1ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com/* 2ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com * Copyright 2006 The Android Open Source Project 3ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com * 4ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com * Use of this source code is governed by a BSD-style license that can be 5ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com * found in the LICENSE file. 6ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com */ 7ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com 88a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#include "SkGeometry.h" 98a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#include "SkMatrix.h" 10c9adb05b64fa0bfadf9d1a782afcda470da68c9emtklein#include "SkNx.h" 118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 126983f66d8b3a489133b751e2cef03e72a03bfeaereed#if 0 13b640203cd5733aaf110277e28e22007c5b541565reedstatic Sk2s from_point(const SkPoint& point) { 14b640203cd5733aaf110277e28e22007c5b541565reed return Sk2s::Load(&point.fX); 15b640203cd5733aaf110277e28e22007c5b541565reed} 16b640203cd5733aaf110277e28e22007c5b541565reed 17b640203cd5733aaf110277e28e22007c5b541565reedstatic SkPoint to_point(const Sk2s& x) { 18b640203cd5733aaf110277e28e22007c5b541565reed SkPoint point; 19b640203cd5733aaf110277e28e22007c5b541565reed x.store(&point.fX); 20b640203cd5733aaf110277e28e22007c5b541565reed return point; 21b640203cd5733aaf110277e28e22007c5b541565reed} 226983f66d8b3a489133b751e2cef03e72a03bfeaereed#endif 23b640203cd5733aaf110277e28e22007c5b541565reed 24b640203cd5733aaf110277e28e22007c5b541565reedstatic SkVector to_vector(const Sk2s& x) { 25b640203cd5733aaf110277e28e22007c5b541565reed SkVector vector; 26b640203cd5733aaf110277e28e22007c5b541565reed x.store(&vector.fX); 27b640203cd5733aaf110277e28e22007c5b541565reed return vector; 28b640203cd5733aaf110277e28e22007c5b541565reed} 29b640203cd5733aaf110277e28e22007c5b541565reed 308a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/** If defined, this makes eval_quad and eval_cubic do more setup (sometimes 318a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com involving integer multiplies by 2 or 3, but fewer calls to SkScalarMul. 328a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com May also introduce overflow of fixed when we compute our setup. 338a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 348f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.com// #define DIRECT_EVAL_OF_POLYNOMIALS 358a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 368a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com//////////////////////////////////////////////////////////////////////// 378a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 38b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgstatic int is_not_monotonic(SkScalar a, SkScalar b, SkScalar c) { 39b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org SkScalar ab = a - b; 40b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org SkScalar bc = b - c; 418f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.com if (ab < 0) { 428f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.com bc = -bc; 438a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 448f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.com return ab == 0 || bc < 0; 458f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.com} 468a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 478a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com//////////////////////////////////////////////////////////////////////// 488a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 49b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgstatic bool is_unit_interval(SkScalar x) { 508a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return x > 0 && x < SK_Scalar1; 518a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 528a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 53b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgstatic int valid_unit_divide(SkScalar numer, SkScalar denom, SkScalar* ratio) { 548a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(ratio); 558a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 56b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (numer < 0) { 578a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com numer = -numer; 588a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com denom = -denom; 598a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 608a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 61b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (denom == 0 || numer == 0 || numer >= denom) { 628a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return 0; 63b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 648a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 6580ea19ca4bdd68c1493666a5fe7e4ce9d43ded8breed SkScalar r = numer / denom; 6615161620bee33efcb706685486c9ce0fb51a72bbreed@android.com if (SkScalarIsNaN(r)) { 6715161620bee33efcb706685486c9ce0fb51a72bbreed@android.com return 0; 6815161620bee33efcb706685486c9ce0fb51a72bbreed@android.com } 6911fca3f29f0117eda798c67fafde40465d9903e1Mike Klein SkASSERTF(r >= 0 && r < SK_Scalar1, "numer %f, denom %f, r %f", numer, denom, r); 70b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (r == 0) { // catch underflow if numer <<<< denom 718a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return 0; 72b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 738a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com *ratio = r; 748a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return 1; 758a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 768a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 778a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/** From Numerical Recipes in C. 788a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 798a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com Q = -1/2 (B + sign(B) sqrt[B*B - 4*A*C]) 808a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com x1 = Q / A 818a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com x2 = C / Q 828a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 83b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgint SkFindUnitQuadRoots(SkScalar A, SkScalar B, SkScalar C, SkScalar roots[2]) { 848a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(roots); 858a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 86b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (A == 0) { 878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return valid_unit_divide(-C, B, roots); 88b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 898a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 908a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar* r = roots; 918a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 92b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org SkScalar R = B*B - 4*A*C; 9315161620bee33efcb706685486c9ce0fb51a72bbreed@android.com if (R < 0 || SkScalarIsNaN(R)) { // complex roots 948a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return 0; 9515161620bee33efcb706685486c9ce0fb51a72bbreed@android.com } 96b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org R = SkScalarSqrt(R); 978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar Q = (B < 0) ? -(B-R)/2 : -(B+R)/2; 998a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com r += valid_unit_divide(Q, A, r); 1008a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com r += valid_unit_divide(C, Q, r); 101b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (r - roots == 2) { 1028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (roots[0] > roots[1]) 1038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkTSwap<SkScalar>(roots[0], roots[1]); 1048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com else if (roots[0] == roots[1]) // nearly-equal? 1058a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com r -= 1; // skip the double root 1068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 1078a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return (int)(r - roots); 1088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 1098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1108f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.com/////////////////////////////////////////////////////////////////////////////// 1118f4d2306fa866a26f9448048ff63f692b2ba43aareed@google.com/////////////////////////////////////////////////////////////////////////////// 1128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 113b640203cd5733aaf110277e28e22007c5b541565reedstatic Sk2s quad_poly_eval(const Sk2s& A, const Sk2s& B, const Sk2s& C, const Sk2s& t) { 114b640203cd5733aaf110277e28e22007c5b541565reed return (A * t + B) * t + C; 115b640203cd5733aaf110277e28e22007c5b541565reed} 116b640203cd5733aaf110277e28e22007c5b541565reed 117b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgstatic SkScalar eval_quad(const SkScalar src[], SkScalar t) { 1188a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(src); 1198a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(t >= 0 && t <= SK_Scalar1); 1208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1218a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#ifdef DIRECT_EVAL_OF_POLYNOMIALS 1228a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar C = src[0]; 1238a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar A = src[4] - 2 * src[2] + C; 1248a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar B = 2 * (src[2] - C); 1258a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C); 1268a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#else 1278a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar ab = SkScalarInterp(src[0], src[2], t); 128fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com SkScalar bc = SkScalarInterp(src[2], src[4], t); 1298a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return SkScalarInterp(ab, bc, t); 1308a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#endif 1318a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 1328a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 133b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgstatic SkScalar eval_quad_derivative(const SkScalar src[], SkScalar t) { 1348a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar A = src[4] - 2 * src[2] + src[0]; 1358a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar B = src[2] - src[0]; 1368a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1378a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return 2 * SkScalarMulAdd(A, t, B); 1388a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 1398a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1406983f66d8b3a489133b751e2cef03e72a03bfeaereedvoid SkQuadToCoeff(const SkPoint pts[3], SkPoint coeff[3]) { 1416983f66d8b3a489133b751e2cef03e72a03bfeaereed Sk2s p0 = from_point(pts[0]); 1426983f66d8b3a489133b751e2cef03e72a03bfeaereed Sk2s p1 = from_point(pts[1]); 1436983f66d8b3a489133b751e2cef03e72a03bfeaereed Sk2s p2 = from_point(pts[2]); 1446983f66d8b3a489133b751e2cef03e72a03bfeaereed 1456983f66d8b3a489133b751e2cef03e72a03bfeaereed Sk2s p1minus2 = p1 - p0; 1466983f66d8b3a489133b751e2cef03e72a03bfeaereed 1476983f66d8b3a489133b751e2cef03e72a03bfeaereed coeff[0] = to_point(p2 - p1 - p1 + p0); // A * t^2 1486983f66d8b3a489133b751e2cef03e72a03bfeaereed coeff[1] = to_point(p1minus2 + p1minus2); // B * t 1496983f66d8b3a489133b751e2cef03e72a03bfeaereed coeff[2] = pts[0]; // C 1506983f66d8b3a489133b751e2cef03e72a03bfeaereed} 1516983f66d8b3a489133b751e2cef03e72a03bfeaereed 15265cb2cd2f7ad4146f055810b8bd77bff03a4e76ereedvoid SkEvalQuadAt(const SkPoint src[3], SkScalar t, SkPoint* pt, SkVector* tangent) { 1538a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(src); 1548a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(t >= 0 && t <= SK_Scalar1); 155950e986b1bc127af1f484572d2494091957486f9mtklein 156b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (pt) { 1578a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com pt->set(eval_quad(&src[0].fX, t), eval_quad(&src[0].fY, t)); 158b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 159b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (tangent) { 1608a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com tangent->set(eval_quad_derivative(&src[0].fX, t), 1618a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com eval_quad_derivative(&src[0].fY, t)); 162b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 1638a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 1648a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 16565cb2cd2f7ad4146f055810b8bd77bff03a4e76ereedSkPoint SkEvalQuadAt(const SkPoint src[3], SkScalar t) { 1668a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(src); 16765cb2cd2f7ad4146f055810b8bd77bff03a4e76ereed SkASSERT(t >= 0 && t <= SK_Scalar1); 1688a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 169b640203cd5733aaf110277e28e22007c5b541565reed const Sk2s t2(t); 170950e986b1bc127af1f484572d2494091957486f9mtklein 171b640203cd5733aaf110277e28e22007c5b541565reed Sk2s P0 = from_point(src[0]); 172b640203cd5733aaf110277e28e22007c5b541565reed Sk2s P1 = from_point(src[1]); 173b640203cd5733aaf110277e28e22007c5b541565reed Sk2s P2 = from_point(src[2]); 174950e986b1bc127af1f484572d2494091957486f9mtklein 175b640203cd5733aaf110277e28e22007c5b541565reed Sk2s B = P1 - P0; 176b640203cd5733aaf110277e28e22007c5b541565reed Sk2s A = P2 - P1 - B; 177950e986b1bc127af1f484572d2494091957486f9mtklein 178b640203cd5733aaf110277e28e22007c5b541565reed return to_point((A * t2 + B+B) * t2 + P0); 1798a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 1808a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 18140b7dd57ef1f4e91af72512d8ca57459b99d71bdreedSkVector SkEvalQuadTangentAt(const SkPoint src[3], SkScalar t) { 18240b7dd57ef1f4e91af72512d8ca57459b99d71bdreed SkASSERT(src); 18340b7dd57ef1f4e91af72512d8ca57459b99d71bdreed SkASSERT(t >= 0 && t <= SK_Scalar1); 18440b7dd57ef1f4e91af72512d8ca57459b99d71bdreed 185b640203cd5733aaf110277e28e22007c5b541565reed Sk2s P0 = from_point(src[0]); 186b640203cd5733aaf110277e28e22007c5b541565reed Sk2s P1 = from_point(src[1]); 187b640203cd5733aaf110277e28e22007c5b541565reed Sk2s P2 = from_point(src[2]); 18840b7dd57ef1f4e91af72512d8ca57459b99d71bdreed 189b640203cd5733aaf110277e28e22007c5b541565reed Sk2s B = P1 - P0; 190b640203cd5733aaf110277e28e22007c5b541565reed Sk2s A = P2 - P1 - B; 191b640203cd5733aaf110277e28e22007c5b541565reed Sk2s T = A * Sk2s(t) + B; 19240b7dd57ef1f4e91af72512d8ca57459b99d71bdreed 193b640203cd5733aaf110277e28e22007c5b541565reed return to_vector(T + T); 19440b7dd57ef1f4e91af72512d8ca57459b99d71bdreed} 19540b7dd57ef1f4e91af72512d8ca57459b99d71bdreed 19640b7dd57ef1f4e91af72512d8ca57459b99d71bdreedstatic inline Sk2s interp(const Sk2s& v0, const Sk2s& v1, const Sk2s& t) { 19740b7dd57ef1f4e91af72512d8ca57459b99d71bdreed return v0 + (v1 - v0) * t; 19840b7dd57ef1f4e91af72512d8ca57459b99d71bdreed} 19940b7dd57ef1f4e91af72512d8ca57459b99d71bdreed 200c08330f1601aeca7f10aeb2194118decbfbf83e1reedvoid SkChopQuadAt(const SkPoint src[3], SkPoint dst[5], SkScalar t) { 20140b7dd57ef1f4e91af72512d8ca57459b99d71bdreed SkASSERT(t > 0 && t < SK_Scalar1); 20240b7dd57ef1f4e91af72512d8ca57459b99d71bdreed 203b640203cd5733aaf110277e28e22007c5b541565reed Sk2s p0 = from_point(src[0]); 204b640203cd5733aaf110277e28e22007c5b541565reed Sk2s p1 = from_point(src[1]); 205b640203cd5733aaf110277e28e22007c5b541565reed Sk2s p2 = from_point(src[2]); 206ce6acc91085c4b6d87d4bac84e66193908e648f9reed Sk2s tt(t); 207c9adb05b64fa0bfadf9d1a782afcda470da68c9emtklein 20840b7dd57ef1f4e91af72512d8ca57459b99d71bdreed Sk2s p01 = interp(p0, p1, tt); 20940b7dd57ef1f4e91af72512d8ca57459b99d71bdreed Sk2s p12 = interp(p1, p2, tt); 21040b7dd57ef1f4e91af72512d8ca57459b99d71bdreed 211b640203cd5733aaf110277e28e22007c5b541565reed dst[0] = to_point(p0); 212b640203cd5733aaf110277e28e22007c5b541565reed dst[1] = to_point(p01); 213b640203cd5733aaf110277e28e22007c5b541565reed dst[2] = to_point(interp(p01, p12, tt)); 214b640203cd5733aaf110277e28e22007c5b541565reed dst[3] = to_point(p12); 215b640203cd5733aaf110277e28e22007c5b541565reed dst[4] = to_point(p2); 21640b7dd57ef1f4e91af72512d8ca57459b99d71bdreed} 21740b7dd57ef1f4e91af72512d8ca57459b99d71bdreed 218b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgvoid SkChopQuadAtHalf(const SkPoint src[3], SkPoint dst[5]) { 219c08330f1601aeca7f10aeb2194118decbfbf83e1reed SkChopQuadAt(src, dst, 0.5f); return; 2208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 2218a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 2228a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/** Quad'(t) = At + B, where 2238a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com A = 2(a - 2b + c) 2248a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com B = 2(b - a) 2258a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com Solve for t, only if it fits between 0 < t < 1 2268a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 227b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgint SkFindQuadExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar tValue[1]) { 2288a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com /* At + B == 0 2298a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com t = -B / A 2308a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com */ 2318a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return valid_unit_divide(a - b, a - b - b + c, tValue); 2328a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 2338a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 234b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgstatic inline void flatten_double_quad_extrema(SkScalar coords[14]) { 2358a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com coords[2] = coords[6] = coords[4]; 2368a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 2378a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 2388a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/* Returns 0 for 1 quad, and 1 for two quads, either way the answer is 23977f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com stored in dst[]. Guarantees that the 1/2 quads will be monotonic. 24077f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com */ 241b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgint SkChopQuadAtYExtrema(const SkPoint src[3], SkPoint dst[5]) { 2428a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(src); 2438a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(dst); 244fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 2458a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar a = src[0].fY; 2468a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar b = src[1].fY; 2478a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar c = src[2].fY; 248fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 249b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (is_not_monotonic(a, b, c)) { 2508a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar tValue; 251b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (valid_unit_divide(a - b, a - b - b + c, &tValue)) { 2528a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkChopQuadAt(src, dst, tValue); 2538a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com flatten_double_quad_extrema(&dst[0].fY); 2548a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return 1; 2558a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 2568a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // if we get here, we need to force dst to be monotonic, even though 2578a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // we couldn't compute a unit_divide value (probably underflow). 2588a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com b = SkScalarAbs(a - b) < SkScalarAbs(b - c) ? a : c; 2598a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 2608a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[0].set(src[0].fX, a); 2618a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[1].set(src[1].fX, b); 2628a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst[2].set(src[2].fX, c); 2638a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return 0; 2648a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 2658a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 26677f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com/* Returns 0 for 1 quad, and 1 for two quads, either way the answer is 26777f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com stored in dst[]. Guarantees that the 1/2 quads will be monotonic. 26877f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com */ 269b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgint SkChopQuadAtXExtrema(const SkPoint src[3], SkPoint dst[5]) { 27077f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com SkASSERT(src); 27177f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com SkASSERT(dst); 272fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 27377f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com SkScalar a = src[0].fX; 27477f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com SkScalar b = src[1].fX; 27577f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com SkScalar c = src[2].fX; 276fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 27777f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com if (is_not_monotonic(a, b, c)) { 27877f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com SkScalar tValue; 27977f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com if (valid_unit_divide(a - b, a - b - b + c, &tValue)) { 28077f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com SkChopQuadAt(src, dst, tValue); 28177f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com flatten_double_quad_extrema(&dst[0].fX); 28277f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com return 1; 28377f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com } 28477f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com // if we get here, we need to force dst to be monotonic, even though 28577f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com // we couldn't compute a unit_divide value (probably underflow). 