are the 962945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // first and last points since this cubic is monotonic 963945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkScalar min_y = SkMinScalar(cubic[0].fY, cubic[3].fY); 964945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkScalar max_y = SkMaxScalar(cubic[0].fY, cubic[3].fY); 965945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com 966945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com if (pt.fY == cubic[0].fY 967945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com || pt.fY < min_y 968945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com || pt.fY > max_y) { 969945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // The query line definitely does not cross the curve 9702e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (ambiguous) { 9712e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org *ambiguous = (pt.fY == cubic[0].fY); 9722e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org } 973945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com return false; 974945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com } 975945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com 9762e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org bool pt_at_extremum = (pt.fY == cubic[3].fY); 9772e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org 978945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkScalar min_x = 979945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkMinScalar( 980945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkMinScalar( 981945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkMinScalar(cubic[0].fX, cubic[1].fX), 982945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com cubic[2].fX), 983945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com cubic[3].fX); 984945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com if (pt.fX < min_x) { 985945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // The query line definitely crosses the curve 9862e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (ambiguous) { 9872e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org *ambiguous = pt_at_extremum; 9882e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org } 989945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com return true; 990945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com } 991945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com 992945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkScalar max_x = 993945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkMaxScalar( 994945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkMaxScalar( 995945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkMaxScalar(cubic[0].fX, cubic[1].fX), 996945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com cubic[2].fX), 997945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com cubic[3].fX); 998945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com if (pt.fX > max_x) { 999945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // The query line definitely does not cross the curve 1000945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com return false; 1001945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com } 1002945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com 1003945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // Do a binary search to find the parameter value which makes y as 1004945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // close as possible to the query point. See whether the query 1005945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // line's origin is to the left of the associated x coordinate. 1006945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com 1007945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // kMaxIter is chosen as the number of mantissa bits for a float, 1008945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // since there's no way we are going to get more precision by 1009945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // iterating more times than that. 1010945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com const int kMaxIter = 23; 1011945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkPoint eval; 1012945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com int iter = 0; 1013945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkScalar upper_t; 1014945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkScalar lower_t; 1015945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // Need to invert direction of t parameter if cubic goes up 1016945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com // instead of down 1017945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com if (cubic[3].fY > cubic[0].fY) { 1018945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com upper_t = SK_Scalar1; 10194b413c8bb123e42ca4b9c7bfa6bc2167283cb84ccommit-bot@chromium.org lower_t = 0; 1020945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com } else { 10214b413c8bb123e42ca4b9c7bfa6bc2167283cb84ccommit-bot@chromium.org upper_t = 0; 1022945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com lower_t = SK_Scalar1; 1023945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com } 1024945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com do { 1025945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkScalar t = SkScalarAve(upper_t, lower_t); 1026945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkEvalCubicAt(cubic, t, &eval, NULL, NULL); 1027945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com if (pt.fY > eval.fY) { 1028945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com lower_t = t; 1029945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com } else { 1030945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com upper_t = t; 1031945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com } 1032945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com } while (++iter < kMaxIter 1033945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com && !SkScalarNearlyZero(eval.fY - pt.fY)); 1034945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com if (pt.fX <= eval.fX) { 10352e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (ambiguous) { 10362e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org *ambiguous = pt_at_extremum; 10372e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org } 1038945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com return true; 1039945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com } 1040945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com return false; 1041945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com} 1042945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com 10432e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.orgint SkNumXRayCrossingsForCubic(const SkXRay& pt, const SkPoint cubic[4], bool* ambiguous) { 1044945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com int num_crossings = 0; 1045945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com SkPoint monotonic_cubics[10]; 1046945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com int num_monotonic_cubics = SkChopCubicAtYExtrema(cubic, monotonic_cubics); 10472e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (ambiguous) { 10482e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org *ambiguous = false; 10492e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org } 10502e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org bool locally_ambiguous; 10512e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (SkXRayCrossesMonotonicCubic(pt, &monotonic_cubics[0], &locally_ambiguous)) 1052945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com ++num_crossings; 10532e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (ambiguous) { 10542e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org *ambiguous |= locally_ambiguous; 10552e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org } 1056945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com if (num_monotonic_cubics > 0) 10572e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (SkXRayCrossesMonotonicCubic(pt, &monotonic_cubics[3], &locally_ambiguous)) 1058945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com ++num_crossings; 10592e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (ambiguous) { 10602e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org *ambiguous |= locally_ambiguous; 10612e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org } 1062945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com if (num_monotonic_cubics > 1) 10632e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (SkXRayCrossesMonotonicCubic(pt, &monotonic_cubics[6], &locally_ambiguous)) 1064945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com ++num_crossings; 10652e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org if (ambiguous) { 10662e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org *ambiguous |= locally_ambiguous; 10672e086190e55a01dc2f7b74df6f2828e8cac2b9abkbr@chromium.org } 1068945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com return num_crossings; 1069945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com} 10708a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com//////////////////////////////////////////////////////////////////////////////// 10718a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 10728a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/* Find t value for quadratic [a, b, c] = d. 10738a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com Return 0 if there is no solution within [0, 1) 10748a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 10758a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic SkScalar quad_solve(SkScalar a, SkScalar b, SkScalar c, SkScalar d) 10768a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 10778a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // At^2 + Bt + C = d 10788a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar A = a - 2 * b + c; 10798a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar B = 2 * (b - a); 10808a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar C = a - d; 10818a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 10828a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar roots[2]; 10838a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com int count = SkFindUnitQuadRoots(A, B, C, roots); 10848a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 10858a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(count <= 1); 10868a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return count == 1 ? roots[0] : 0; 10878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 10888a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1089e1b75b4096c8ba9a569ae33d580806edd3c4a97arobertphillips@google.com/* given a quad-curve and a point (x,y), chop the quad at that point and place 109050df4d013f840749f70d1759c23c4217e727fd54skia.committer@gmail.com the new off-curve point and endpoint into 'dest'. 10919e1ec1a52985cce9db3a0d0e8d448b82a32e70cbskia.committer@gmail.com Should only return false if the computed pos is the start of the curve 1092e1b75b4096c8ba9a569ae33d580806edd3c4a97arobertphillips@google.com (i.e. root == 0) 10938a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 1094e1b75b4096c8ba9a569ae33d580806edd3c4a97arobertphillips@google.comstatic bool truncate_last_curve(const SkPoint quad[3], SkScalar x, SkScalar y, SkPoint* dest) 10958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 10968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com const SkScalar* base; 10978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar value; 10988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 10998a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (SkScalarAbs(x) < SkScalarAbs(y)) { 11008a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com base = &quad[0].fX; 11018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com value = x; 11028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } else { 11038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com base = &quad[0].fY; 11048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com value = y; 11058a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 11068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 