28677f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com b = SkScalarAbs(a - b) < SkScalarAbs(b - c) ? a : c; 28777f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com } 28877f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com dst[0].set(a, src[0].fY); 28977f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com dst[1].set(b, src[1].fY); 29077f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com dst[2].set(c, src[2].fY); 29177f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com return 0; 29277f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com} 29377f0ef726f1f8b6769ed2509171afce8bac00b23reed@android.com 2948a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// F(t) = a (1 - t) ^ 2 + 2 b t (1 - t) + c t ^ 2 2958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// F'(t) = 2 (b - a) + 2 (a - 2b + c) t 2968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// F''(t) = 2 (a - 2b + c) 2978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// 2988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// A = 2 (b - a) 2998a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// B = 2 (a - 2b + c) 3008a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// 3018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// Maximum curvature for a quadratic means solving 3028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// Fx' Fx'' + Fy' Fy'' = 0 3038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// 3048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// t = - (Ax Bx + Ay By) / (Bx ^ 2 + By ^ 2) 3058a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com// 306b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgSkScalar SkFindQuadMaxCurvature(const SkPoint src[3]) { 3078a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar Ax = src[1].fX - src[0].fX; 3088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar Ay = src[1].fY - src[0].fY; 3098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar Bx = src[0].fX - src[1].fX - src[1].fX + src[2].fX; 3108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar By = src[0].fY - src[1].fY - src[1].fY + src[2].fY; 3118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar t = 0; // 0 means don't chop 3128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 3138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com (void)valid_unit_divide(-(Ax * Bx + Ay * By), Bx * Bx + By * By, &t); 3145383a7525355dec72efa2083aeadffdd09a962b9egdaniel@google.com return t; 3155383a7525355dec72efa2083aeadffdd09a962b9egdaniel@google.com} 3168a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 317b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgint SkChopQuadAtMaxCurvature(const SkPoint src[3], SkPoint dst[5]) { 3185383a7525355dec72efa2083aeadffdd09a962b9egdaniel@google.com SkScalar t = SkFindQuadMaxCurvature(src); 3195383a7525355dec72efa2083aeadffdd09a962b9egdaniel@google.com if (t == 0) { 3208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com memcpy(dst, src, 3 * sizeof(SkPoint)); 3218a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return 1; 3225383a7525355dec72efa2083aeadffdd09a962b9egdaniel@google.com } else { 3238a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkChopQuadAt(src, dst, t); 3248a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return 2; 3258a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 3268a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 3278a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 3286fc321a18acc8c6437735007240eefe7054e83b0reed@google.comvoid SkConvertQuadToCubic(const SkPoint src[3], SkPoint dst[4]) { 329daee7eadd1b704078217e9a0f5ad218fcaeae099reed Sk2s scale(SkDoubleToScalar(2.0 / 3.0)); 330daee7eadd1b704078217e9a0f5ad218fcaeae099reed Sk2s s0 = from_point(src[0]); 331daee7eadd1b704078217e9a0f5ad218fcaeae099reed Sk2s s1 = from_point(src[1]); 332daee7eadd1b704078217e9a0f5ad218fcaeae099reed Sk2s s2 = from_point(src[2]); 333daee7eadd1b704078217e9a0f5ad218fcaeae099reed 3346fc321a18acc8c6437735007240eefe7054e83b0reed@google.com dst[0] = src[0]; 335daee7eadd1b704078217e9a0f5ad218fcaeae099reed dst[1] = to_point(s0 + (s1 - s0) * scale); 336daee7eadd1b704078217e9a0f5ad218fcaeae099reed dst[2] = to_point(s2 + (s1 - s2) * scale); 3376fc321a18acc8c6437735007240eefe7054e83b0reed@google.com dst[3] = src[2]; 338945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com} 339945a139553a9c9da03766213661d7f5fd6ed3042reed@android.com 340b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org////////////////////////////////////////////////////////////////////////////// 341b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org///// CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS ///// 342b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org////////////////////////////////////////////////////////////////////////////// 3438a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 344b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgstatic SkScalar eval_cubic(const SkScalar src[], SkScalar t) { 3458a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(src); 3468a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(t >= 0 && t <= SK_Scalar1); 3478a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 348b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (t == 0) { 3498a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return src[0]; 350b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 3518a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 3528a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#ifdef DIRECT_EVAL_OF_POLYNOMIALS 3538a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar D = src[0]; 3548a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar A = src[6] + 3*(src[2] - src[4]) - D; 3558a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar B = 3*(src[4] - src[2] - src[2] + D); 3568a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar C = 3*(src[2] - D); 3578a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 3588a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return SkScalarMulAdd(SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C), t, D); 3598a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#else 3608a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar ab = SkScalarInterp(src[0], src[2], t); 3618a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar bc = SkScalarInterp(src[2], src[4], t); 3628a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar cd = SkScalarInterp(src[4], src[6], t); 3638a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar abc = SkScalarInterp(ab, bc, t); 3648a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar bcd = SkScalarInterp(bc, cd, t); 3658a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return SkScalarInterp(abc, bcd, t); 3668a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#endif 3678a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 3688a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 3698a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/** return At^2 + Bt + C 3708a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 371b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgstatic SkScalar eval_quadratic(SkScalar A, SkScalar B, SkScalar C, SkScalar t) { 3728a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(t >= 0 && t <= SK_Scalar1); 3738a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 3748a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C); 3758a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 3768a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 377b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgstatic SkScalar eval_cubic_derivative(const SkScalar src[], SkScalar t) { 3788a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar A = src[6] + 3*(src[2] - src[4]) - src[0]; 3798a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar B = 2*(src[4] - 2 * src[2] + src[0]); 3808a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar C = src[2] - src[0]; 3818a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 3828a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return eval_quadratic(A, B, C, t); 3838a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 3848a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 385b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgstatic SkScalar eval_cubic_2ndDerivative(const SkScalar src[], SkScalar t) { 3868a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar A = src[6] + 3*(src[2] - src[4]) - src[0]; 3878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar B = src[4] - 2 * src[2] + src[0]; 3888a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 3898a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return SkScalarMulAdd(A, t, B); 3908a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 3918a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 392b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgvoid SkEvalCubicAt(const SkPoint src[4], SkScalar t, SkPoint* loc, 393b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org SkVector* tangent, SkVector* curvature) { 3948a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(src); 3958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(t >= 0 && t <= SK_Scalar1); 3968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 397b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (loc) { 3988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com loc->set(eval_cubic(&src[0].fX, t), eval_cubic(&src[0].fY, t)); 399b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 400b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (tangent) { 4018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com tangent->set(eval_cubic_derivative(&src[0].fX, t), 4028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com eval_cubic_derivative(&src[0].fY, t)); 403b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 404b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (curvature) { 4058a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com curvature->set(eval_cubic_2ndDerivative(&src[0].fX, t), 4068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com eval_cubic_2ndDerivative(&src[0].fY, t)); 407b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 4088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 4098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/** Cubic'(t) = At^2 + Bt + C, where 4118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com A = 3(-a + 3(b - c) + d) 4128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com B = 6(a - 2b + c) 4138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com C = 3(b - a) 4148a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com Solve for t, keeping only those that fit betwee 0 < t < 1 4158a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 416b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgint SkFindCubicExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar d, 417b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org SkScalar tValues[2]) { 4188a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // we divide A,B,C by 3 to simplify 4198a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar A = d - a + 3*(b - c); 4208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar B = 2*(a - b - b + c); 4218a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar C = b - a; 4228a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4238a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return SkFindUnitQuadRoots(A, B, C, tValues); 4248a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 4258a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 426b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgvoid SkChopCubicAt(const SkPoint src[4], SkPoint dst[7], SkScalar t) { 4278a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(t > 0 && t < SK_Scalar1); 4288a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 4296b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed Sk2s p0 = from_point(src[0]); 4306b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed Sk2s p1 = from_point(src[1]); 4316b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed Sk2s p2 = from_point(src[2]); 4326b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed Sk2s p3 = from_point(src[3]); 4336b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed Sk2s tt(t); 4346b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed 4356b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed Sk2s ab = interp(p0, p1, tt); 4366b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed Sk2s bc = interp(p1, p2, tt); 4376b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed Sk2s cd = interp(p2, p3, tt); 4386b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed Sk2s abc = interp(ab, bc, tt); 4396b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed Sk2s bcd = interp(bc, cd, tt); 4406b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed Sk2s abcd = interp(abc, bcd, tt); 441c9adb05b64fa0bfadf9d1a782afcda470da68c9emtklein 4426b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed dst[0] = src[0]; 4436b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed dst[1] = to_point(ab); 4446b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed dst[2] = to_point(abc); 4456b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed dst[3] = to_point(abcd); 4466b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed dst[4] = to_point(bcd); 