11078a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // note: this returns 0 if it thinks value is out of range, meaning the 11088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // root might return something outside of [0, 1) 11098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar t = quad_solve(base[0], base[2], base[4], value); 11108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 11118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (t > 0) 11128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 11138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkPoint tmp[5]; 11148a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkChopQuadAt(quad, tmp, t); 1115e1b75b4096c8ba9a569ae33d580806edd3c4a97arobertphillips@google.com dest[0] = tmp[1]; 1116b0889a5aa610552bf306edc8d9a35d2d601acdb9robertphillips@google.com dest[1].set(x, y); 11178a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return true; 11188a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } else { 11198a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com /* t == 0 means either the value triggered a root outside of [0, 1) 11208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com For our purposes, we can ignore the <= 0 roots, but we want to 11218a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com catch the >= 1 roots (which given our caller, will basically mean 11228a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com a root of 1, give-or-take numerical instability). If we are in the 11238a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com >= 1 case, return the existing offCurve point. 1124fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 11258a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com The test below checks to see if we are close to the "end" of the 11268a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com curve (near base[4]). Rather than specifying a tolerance, I just 11278a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com check to see if value is on to the right/left of the middle point 11288a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com (depending on the direction/sign of the end points). 11298a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com */ 11308a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if ((base[0] < base[4] && value > base[2]) || 11318a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com (base[0] > base[4] && value < base[2])) // should root have been 1 11328a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 1133e1b75b4096c8ba9a569ae33d580806edd3c4a97arobertphillips@google.com dest[0] = quad[1]; 1134e1b75b4096c8ba9a569ae33d580806edd3c4a97arobertphillips@google.com dest[1].set(x, y); 11358a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return true; 11368a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 11378a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 11388a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return false; 11398a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 11408a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 11418a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic const SkPoint gQuadCirclePts[kSkBuildQuadArcStorage] = { 1142f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org// The mid point of the quadratic arc approximation is half way between the two 1143f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org// control points. The float epsilon adjustment moves the on curve point out by 1144f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org// two bits, distributing the convex test error between the round rect approximation 1145f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org// and the convex cross product sign equality test. 1146f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org#define SK_MID_RRECT_OFFSET (SK_Scalar1 + SK_ScalarTanPIOver8 + FLT_EPSILON * 4) / 2 1147f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { SK_Scalar1, 0 }, 1148f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { SK_Scalar1, SK_ScalarTanPIOver8 }, 1149f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { SK_MID_RRECT_OFFSET, SK_MID_RRECT_OFFSET }, 1150f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { SK_ScalarTanPIOver8, SK_Scalar1 }, 1151f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org 1152f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { 0, SK_Scalar1 }, 1153f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { -SK_ScalarTanPIOver8, SK_Scalar1 }, 1154f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { -SK_MID_RRECT_OFFSET, SK_MID_RRECT_OFFSET }, 1155f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { -SK_Scalar1, SK_ScalarTanPIOver8 }, 1156f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org 1157f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { -SK_Scalar1, 0 }, 1158f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { -SK_Scalar1, -SK_ScalarTanPIOver8 }, 1159f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { -SK_MID_RRECT_OFFSET, -SK_MID_RRECT_OFFSET }, 1160f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { -SK_ScalarTanPIOver8, -SK_Scalar1 }, 1161f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org 1162f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { 0, -SK_Scalar1 }, 1163f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { SK_ScalarTanPIOver8, -SK_Scalar1 }, 1164f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { SK_MID_RRECT_OFFSET, -SK_MID_RRECT_OFFSET }, 1165f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { SK_Scalar1, -SK_ScalarTanPIOver8 }, 1166f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org 1167f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { SK_Scalar1, 0 } 1168f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org#undef SK_MID_RRECT_OFFSET 11698a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com}; 11708a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 11718a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comint SkBuildQuadArc(const SkVector& uStart, const SkVector& uStop, 11728a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkRotationDirection dir, const SkMatrix* userMatrix, 