4476b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed dst[5] = to_point(cd); 4486b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed dst[6] = src[3]; 4496b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed} 4506b9ef90c029c7c783f156ffd6fb1ba047bec63e0reed 4516983f66d8b3a489133b751e2cef03e72a03bfeaereedvoid SkCubicToCoeff(const SkPoint pts[4], SkPoint coeff[4]) { 4526983f66d8b3a489133b751e2cef03e72a03bfeaereed Sk2s p0 = from_point(pts[0]); 4536983f66d8b3a489133b751e2cef03e72a03bfeaereed Sk2s p1 = from_point(pts[1]); 4546983f66d8b3a489133b751e2cef03e72a03bfeaereed Sk2s p2 = from_point(pts[2]); 4556983f66d8b3a489133b751e2cef03e72a03bfeaereed Sk2s p3 = from_point(pts[3]); 4566983f66d8b3a489133b751e2cef03e72a03bfeaereed 4576983f66d8b3a489133b751e2cef03e72a03bfeaereed const Sk2s three(3); 4586983f66d8b3a489133b751e2cef03e72a03bfeaereed Sk2s p1minusp2 = p1 - p2; 4596983f66d8b3a489133b751e2cef03e72a03bfeaereed 4606983f66d8b3a489133b751e2cef03e72a03bfeaereed Sk2s D = p0; 4616983f66d8b3a489133b751e2cef03e72a03bfeaereed Sk2s A = p3 + three * p1minusp2 - D; 4626983f66d8b3a489133b751e2cef03e72a03bfeaereed Sk2s B = three * (D - p1minusp2 - p1); 4636983f66d8b3a489133b751e2cef03e72a03bfeaereed Sk2s C = three * (p1 - D); 4646983f66d8b3a489133b751e2cef03e72a03bfeaereed 4656983f66d8b3a489133b751e2cef03e72a03bfeaereed coeff[0] = to_point(A); 4666983f66d8b3a489133b751e2cef03e72a03bfeaereed coeff[1] = to_point(B); 4676983f66d8b3a489133b751e2cef03e72a03bfeaereed coeff[2] = to_point(C); 4686983f66d8b3a489133b751e2cef03e72a03bfeaereed coeff[3] = to_point(D); 4696983f66d8b3a489133b751e2cef03e72a03bfeaereed} 4706983f66d8b3a489133b751e2cef03e72a03bfeaereed 471a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com/* http://code.google.com/p/skia/issues/detail?id=32 472fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 473a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com This test code would fail when we didn't check the return result of 474a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com valid_unit_divide in SkChopCubicAt(... tValues[], int roots). The reason is 475a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com that after the first chop, the parameters to valid_unit_divide are equal 476a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com (thanks to finite float precision and rounding in the subtracts). Thus 477a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com even though the 2nd tValue looks < 1.0, after we renormalize it, we end 478a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com up with 1.0, hence the need to check and just return the last cubic as 479a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com a degenerate clump of 4 points in the sampe place. 480a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com 481a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com static void test_cubic() { 482a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com SkPoint src[4] = { 483a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com { 556.25000, 523.03003 }, 484a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com { 556.23999, 522.96002 }, 485a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com { 556.21997, 522.89001 }, 486a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com { 556.21997, 522.82001 } 487a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com }; 488a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com SkPoint dst[10]; 489a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com SkScalar tval[] = { 0.33333334f, 0.99999994f }; 490a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com SkChopCubicAt(src, dst, tval, 2); 491a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com } 492a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com */ 493a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com 494b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgvoid SkChopCubicAt(const SkPoint src[4], SkPoint dst[], 495b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org const SkScalar tValues[], int roots) { 4968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#ifdef SK_DEBUG 4978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 4988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com for (int i = 0; i < roots - 1; i++) 4998a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 5008a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(is_unit_interval(tValues[i])); 5018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(is_unit_interval(tValues[i+1])); 5028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(tValues[i] < tValues[i+1]); 5038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 5048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 5058a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#endif 5068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 507b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (dst) { 508b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (roots == 0) { // nothing to chop 5098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com memcpy(dst, src, 4*sizeof(SkPoint)); 510b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } else { 5118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar t = tValues[0]; 5128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkPoint tmp[4]; 5138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 514b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org for (int i = 0; i < roots; i++) { 5158a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkChopCubicAt(src, dst, t); 516b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (i == roots - 1) { 5178a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com break; 518b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 5198a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 5208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com dst += 3; 521a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com // have src point to the remaining cubic (after the chop) 5228a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com memcpy(tmp, dst, 4 * sizeof(SkPoint)); 5238a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com src = tmp; 524a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com 525a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com // watch out in case the renormalized t isn't in range 526a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com if (!valid_unit_divide(tValues[i+1] - tValues[i], 527a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com SK_Scalar1 - tValues[i], &t)) { 528a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com // if we can't, just create a degenerate cubic 529a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com dst[4] = dst[5] = dst[6] = src[3]; 530a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com break; 531a964028843ec3f69b3b2e556426ff881d1fcb4b2reed@android.com } 5328a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 5338a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 5348a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 5358a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 5368a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 537b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgvoid SkChopCubicAtHalf(const SkPoint src[4], SkPoint dst[7]) { 538c08330f1601aeca7f10aeb2194118decbfbf83e1reed SkChopCubicAt(src, dst, 0.5f); 5398a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 5408a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 541b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgstatic void flatten_double_cubic_extrema(SkScalar coords[14]) { 5428a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com coords[4] = coords[8] = coords[6]; 5438a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 5448a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 5458a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/** Given 4 points on a cubic bezier, chop it into 1, 2, 3 beziers such that 546def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org the resulting beziers are monotonic in Y. This is called by the scan 547def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org converter. Depending on what is returned, dst[] is treated as follows: 5488a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 0 dst[0..3] is the original cubic 5498a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1 dst[0..3] and dst[3..6] are the two new cubics 5508a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 2 dst[0..3], dst[3..6], dst[6..9] are the three new cubics 5518a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com If dst == null, it is ignored and only the count is returned. 5528a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 553bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.comint SkChopCubicAtYExtrema(const SkPoint src[4], SkPoint dst[10]) { 5548a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar tValues[2]; 555bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com int roots = SkFindCubicExtrema(src[0].fY, src[1].fY, src[2].fY, 556bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com src[3].fY, tValues); 557fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 5588a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkChopCubicAt(src, dst, tValues, roots); 559bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com if (dst && roots > 0) { 5608a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // we do some cleanup to ensure our Y extrema are flat 5618a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com flatten_double_cubic_extrema(&dst[0].fY); 562bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com if (roots == 2) { 5638a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com flatten_double_cubic_extrema(&dst[3].fY); 564bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com } 565bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com } 566bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com return roots; 567bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com} 568bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com 569bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.comint SkChopCubicAtXExtrema(const SkPoint src[4], SkPoint dst[10]) { 570bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com SkScalar tValues[2]; 571bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com int roots = SkFindCubicExtrema(src[0].fX, src[1].fX, src[2].fX, 572bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com src[3].fX, tValues); 573fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 574bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com SkChopCubicAt(src, dst, tValues, roots); 575bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com if (dst && roots > 0) { 576bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com // we do some cleanup to ensure our Y extrema are flat 577bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com flatten_double_cubic_extrema(&dst[0].fX); 578bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com if (roots == 2) { 579bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com flatten_double_cubic_extrema(&dst[3].fX); 580bb13586591bd412a0372aeb85d44159d2fa3f947reed@android.com } 5818a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 5828a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return roots; 5838a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 5848a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 5858a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/** http://www.faculty.idc.ac.il/arik/quality/appendixA.html 5868a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 5878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com Inflection means that curvature is zero. 5888a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com Curvature is [F' x F''] / [F'^3] 5898a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com