11738a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkPoint quadPoints[]) 11748a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com{ 11758a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // rotate by x,y so that uStart is (1.0) 11768a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar x = SkPoint::DotProduct(uStart, uStop); 11778a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar y = SkPoint::CrossProduct(uStart, uStop); 11788a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 11798a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar absX = SkScalarAbs(x); 11808a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar absY = SkScalarAbs(y); 11818a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 11828a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com int pointCount; 11838a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 11848a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // check for (effectively) coincident vectors 11858a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // this can happen if our angle is nearly 0 or nearly 180 (y == 0) 11868a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // ... we use the dot-prod to distinguish between 0 and 180 (x > 0) 11878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (absY <= SK_ScalarNearlyZero && x > 0 && 11888a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com ((y >= 0 && kCW_SkRotationDirection == dir) || 11898a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com (y <= 0 && kCCW_SkRotationDirection == dir))) { 1190fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 11918a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // just return the start-point 11928a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com quadPoints[0].set(SK_Scalar1, 0); 11938a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com pointCount = 1; 11948a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } else { 11958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (dir == kCCW_SkRotationDirection) 11968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com y = -y; 11978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 11988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // what octant (quadratic curve) is [xy] in? 11998a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com int oct = 0; 12008a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com bool sameSign = true; 12018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 12028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (0 == y) 12038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 12048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com oct = 4; // 180 12058a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(SkScalarAbs(x + SK_Scalar1) <= SK_ScalarNearlyZero); 12068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 12078a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com else if (0 == x) 12088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 12098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(absY - SK_Scalar1 <= SK_ScalarNearlyZero); 12108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (y > 0) 12118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com oct = 2; // 90 12128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com else 12138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com oct = 6; // 270 12148a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 12158a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com else 12168a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 12178a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (y < 0) 12188a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com oct += 4; 12198a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if ((x < 0) != (y < 0)) 12208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 12218a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com oct += 2; 12228a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com sameSign = false; 12238a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 12248a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if ((absX < absY) == sameSign) 12258a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com oct += 1; 12268a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 12278a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 12288a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com int wholeCount = oct << 1; 12298a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com memcpy(quadPoints, gQuadCirclePts, (wholeCount + 1) * sizeof(SkPoint)); 12308a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 12318a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com const SkPoint* arc = &gQuadCirclePts[wholeCount]; 1232e1b75b4096c8ba9a569ae33d580806edd3c4a97arobertphillips@google.com if (truncate_last_curve(arc, x, y, &quadPoints[wholeCount + 1])) 12338a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 12348a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com wholeCount += 2; 12358a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 12368a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com pointCount = wholeCount + 1; 12378a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 12388a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 12398a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // now handle counter-clockwise and the initial unitStart rotation 12408a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkMatrix matrix; 12418a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com matrix.setSinCos(uStart.fY, uStart.fX); 12428a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (dir == kCCW_SkRotationDirection) { 12438a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com matrix.preScale(SK_Scalar1, -SK_Scalar1); 12448a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 12458a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (userMatrix) { 12468a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com matrix.postConcat(*userMatrix); 12478a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 12488a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com matrix.mapPoints(quadPoints, pointCount); 12498a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return pointCount; 12508a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 1251c518710d9a99c4d0adf759a102f4a1cb582f5939reed@google.com 1252c518710d9a99c4d0adf759a102f4a1cb582f5939reed@google.com/////////////////////////////////////////////////////////////////////////////// 1253c518710d9a99c4d0adf759a102f4a1cb582f5939reed@google.com 125417a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// F = (A (1 - t)^2 + C t^2 + 2 B (1 - t) t w) 125517a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// ------------------------------------------ 125617a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// ((1 - t)^2 + t^2 + 2 (1 - t) t w) 125717a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// 125817a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// = {t^2 (P0 + P2 - 2 P1 w), t (-2 P0 + 2 P1 w), P0} 125917a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// ------------------------------------------------ 126017a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// {t^2 (2 - 2 w), t (-2 + 2 w), 1} 126117a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// 126217a2c919d095797c364d407a5dbdb4d60533b953reed@google.com 126317a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// Take the parametric specification for the conic (either X or Y) and return 126417a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// in coeff[] the coefficients for the simple quadratic polynomial 126517a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// coeff[0] for t^2 126617a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// coeff[1] for t 126717a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// coeff[2] for constant term 126817a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// 12696862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.orgstatic SkScalar conic_eval_pos(const SkScalar src[], SkScalar w, SkScalar t) { 12700c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkASSERT(src); 12710c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkASSERT(t >= 0 && t <= SK_Scalar1); 127245fb8b60137c65106b7903285672d0f8a8041f97skia.committer@gmail.com 12730c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar src2w = SkScalarMul(src[2], w); 12740c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar C = src[0]; 12750c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar A = src[4] - 2 * src2w + C; 12760c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar B = 2 * (src2w - C); 12770c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar numer = SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C); 127845fb8b60137c65106b7903285672d0f8a8041f97skia.committer@gmail.com 12790c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org B = 2 * (w - SK_Scalar1); 12800c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org C = SK_Scalar1; 12810c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org A = -B; 12820c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar denom = SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C); 128345fb8b60137c65106b7903285672d0f8a8041f97skia.committer@gmail.com 12840c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org return SkScalarDiv(numer, denom); 12850c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org} 128617a2c919d095797c364d407a5dbdb4d60533b953reed@google.com 12870c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org// F' = 2 (C t (1 + t (-1 + w)) - A (-1 + t) (t (-1 + w) - w) + B (1 - 2 t) w) 12880c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org// 12896862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org// t^2 : (2 P0 - 2 P2 - 2 P0 w + 2 P2 w) 12906862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org// t^1 : (-2 P0 + 2 P2 + 4 P0 w - 4 P1 w) 12916862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org// t^0 : -2 P0 w + 2 P1 w 12926862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org// 12936862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org// We disregard magnitude, so we can freely ignore the denominator of F', and 12946862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org// divide the numerator by 2 12950c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org// 129617a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// coeff[0] for t^2 12976862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org// coeff[1] for t^1 12986862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org// coeff[2] for t^0 129917a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// 13006862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.orgstatic void conic_deriv_coeff(const SkScalar src[], SkScalar w, SkScalar coeff[3]) { 13016862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org const SkScalar P20 = src[4] - src[0]; 13026862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org const SkScalar P10 = src[2] - src[0]; 13036862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org const SkScalar wP10 = w * P10; 13046862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org coeff[0] = w * P20 - P20; 13056862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org coeff[1] = P20 - 2 * wP10; 13066862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org coeff[2] = wP10; 13076862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org} 13086862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org 13096862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.orgstatic SkScalar conic_eval_tan(const SkScalar coord[], SkScalar w, SkScalar t) { 13106862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org SkScalar coeff[3]; 13116862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org conic_deriv_coeff(coord, w, coeff); 13126862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org return t * (t * coeff[0] + coeff[1]) + coeff[2]; 13130c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org} 13140c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org 13156862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.orgstatic bool conic_find_extrema(const SkScalar src[], SkScalar w, SkScalar* t) { 13160c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar coeff[3]; 13176862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org