So we solve F'x X F''y - F'y X F''y == 0 5908a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com After some canceling of the cubic term, we get 5918a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com A = b - a 5928a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com B = c - 2b + a 5938a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com C = d - 3c + 3b - a 5948a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com (BxCy - ByCx)t^2 + (AxCy - AyCx)t + AxBy - AyBx == 0 5958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 596b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgint SkFindCubicInflections(const SkPoint src[4], SkScalar tValues[]) { 5978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar Ax = src[1].fX - src[0].fX; 5988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar Ay = src[1].fY - src[0].fY; 5998a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar Bx = src[2].fX - 2 * src[1].fX + src[0].fX; 6008a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar By = src[2].fY - 2 * src[1].fY + src[0].fY; 6018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar Cx = src[3].fX + 3 * (src[1].fX - src[2].fX) - src[0].fX; 6028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar Cy = src[3].fY + 3 * (src[1].fY - src[2].fY) - src[0].fY; 6038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 604def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org return SkFindUnitQuadRoots(Bx*Cy - By*Cx, 605def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org Ax*Cy - Ay*Cx, 606def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org Ax*By - Ay*Bx, 607def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org tValues); 6088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 6098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 610b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgint SkChopCubicAtInflections(const SkPoint src[], SkPoint dst[10]) { 6118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar tValues[2]; 6128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com int count = SkFindCubicInflections(src, tValues); 6138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 614b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (dst) { 615b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (count == 0) { 6168a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com memcpy(dst, src, 4 * sizeof(SkPoint)); 617b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } else { 6188a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkChopCubicAt(src, dst, tValues, count); 619b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 6208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 6218a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return count + 1; 6228a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 6238a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 6248dd31cf69e24ff82865309781107dfab948b6a02caryclark// See http://http.developer.nvidia.com/GPUGems3/gpugems3_ch25.html (from the book GPU Gems 3) 6258dd31cf69e24ff82865309781107dfab948b6a02caryclark// discr(I) = d0^2 * (3*d1^2 - 4*d0*d2) 6268dd31cf69e24ff82865309781107dfab948b6a02caryclark// Classification: 6278dd31cf69e24ff82865309781107dfab948b6a02caryclark// discr(I) > 0 Serpentine 6288dd31cf69e24ff82865309781107dfab948b6a02caryclark// discr(I) = 0 Cusp 6298dd31cf69e24ff82865309781107dfab948b6a02caryclark// discr(I) < 0 Loop 6308dd31cf69e24ff82865309781107dfab948b6a02caryclark// d0 = d1 = 0 Quadratic 6318dd31cf69e24ff82865309781107dfab948b6a02caryclark// d0 = d1 = d2 = 0 Line 6328dd31cf69e24ff82865309781107dfab948b6a02caryclark// p0 = p1 = p2 = p3 Point 6338dd31cf69e24ff82865309781107dfab948b6a02caryclarkstatic SkCubicType classify_cubic(const SkPoint p[4], const SkScalar d[3]) { 6348dd31cf69e24ff82865309781107dfab948b6a02caryclark if (p[0] == p[1] && p[0] == p[2] && p[0] == p[3]) { 6358dd31cf69e24ff82865309781107dfab948b6a02caryclark return kPoint_SkCubicType; 6368dd31cf69e24ff82865309781107dfab948b6a02caryclark } 6378dd31cf69e24ff82865309781107dfab948b6a02caryclark const SkScalar discr = d[0] * d[0] * (3.f * d[1] * d[1] - 4.f * d[0] * d[2]); 6388dd31cf69e24ff82865309781107dfab948b6a02caryclark if (discr > SK_ScalarNearlyZero) { 6398dd31cf69e24ff82865309781107dfab948b6a02caryclark return kSerpentine_SkCubicType; 6408dd31cf69e24ff82865309781107dfab948b6a02caryclark } else if (discr < -SK_ScalarNearlyZero) { 6418dd31cf69e24ff82865309781107dfab948b6a02caryclark return kLoop_SkCubicType; 6428dd31cf69e24ff82865309781107dfab948b6a02caryclark } else { 6438dd31cf69e24ff82865309781107dfab948b6a02caryclark if (0.f == d[0] && 0.f == d[1]) { 6448dd31cf69e24ff82865309781107dfab948b6a02caryclark return (0.f == d[2] ? kLine_SkCubicType : kQuadratic_SkCubicType); 6458dd31cf69e24ff82865309781107dfab948b6a02caryclark } else { 6468dd31cf69e24ff82865309781107dfab948b6a02caryclark return kCusp_SkCubicType; 6478dd31cf69e24ff82865309781107dfab948b6a02caryclark } 6488dd31cf69e24ff82865309781107dfab948b6a02caryclark } 6498dd31cf69e24ff82865309781107dfab948b6a02caryclark} 6508dd31cf69e24ff82865309781107dfab948b6a02caryclark 6518dd31cf69e24ff82865309781107dfab948b6a02caryclark// Assumes the third component of points is 1. 6528dd31cf69e24ff82865309781107dfab948b6a02caryclark// Calcs p0 . (p1 x p2) 6538dd31cf69e24ff82865309781107dfab948b6a02caryclarkstatic SkScalar calc_dot_cross_cubic(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2) { 6548dd31cf69e24ff82865309781107dfab948b6a02caryclark const SkScalar xComp = p0.fX * (p1.fY - p2.fY); 6558dd31cf69e24ff82865309781107dfab948b6a02caryclark const SkScalar yComp = p0.fY * (p2.fX - p1.fX); 6568dd31cf69e24ff82865309781107dfab948b6a02caryclark const SkScalar wComp = p1.fX * p2.fY - p1.fY * p2.fX; 6578dd31cf69e24ff82865309781107dfab948b6a02caryclark return (xComp + yComp + wComp); 6588dd31cf69e24ff82865309781107dfab948b6a02caryclark} 6598dd31cf69e24ff82865309781107dfab948b6a02caryclark 6608dd31cf69e24ff82865309781107dfab948b6a02caryclark// Calc coefficients of I(s,t) where roots of I are inflection points of curve 6618dd31cf69e24ff82865309781107dfab948b6a02caryclark// I(s,t) = t*(3*d0*s^2 - 3*d1*s*t + d2*t^2) 6628dd31cf69e24ff82865309781107dfab948b6a02caryclark// d0 = a1 - 2*a2+3*a3 6638dd31cf69e24ff82865309781107dfab948b6a02caryclark// d1 = -a2 + 3*a3 6648dd31cf69e24ff82865309781107dfab948b6a02caryclark// d2 = 3*a3 6658dd31cf69e24ff82865309781107dfab948b6a02caryclark// a1 = p0 . (p3 x p2) 6668dd31cf69e24ff82865309781107dfab948b6a02caryclark// a2 = p1 . (p0 x p3) 6678dd31cf69e24ff82865309781107dfab948b6a02caryclark// a3 = p2 . (p1 x p0) 6688dd31cf69e24ff82865309781107dfab948b6a02caryclark// Places the values of d1, d2, d3 in array d passed in 6698dd31cf69e24ff82865309781107dfab948b6a02caryclarkstatic void calc_cubic_inflection_func(const SkPoint p[4], SkScalar d[3]) { 6708dd31cf69e24ff82865309781107dfab948b6a02caryclark SkScalar a1 = calc_dot_cross_cubic(p[0], p[3], p[2]); 6718dd31cf69e24ff82865309781107dfab948b6a02caryclark SkScalar a2 = calc_dot_cross_cubic(p[1], p[0], p[3]); 6728dd31cf69e24ff82865309781107dfab948b6a02caryclark SkScalar a3 = calc_dot_cross_cubic(p[2], p[1], p[0]); 6738dd31cf69e24ff82865309781107dfab948b6a02caryclark 6748dd31cf69e24ff82865309781107dfab948b6a02caryclark // need to scale a's or values in later calculations will grow to high 6758dd31cf69e24ff82865309781107dfab948b6a02caryclark SkScalar max = SkScalarAbs(a1); 6768dd31cf69e24ff82865309781107dfab948b6a02caryclark max = SkMaxScalar(max, SkScalarAbs(a2)); 6778dd31cf69e24ff82865309781107dfab948b6a02caryclark max = SkMaxScalar(max, SkScalarAbs(a3)); 6788dd31cf69e24ff82865309781107dfab948b6a02caryclark max = 1.f/max; 6798dd31cf69e24ff82865309781107dfab948b6a02caryclark a1 = a1 * max; 6808dd31cf69e24ff82865309781107dfab948b6a02caryclark a2 = a2 * max; 6818dd31cf69e24ff82865309781107dfab948b6a02caryclark a3 = a3 * max; 6828dd31cf69e24ff82865309781107dfab948b6a02caryclark 6838dd31cf69e24ff82865309781107dfab948b6a02caryclark d[2] = 3.f * a3; 6848dd31cf69e24ff82865309781107dfab948b6a02caryclark d[1] = d[2] - a2; 6858dd31cf69e24ff82865309781107dfab948b6a02caryclark d[0] = d[1] - a2 + a1; 6868dd31cf69e24ff82865309781107dfab948b6a02caryclark} 6878dd31cf69e24ff82865309781107dfab948b6a02caryclark 6888dd31cf69e24ff82865309781107dfab948b6a02caryclarkSkCubicType SkClassifyCubic(const SkPoint src[4], SkScalar d[3]) { 6898dd31cf69e24ff82865309781107dfab948b6a02caryclark calc_cubic_inflection_func(src, d); 6908dd31cf69e24ff82865309781107dfab948b6a02caryclark return classify_cubic(src, d); 6918dd31cf69e24ff82865309781107dfab948b6a02caryclark} 6928dd31cf69e24ff82865309781107dfab948b6a02caryclark 693b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgtemplate <typename T> void bubble_sort(T array[], int count) { 6948a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com for (int i = count - 1; i > 0; --i) 6958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com for (int j = i; j > 0; --j) 6968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (array[j] < array[j-1]) 6978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 6988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com T tmp(array[j]); 6998a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com array[j] = array[j-1]; 7008a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com array[j-1] = tmp; 7018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 7028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 7038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 704087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com/** 705087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com * Given an array and count, remove all pair-wise duplicates from the array, 706087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com * keeping the existing sorting, and return the new count 707087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com */ 708b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgstatic int collaps_duplicates(SkScalar array[], int count) { 709087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com for (int n = count; n > 1; --n) { 710087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com if (array[0] == array[1]) { 711087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com for (int i = 1; i < n; ++i) { 712087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com array[i - 1] = array[i]; 713087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com } 714087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com count -= 1; 715087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com } else { 716087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com array += 1; 717087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com } 718087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com } 719087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com return count; 720087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com} 721087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com 722087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com#ifdef SK_DEBUG 723087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com 724087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com#define TEST_COLLAPS_ENTRY(array) array, SK_ARRAY_COUNT(array) 725087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com 726087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.comstatic void test_collaps_duplicates() { 727087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com static bool gOnce; 728087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com if (gOnce) { return; } 729087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com gOnce = true; 730b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org const SkScalar src0[] = { 0 }; 731b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org const SkScalar src1[] = { 0, 0 }; 