conic_deriv_coeff(src, w, coeff); 13180c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org 13190c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar tValues[2]; 13200c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org int roots = SkFindUnitQuadRoots(coeff[0], coeff[1], coeff[2], tValues); 13210c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkASSERT(0 == roots || 1 == roots); 132245fb8b60137c65106b7903285672d0f8a8041f97skia.committer@gmail.com 13230c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org if (1 == roots) { 13240c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org *t = tValues[0]; 13250c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org return true; 13260c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org } 13270c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org return false; 132817a2c919d095797c364d407a5dbdb4d60533b953reed@google.com} 132917a2c919d095797c364d407a5dbdb4d60533b953reed@google.com 13300d099557feb99707c8f601746f46f5a295eb33b7reed@google.comstruct SkP3D { 13310d099557feb99707c8f601746f46f5a295eb33b7reed@google.com SkScalar fX, fY, fZ; 13324bb50b22fce5c4031549976cf7b04d63cc22e624skia.committer@gmail.com 13330d099557feb99707c8f601746f46f5a295eb33b7reed@google.com void set(SkScalar x, SkScalar y, SkScalar z) { 13340d099557feb99707c8f601746f46f5a295eb33b7reed@google.com fX = x; fY = y; fZ = z; 13350d099557feb99707c8f601746f46f5a295eb33b7reed@google.com } 13364bb50b22fce5c4031549976cf7b04d63cc22e624skia.committer@gmail.com 13370d099557feb99707c8f601746f46f5a295eb33b7reed@google.com void projectDown(SkPoint* dst) const { 13380d099557feb99707c8f601746f46f5a295eb33b7reed@google.com dst->set(fX / fZ, fY / fZ); 13390d099557feb99707c8f601746f46f5a295eb33b7reed@google.com } 13400d099557feb99707c8f601746f46f5a295eb33b7reed@google.com}; 13410d099557feb99707c8f601746f46f5a295eb33b7reed@google.com 13420d099557feb99707c8f601746f46f5a295eb33b7reed@google.com// we just return the middle 3 points, since the first and last are dups of src 13430d099557feb99707c8f601746f46f5a295eb33b7reed@google.com// 13440d099557feb99707c8f601746f46f5a295eb33b7reed@google.comstatic void p3d_interp(const SkScalar src[3], SkScalar dst[3], SkScalar t) { 13450d099557feb99707c8f601746f46f5a295eb33b7reed@google.com SkScalar ab = SkScalarInterp(src[0], src[3], t); 13460d099557feb99707c8f601746f46f5a295eb33b7reed@google.com SkScalar bc = SkScalarInterp(src[3], src[6], t); 13470d099557feb99707c8f601746f46f5a295eb33b7reed@google.com dst[0] = ab; 13480d099557feb99707c8f601746f46f5a295eb33b7reed@google.com dst[3] = SkScalarInterp(ab, bc, t); 13490d099557feb99707c8f601746f46f5a295eb33b7reed@google.com dst[6] = bc; 13500d099557feb99707c8f601746f46f5a295eb33b7reed@google.com} 13510d099557feb99707c8f601746f46f5a295eb33b7reed@google.com 13520d099557feb99707c8f601746f46f5a295eb33b7reed@google.comstatic void ratquad_mapTo3D(const SkPoint src[3], SkScalar w, SkP3D dst[]) { 13530d099557feb99707c8f601746f46f5a295eb33b7reed@google.com dst[0].set(src[0].fX * 1, src[0].fY * 1, 1); 13540d099557feb99707c8f601746f46f5a295eb33b7reed@google.com dst[1].set(src[1].fX * w, src[1].fY * w, w); 13550d099557feb99707c8f601746f46f5a295eb33b7reed@google.com dst[2].set(src[2].fX * 1, src[2].fY * 1, 1); 13560d099557feb99707c8f601746f46f5a295eb33b7reed@google.com} 13570d099557feb99707c8f601746f46f5a295eb33b7reed@google.com 135824bd210f2e2cf66f356b4e98f7801631089b8aa3reed@google.comvoid SkConic::evalAt(SkScalar t, SkPoint* pt, SkVector* tangent) const { 1359c518710d9a99c4d0adf759a102f4a1cb582f5939reed@google.com SkASSERT(t >= 0 && t <= SK_Scalar1); 13604bb50b22fce5c4031549976cf7b04d63cc22e624skia.committer@gmail.com 1361c518710d9a99c4d0adf759a102f4a1cb582f5939reed@google.com if (pt) { 13626862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org pt->set(conic_eval_pos(&fPts[0].fX, fW, t), 13636862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org conic_eval_pos(&fPts[0].fY, fW, t)); 1364c518710d9a99c4d0adf759a102f4a1cb582f5939reed@google.com } 136524bd210f2e2cf66f356b4e98f7801631089b8aa3reed@google.com if (tangent) { 136624bd210f2e2cf66f356b4e98f7801631089b8aa3reed@google.com tangent->set(conic_eval_tan(&fPts[0].fX, fW, t), 136724bd210f2e2cf66f356b4e98f7801631089b8aa3reed@google.com conic_eval_tan(&fPts[0].fY, fW, t)); 136824bd210f2e2cf66f356b4e98f7801631089b8aa3reed@google.com } 1369c518710d9a99c4d0adf759a102f4a1cb582f5939reed@google.com} 1370c518710d9a99c4d0adf759a102f4a1cb582f5939reed@google.com 137128552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgvoid SkConic::chopAt(SkScalar t, SkConic dst[2]) const { 13720d099557feb99707c8f601746f46f5a295eb33b7reed@google.com SkP3D tmp[3], tmp2[3]; 13730d099557feb99707c8f601746f46f5a295eb33b7reed@google.com 13740d099557feb99707c8f601746f46f5a295eb33b7reed@google.com ratquad_mapTo3D(fPts, fW, tmp); 13754bb50b22fce5c4031549976cf7b04d63cc22e624skia.committer@gmail.com 13760d099557feb99707c8f601746f46f5a295eb33b7reed@google.com p3d_interp(&tmp[0].fX, &tmp2[0].fX, t); 13770d099557feb99707c8f601746f46f5a295eb33b7reed@google.com p3d_interp(&tmp[0].fY, &tmp2[0].fY, t); 13780d099557feb99707c8f601746f46f5a295eb33b7reed@google.com p3d_interp(&tmp[0].fZ, &tmp2[0].fZ, t); 13794bb50b22fce5c4031549976cf7b04d63cc22e624skia.committer@gmail.com 13800d099557feb99707c8f601746f46f5a295eb33b7reed@google.com dst[0].fPts[0] = fPts[0]; 13810d099557feb99707c8f601746f46f5a295eb33b7reed@google.com tmp2[0].projectDown(&dst[0].fPts[1]); 13820d099557feb99707c8f601746f46f5a295eb33b7reed@google.com tmp2[1].projectDown(&dst[0].fPts[2]); dst[1].fPts[0] = dst[0].fPts[2]; 13830d099557feb99707c8f601746f46f5a295eb33b7reed@google.com tmp2[2].projectDown(&dst[1].fPts[1]); 13840d099557feb99707c8f601746f46f5a295eb33b7reed@google.com dst[1].fPts[2] = fPts[2]; 13850d099557feb99707c8f601746f46f5a295eb33b7reed@google.com 13864af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org // to put in "standard form", where w0 and w2 are both 1, we compute the 13874af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org // new w1 as sqrt(w1*w1/w0*w2) 13884af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org // or 13894af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org // w1 /= sqrt(w0*w2) 13904af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org // 13914af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org // However, in our case, we know that for dst[0], w0 == 1, and for dst[1], w2 == 1 13924af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org // 13934af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org SkScalar root = SkScalarSqrt(tmp2[1].fZ); 13944af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org dst[0].fW = tmp2[0].fZ / root; 13954af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org dst[1].fW = tmp2[2].fZ / root; 1396c518710d9a99c4d0adf759a102f4a1cb582f5939reed@google.com} 13978d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org 13983df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.orgstatic SkScalar subdivide_w_value(SkScalar w) { 13996862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org return SkScalarSqrt(SK_ScalarHalf + w * SK_ScalarHalf); 14003df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org} 14013df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org 140228552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgvoid SkConic::chop(SkConic dst[2]) const { 14038d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org SkScalar scale = SkScalarInvert(SK_Scalar1 + fW); 14048d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org SkScalar p1x = fW * fPts[1].fX; 14058d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org SkScalar p1y = fW * fPts[1].fY; 14068d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org SkScalar mx = (fPts[0].fX + 2 * p1x + fPts[2].fX) * scale * SK_ScalarHalf; 14078d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org SkScalar my = (fPts[0].fY + 2 * p1y + fPts[2].fY) * scale * SK_ScalarHalf; 14088d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org 14098d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org dst[0].fPts[0] = fPts[0]; 14108d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org dst[0].fPts[1].set((fPts[0].fX + p1x) * scale, 14118d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org (fPts[0].fY + p1y) * scale); 14128d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org dst[0].fPts[2].set(mx, my); 14138d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org 14148d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org dst[1].fPts[0].set(mx, my); 14158d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org dst[1].fPts[1].set((p1x + fPts[2].fX) * scale, 14168d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org (p1y + fPts[2].fY) * scale); 14178d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org dst[1].fPts[2] = fPts[2]; 14188d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org 14193df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org dst[0].fW = dst[1].fW = subdivide_w_value(fW); 14203df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org} 14213df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org 142297514f22e4cb85a0d79b089a1eecd54d4a952291mike@reedtribe.org/* 142397514f22e4cb85a0d79b089a1eecd54d4a952291mike@reedtribe.org * "High order approximation of conic sections by quadratic splines" 142497514f22e4cb85a0d79b089a1eecd54d4a952291mike@reedtribe.org * by Michael Floater, 1993 142597514f22e4cb85a0d79b089a1eecd54d4a952291mike@reedtribe.org */ 1426af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org#define AS_QUAD_ERROR_SETUP \ 1427af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org SkScalar a = fW - 1; \ 1428af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org SkScalar k = a / (4 * (2 + a)); \ 1429af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org SkScalar x = k * (fPts[0].fX - 2 * fPts[1].fX + fPts[2].fX); \ 1430af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org SkScalar y = k * (fPts[0].fY - 2 * fPts[1].fY + fPts[2].fY); 1431af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org 1432af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.orgvoid SkConic::computeAsQuadError(SkVector* err) const { 1433af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org AS_QUAD_ERROR_SETUP 1434af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org err->set(x, y); 1435af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org} 1436af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org 1437af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.orgbool SkConic::asQuadTol(SkScalar tol) const { 1438af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org AS_QUAD_ERROR_SETUP 1439af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org return (x * x + y * y) <= tol * tol; 144097514f22e4cb85a0d79b089a1eecd54d4a952291mike@reedtribe.org} 14417841c63136e8aa2d3aadbeab8432405abcd73c32skia.committer@gmail.com 144297514f22e4cb85a0d79b089a1eecd54d4a952291mike@reedtribe.orgint SkConic::computeQuadPOW2(SkScalar tol) const { 1443af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org AS_QUAD_ERROR_SETUP 1444af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org SkScalar error = SkScalarSqrt(x * x + y * y) - tol; 1445af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org 1446af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org if (error <= 0) { 144797514f22e4cb85a0d79b089a1eecd54d4a952291mike@reedtribe.org return 0; 14483df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org } 144997514f22e4cb85a0d79b089a1eecd54d4a952291mike@reedtribe.org uint32_t ierr = (uint32_t)error; 1450af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org return (34 - SkCLZ(ierr)) >> 1; 14513df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org} 14523df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org 145328552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgstatic SkPoint* subdivide(const SkConic& src, SkPoint pts[], int level) { 14543df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org SkASSERT(level >= 0); 1455af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org 14563df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org if (0 == level) { 14573df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org memcpy(pts, &src.fPts[1], 2 * sizeof(SkPoint)); 14583df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org return pts + 2; 