732b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org const SkScalar src2[] = { 0, 1 }; 733b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org const SkScalar src3[] = { 0, 0, 0 }; 734b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org const SkScalar src4[] = { 0, 0, 1 }; 735b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org const SkScalar src5[] = { 0, 1, 1 }; 736b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org const SkScalar src6[] = { 0, 1, 2 }; 737087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com const struct { 738b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org const SkScalar* fData; 739087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com int fCount; 740087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com int fCollapsedCount; 741087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com } data[] = { 742087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com { TEST_COLLAPS_ENTRY(src0), 1 }, 743087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com { TEST_COLLAPS_ENTRY(src1), 1 }, 744087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com { TEST_COLLAPS_ENTRY(src2), 2 }, 745087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com { TEST_COLLAPS_ENTRY(src3), 1 }, 746087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com { TEST_COLLAPS_ENTRY(src4), 2 }, 747087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com { TEST_COLLAPS_ENTRY(src5), 2 }, 748087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com { TEST_COLLAPS_ENTRY(src6), 3 }, 749087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com }; 750087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com for (size_t i = 0; i < SK_ARRAY_COUNT(data); ++i) { 751b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org SkScalar dst[3]; 752087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com memcpy(dst, data[i].fData, data[i].fCount * sizeof(dst[0])); 753087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com int count = collaps_duplicates(dst, data[i].fCount); 754087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com SkASSERT(data[i].fCollapsedCount == count); 755087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com for (int j = 1; j < count; ++j) { 756087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com SkASSERT(dst[j-1] < dst[j]); 757087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com } 758087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com } 759087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com} 760087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com#endif 761087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com 7623c12840b234e614faf569e80f311a77ce65d9fe0reed@google.comstatic SkScalar SkScalarCubeRoot(SkScalar x) { 763b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org return SkScalarPow(x, 0.3333333f); 7643c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com} 7653c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com 7668a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/* Solve coeff(t) == 0, returning the number of roots that 7678a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com lie withing 0 < t < 1. 7688a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com coeff[0]t^3 + coeff[1]t^2 + coeff[2]t + coeff[3] 769fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 770087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com Eliminates repeated roots (so that all tValues are distinct, and are always 771087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com in increasing order. 7728a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 773b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgstatic int solve_cubic_poly(const SkScalar coeff[4], SkScalar tValues[3]) { 774b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (SkScalarNearlyZero(coeff[0])) { // we're just a quadratic 7758a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return SkFindUnitQuadRoots(coeff[1], coeff[2], coeff[3], tValues); 7768a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 7778a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 7783c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com SkScalar a, b, c, Q, R; 7798a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 7808a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 7818a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(coeff[0] != 0); 7828a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 7833c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com SkScalar inva = SkScalarInvert(coeff[0]); 7843c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com a = coeff[1] * inva; 7853c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com b = coeff[2] * inva; 7863c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com c = coeff[3] * inva; 7878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 7883c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com Q = (a*a - b*3) / 9; 7893c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com R = (2*a*a*a - 9*a*b + 27*c) / 54; 7908a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 7913c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com SkScalar Q3 = Q * Q * Q; 7923c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com SkScalar R2MinusQ3 = R * R - Q3; 7933c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com SkScalar adiv3 = a / 3; 7948a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 7958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar* roots = tValues; 7968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar r; 7978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 798b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (R2MinusQ3 < 0) { // we have 3 real roots 799b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org SkScalar theta = SkScalarACos(R / SkScalarSqrt(Q3)); 800b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org SkScalar neg2RootQ = -2 * SkScalarSqrt(Q); 8018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 802b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org r = neg2RootQ * SkScalarCos(theta/3) - adiv3; 803b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (is_unit_interval(r)) { 8048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com *roots++ = r; 805b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 806b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org r = neg2RootQ * SkScalarCos((theta + 2*SK_ScalarPI)/3) - adiv3; 807b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (is_unit_interval(r)) { 8088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com *roots++ = r; 809b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 810b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org r = neg2RootQ * SkScalarCos((theta - 2*SK_ScalarPI)/3) - adiv3; 811b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (is_unit_interval(r)) { 8128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com *roots++ = r; 813b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 814087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com SkDEBUGCODE(test_collaps_duplicates();) 815087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com 8168a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // now sort the roots 817087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com int count = (int)(roots - tValues); 818087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com SkASSERT((unsigned)count <= 3); 819087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com bubble_sort(tValues, count); 820087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com count = collaps_duplicates(tValues, count); 821087d5aafb18b88dfc6c6a5dbf59160c8be914e62reed@google.com roots = tValues + count; // so we compute the proper count below 822b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } else { // we have 1 real root 8233c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com SkScalar A = SkScalarAbs(R) + SkScalarSqrt(R2MinusQ3); 8243c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com A = SkScalarCubeRoot(A); 825b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (R > 0) { 8263c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com A = -A; 827b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 828b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (A != 0) { 8293c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com A += Q / A; 830b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 8313c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com r = A - adiv3; 832b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (is_unit_interval(r)) { 8338a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com *roots++ = r; 834b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 8358a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 8368a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8378a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return (int)(roots - tValues); 8388a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 8398a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8408a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/* Looking for F' dot F'' == 0 841fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 8428a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com A = b - a 8438a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com B = c - 2b + a 8448a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com C = d - 3c + 3b - a 8458a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8468a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com F' = 3Ct^2 + 6Bt + 3A 8478a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com F'' = 6Ct + 6B 8488a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8498a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB 8508a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 851b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgstatic void formulate_F1DotF2(const SkScalar src[], SkScalar coeff[4]) { 8528a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar a = src[2] - src[0]; 8538a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar b = src[4] - 2 * src[2] + src[0]; 8548a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar c = src[6] + 3 * (src[2] - src[4]) - src[0]; 8558a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8563c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com coeff[0] = c * c; 8573c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com coeff[1] = 3 * b * c; 8583c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com coeff[2] = 2 * b * b + c * a; 8593c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com coeff[3] = a * b; 8608a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 8618a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8628a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/* Looking for F' dot F'' == 0 863fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 8648a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com A = b - a 8658a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com B = c - 2b + a 8668a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com C = d - 3c + 3b - a 8678a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8688a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com F' = 3Ct^2 + 6Bt + 3A 8698a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com F'' = 6Ct + 6B 8708a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8718a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB 8728a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 873b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgint SkFindCubicMaxCurvature(const SkPoint src[4], SkScalar tValues[3]) { 8743c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com SkScalar coeffX[4], coeffY[4]; 8753c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com int i; 8768a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8778a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com formulate_F1DotF2(&src[0].fX, coeffX); 8788a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com formulate_F1DotF2(&src[0].fY, coeffY); 8798a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 880b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org for (i = 0; i < 4; i++) { 8813c12840b234e614faf569e80f311a77ce65d9fe0reed@google.com coeffX[i] += coeffY[i]; 882b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 8838a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8848a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar t[3]; 885b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org int count = solve_cubic_poly(coeffX, t); 8868a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com int maxCount = 0; 8878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 8888a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // now remove extrema where the curvature is zero (mins) 8898a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // !!!! need a test for this !!!! 890b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org for (i = 0; i < count; i++) { 8918a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // if (not_min_curvature()) 892b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (t[i] > 0 && t[i] < SK_Scalar1) { 8938a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com tValues[maxCount++] = t[i]; 894b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 8958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 8968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return maxCount; 8978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 8988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 899b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgint SkChopCubicAtMaxCurvature(const SkPoint src[4], SkPoint dst[13], 900b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org SkScalar tValues[3]) { 9018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar t_storage[3]; 9028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 903b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (tValues == NULL) { 9048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com tValues = t_storage; 905b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 9068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9078a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com int count = SkFindCubicMaxCurvature(src, tValues); 9088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9095383a7525355dec72efa2083aeadffdd09a962b9egdaniel@google.com if (dst) { 910b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (count == 0) { 9118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com memcpy(dst, src, 4 * sizeof(SkPoint)); 912b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } else { 9138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkChopCubicAt(src, dst, tValues, count); 914b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 9158a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 9168a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return count + 1; 9178a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 9188a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 919dc3088570f945ed0ede84f0af0016eedc267dda3reed#include "../pathops/SkPathOpsCubic.h" 920dc3088570f945ed0ede84f0af0016eedc267dda3reed 921dc3088570f945ed0ede84f0af0016eedc267dda3reedtypedef int (SkDCubic::*InterceptProc)(double intercept, double roots[3]) const; 922dc3088570f945ed0ede84f0af0016eedc267dda3reed 923dc3088570f945ed0ede84f0af0016eedc267dda3reedstatic bool cubic_dchop_at_intercept(const SkPoint src[4], SkScalar intercept, SkPoint dst[7], 924dc3088570f945ed0ede84f0af0016eedc267dda3reed InterceptProc method) { 925dc3088570f945ed0ede84f0af0016eedc267dda3reed SkDCubic cubic; 926dc3088570f945ed0ede84f0af0016eedc267dda3reed double roots[3]; 927dc3088570f945ed0ede84f0af0016eedc267dda3reed int count = (cubic.set(src).*method)(intercept, roots); 928dc3088570f945ed0ede84f0af0016eedc267dda3reed if (count > 0) { 929dc3088570f945ed0ede84f0af0016eedc267dda3reed SkDCubicPair pair = cubic.chopAt(roots[0]); 930dc3088570f945ed0ede84f0af0016eedc267dda3reed for (int i = 0; i < 7; ++i) { 931dc3088570f945ed0ede84f0af0016eedc267dda3reed dst[i] = pair.pts[i].asSkPoint(); 932dc3088570f945ed0ede84f0af0016eedc267dda3reed } 933dc3088570f945ed0ede84f0af0016eedc267dda3reed return true; 934dc3088570f945ed0ede84f0af0016eedc267dda3reed } 935dc3088570f945ed0ede84f0af0016eedc267dda3reed return false; 936dc3088570f945ed0ede84f0af0016eedc267dda3reed} 937dc3088570f945ed0ede84f0af0016eedc267dda3reed 938dc3088570f945ed0ede84f0af0016eedc267dda3reedbool SkChopMonoCubicAtY(SkPoint src[4], SkScalar y, SkPoint dst[7]) { 939dc3088570f945ed0ede84f0af0016eedc267dda3reed return cubic_dchop_at_intercept(src, y, dst, &SkDCubic::horizontalIntersect); 940dc3088570f945ed0ede84f0af0016eedc267dda3reed} 941dc3088570f945ed0ede84f0af0016eedc267dda3reed 942dc3088570f945ed0ede84f0af0016eedc267dda3reedbool SkChopMonoCubicAtX(SkPoint src[4], SkScalar x, SkPoint dst[7]) { 943dc3088570f945ed0ede84f0af0016eedc267dda3reed return cubic_dchop_at_intercept(src, x, dst, &SkDCubic::verticalIntersect); 944dc3088570f945ed0ede84f0af0016eedc267dda3reed} 945dc3088570f945ed0ede84f0af0016eedc267dda3reed 946b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org/////////////////////////////////////////////////////////////////////////////// 9478a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9488a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/* Find t value for quadratic [a, b, c] = d. 9498a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com Return 0 if there is no solution within [0, 1) 9508a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 951b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgstatic SkScalar quad_solve(SkScalar a, SkScalar b, SkScalar c, SkScalar d) { 9528a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // At^2 + Bt + C = d 9538a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar A = a - 2 * b + c; 9548a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar B = 2 * (b - a); 9558a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar C = a - d; 9568a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9578a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar roots[2]; 9588a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com int count = SkFindUnitQuadRoots(A, B, C, roots); 9598a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9608a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(count <= 1); 9618a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return count == 1 ? roots[0] : 0; 9628a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 9638a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 964e1b75b4096c8ba9a569ae33d580806edd3c4a97arobertphillips@google.com/* given a quad-curve and a point (x,y), chop the quad at that point and place 96550df4d013f840749f70d1759c23c4217e727fd54skia.committer@gmail.com the new off-curve point and endpoint into 'dest'. 9669e1ec1a52985cce9db3a0d0e8d448b82a32e70cbskia.committer@gmail.com Should only return false if the computed pos is the start of the curve 967e1b75b4096c8ba9a569ae33d580806edd3c4a97arobertphillips@google.com (i.e. root == 0) 9688a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/ 969b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.orgstatic bool truncate_last_curve(const SkPoint quad[3], SkScalar x, SkScalar y, 970b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org SkPoint* dest) { 9718a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com const SkScalar* base; 9728a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar value; 9738a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9748a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (SkScalarAbs(x) < SkScalarAbs(y)) { 9758a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com base = &quad[0].fX; 9768a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com value = x; 9778a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } else { 9788a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com base = &quad[0].fY; 9798a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com value = y; 9808a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 9818a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9828a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // note: this returns 0 if it thinks value is out of range, meaning the 9838a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // root might return something outside of [0, 1) 9848a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar t = quad_solve(base[0], base[2], base[4], value); 9858a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 986b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (t > 0) { 9878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkPoint tmp[5]; 9888a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkChopQuadAt(quad, tmp, t); 989e1b75b4096c8ba9a569ae33d580806edd3c4a97arobertphillips@google.com dest[0] = tmp[1]; 990b0889a5aa610552bf306edc8d9a35d2d601acdb9robertphillips@google.com dest[1].set(x, y); 9918a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return true; 9928a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } else { 9938a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com /* t == 0 means either the value triggered a root outside of [0, 1) 9948a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com For our purposes, we can ignore the <= 0 roots, but we want to 9958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com catch the >= 1 roots (which given our caller, will basically mean 9968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com a root of 1, give-or-take numerical instability). If we are in the 9978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com >= 1 case, return the existing offCurve point. 998fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 9998a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com The test below checks to see if we are close to the "end" of the 10008a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com curve (near base[4]). Rather than specifying a tolerance, I just 10018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com check to see if value is on to the right/left of the middle point 10028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com (depending on the direction/sign of the end points). 