14593df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org } else { 146028552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.org SkConic dst[2]; 14613df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org src.chop(dst); 14623df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org --level; 14633df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org pts = subdivide(dst[0], pts, level); 14643df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org return subdivide(dst[1], pts, level); 14653df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org } 14668d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org} 14673df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org 146828552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgint SkConic::chopIntoQuadsPOW2(SkPoint pts[], int pow2) const { 1469af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org SkASSERT(pow2 >= 0); 14703df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org *pts = fPts[0]; 1471aebfa7e1b1e94f693f3e7beb6ad43cfcb0f69e98reed@google.com SkDEBUGCODE(SkPoint* endPts =) subdivide(*this, pts + 1, pow2); 14723df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org SkASSERT(endPts - pts == (2 * (1 << pow2) + 1)); 14733df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org return 1 << pow2; 14743df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org} 14750c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org 147628552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgbool SkConic::findXExtrema(SkScalar* t) const { 14776862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org return conic_find_extrema(&fPts[0].fX, fW, t); 14780c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org} 14790c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org 148028552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgbool SkConic::findYExtrema(SkScalar* t) const { 14816862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org return conic_find_extrema(&fPts[0].fY, fW, t); 14820c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org} 14830c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org 148428552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgbool SkConic::chopAtXExtrema(SkConic dst[2]) const { 14850c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar t; 14860c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org if (this->findXExtrema(&t)) { 14870c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org this->chopAt(t, dst); 14880c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org // now clean-up the middle, since we know t was meant to be at 14890c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org // an X-extrema 14900c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar value = dst[0].fPts[2].fX; 14910c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org dst[0].fPts[1].fX = value; 14920c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org dst[1].fPts[0].fX = value; 14930c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org dst[1].fPts[1].fX = value; 14940c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org return true; 14950c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org } 14960c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org return false; 14970c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org} 14980c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org 149928552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgbool SkConic::chopAtYExtrema(SkConic dst[2]) const { 15000c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar t; 15010c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org if (this->findYExtrema(&t)) { 15020c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org this->chopAt(t, dst); 15030c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org // now clean-up the middle, since we know t was meant to be at 15040c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org // an Y-extrema 15050c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar value = dst[0].fPts[2].fY; 15060c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org dst[0].fPts[1].fY = value; 15070c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org dst[1].fPts[0].fY = value; 15080c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org dst[1].fPts[1].fY = value; 15090c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org return true; 15100c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org } 15110c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org return false; 15120c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org} 15130c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org 151428552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgvoid SkConic::computeTightBounds(SkRect* bounds) const { 15155c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org SkPoint pts[4]; 15165c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org pts[0] = fPts[0]; 15175c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org pts[1] = fPts[2]; 15185c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org int count = 2; 15195c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org 15205c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org SkScalar t; 15215c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org if (this->findXExtrema(&t)) { 15225c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org this->evalAt(t, &pts[count++]); 15235c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org } 15245c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org if (this->findYExtrema(&t)) { 15255c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org this->evalAt(t, &pts[count++]); 15265c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org } 15275c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org bounds->set(pts, count); 15285c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org} 15295c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org 153028552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgvoid SkConic::computeFastBounds(SkRect* bounds) const { 15315c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org bounds->set(fPts, 3); 15325c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org} 1533