10038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com */ 10048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if ((base[0] < base[4] && value > base[2]) || 10058a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com (base[0] > base[4] && value < base[2])) // should root have been 1 10068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com { 1007e1b75b4096c8ba9a569ae33d580806edd3c4a97arobertphillips@google.com dest[0] = quad[1]; 1008e1b75b4096c8ba9a569ae33d580806edd3c4a97arobertphillips@google.com dest[1].set(x, y); 10098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return true; 10108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 10118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 10128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return false; 10138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 10148a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 10158a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic const SkPoint gQuadCirclePts[kSkBuildQuadArcStorage] = { 1016f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org// The mid point of the quadratic arc approximation is half way between the two 1017f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org// control points. The float epsilon adjustment moves the on curve point out by 1018def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org// two bits, distributing the convex test error between the round rect 1019def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org// approximation and the convex cross product sign equality test. 1020def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org#define SK_MID_RRECT_OFFSET \ 1021def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org (SK_Scalar1 + SK_ScalarTanPIOver8 + FLT_EPSILON * 4) / 2 1022f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { SK_Scalar1, 0 }, 1023f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { SK_Scalar1, SK_ScalarTanPIOver8 }, 1024f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { SK_MID_RRECT_OFFSET, SK_MID_RRECT_OFFSET }, 1025f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { SK_ScalarTanPIOver8, SK_Scalar1 }, 1026f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org 1027f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { 0, SK_Scalar1 }, 1028f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { -SK_ScalarTanPIOver8, SK_Scalar1 }, 1029f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { -SK_MID_RRECT_OFFSET, SK_MID_RRECT_OFFSET }, 1030f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { -SK_Scalar1, SK_ScalarTanPIOver8 }, 1031f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org 1032f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { -SK_Scalar1, 0 }, 1033f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { -SK_Scalar1, -SK_ScalarTanPIOver8 }, 1034f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { -SK_MID_RRECT_OFFSET, -SK_MID_RRECT_OFFSET }, 1035f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { -SK_ScalarTanPIOver8, -SK_Scalar1 }, 1036f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org 1037f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { 0, -SK_Scalar1 }, 1038f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { SK_ScalarTanPIOver8, -SK_Scalar1 }, 1039f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { SK_MID_RRECT_OFFSET, -SK_MID_RRECT_OFFSET }, 1040f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { SK_Scalar1, -SK_ScalarTanPIOver8 }, 1041f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org 1042f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org { SK_Scalar1, 0 } 1043f91aaecbe9d3630123d803d80f7b29f06c8976c7commit-bot@chromium.org#undef SK_MID_RRECT_OFFSET 10448a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com}; 10458a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 10468a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comint SkBuildQuadArc(const SkVector& uStart, const SkVector& uStop, 10478a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkRotationDirection dir, const SkMatrix* userMatrix, 1048b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org SkPoint quadPoints[]) { 10498a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // rotate by x,y so that uStart is (1.0) 10508a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar x = SkPoint::DotProduct(uStart, uStop); 10518a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar y = SkPoint::CrossProduct(uStart, uStop); 10528a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 10538a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar absX = SkScalarAbs(x); 10548a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkScalar absY = SkScalarAbs(y); 10558a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 10568a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com int pointCount; 10578a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 10588a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // check for (effectively) coincident vectors 10598a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // this can happen if our angle is nearly 0 or nearly 180 (y == 0) 10608a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // ... we use the dot-prod to distinguish between 0 and 180 (x > 0) 10618a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (absY <= SK_ScalarNearlyZero && x > 0 && 10628a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com ((y >= 0 && kCW_SkRotationDirection == dir) || 10638a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com (y <= 0 && kCCW_SkRotationDirection == dir))) { 1064fbfcd5602128ec010c82cb733c9cdc0a3254f9f3rmistry@google.com 10658a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // just return the start-point 10668a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com quadPoints[0].set(SK_Scalar1, 0); 10678a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com pointCount = 1; 10688a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } else { 1069b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (dir == kCCW_SkRotationDirection) { 10708a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com y = -y; 1071b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 10728a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // what octant (quadratic curve) is [xy] in? 10738a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com int oct = 0; 10748a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com bool sameSign = true; 10758a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1076b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (0 == y) { 10778a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com oct = 4; // 180 10788a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(SkScalarAbs(x + SK_Scalar1) <= SK_ScalarNearlyZero); 1079b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } else if (0 == x) { 10808a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(absY - SK_Scalar1 <= SK_ScalarNearlyZero); 1081b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org oct = y > 0 ? 2 : 6; // 90 : 270 1082b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } else { 1083b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (y < 0) { 10848a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com oct += 4; 1085b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 1086b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if ((x < 0) != (y < 0)) { 10878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com oct += 2; 10888a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com sameSign = false; 10898a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 1090b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if ((absX < absY) == sameSign) { 10918a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com oct += 1; 1092b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org } 10938a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 10948a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 10958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com int wholeCount = oct << 1; 10968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com memcpy(quadPoints, gQuadCirclePts, (wholeCount + 1) * sizeof(SkPoint)); 10978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 10988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com const SkPoint* arc = &gQuadCirclePts[wholeCount]; 1099b39d5617f60e8c26f76011cfcd984d7ad42d9fa9commit-bot@chromium.org if (truncate_last_curve(arc, x, y, &quadPoints[wholeCount + 1])) { 11008a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com wholeCount += 2; 11018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 11028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com pointCount = wholeCount + 1; 11038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 11048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 11058a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // now handle counter-clockwise and the initial unitStart rotation 11068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkMatrix matrix; 11078a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com matrix.setSinCos(uStart.fY, uStart.fX); 11088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (dir == kCCW_SkRotationDirection) { 11098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com matrix.preScale(SK_Scalar1, -SK_Scalar1); 11108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 11118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (userMatrix) { 11128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com matrix.postConcat(*userMatrix); 11138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 11148a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com matrix.mapPoints(quadPoints, pointCount); 11158a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return pointCount; 11168a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 1117c518710d9a99c4d0adf759a102f4a1cb582f5939reed@google.com 1118c518710d9a99c4d0adf759a102f4a1cb582f5939reed@google.com 1119def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org/////////////////////////////////////////////////////////////////////////////// 1120def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org// 1121def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org// NURB representation for conics. Helpful explanations at: 1122def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org// 1123def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org// http://citeseerx.ist.psu.edu/viewdoc/ 1124def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org// download?doi=10.1.1.44.5740&rep=rep1&type=ps 1125def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org// and 1126def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org// http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/NURBS/RB-conics.html 1127def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org// 112817a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// F = (A (1 - t)^2 + C t^2 + 2 B (1 - t) t w) 112917a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// ------------------------------------------ 113017a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// ((1 - t)^2 + t^2 + 2 (1 - t) t w) 113117a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// 113217a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// = {t^2 (P0 + P2 - 2 P1 w), t (-2 P0 + 2 P1 w), P0} 113317a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// ------------------------------------------------ 113417a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// {t^2 (2 - 2 w), t (-2 + 2 w), 1} 113517a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// 113617a2c919d095797c364d407a5dbdb4d60533b953reed@google.com 11376862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.orgstatic SkScalar conic_eval_pos(const SkScalar src[], SkScalar w, SkScalar t) { 11380c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkASSERT(src); 11390c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkASSERT(t >= 0 && t <= SK_Scalar1); 114045fb8b60137c65106b7903285672d0f8a8041f97skia.committer@gmail.com 11410c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar src2w = SkScalarMul(src[2], w); 11420c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar C = src[0]; 11430c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar A = src[4] - 2 * src2w + C; 11440c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar B = 2 * (src2w - C); 11450c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar numer = SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C); 114645fb8b60137c65106b7903285672d0f8a8041f97skia.committer@gmail.com 11470c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org B = 2 * (w - SK_Scalar1); 11480c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org C = SK_Scalar1; 11490c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org A = -B; 11500c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar denom = SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C); 115145fb8b60137c65106b7903285672d0f8a8041f97skia.committer@gmail.com 115280ea19ca4bdd68c1493666a5fe7e4ce9d43ded8breed return numer / denom; 11530c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org} 115417a2c919d095797c364d407a5dbdb4d60533b953reed@google.com 11550c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org// F' = 2 (C t (1 + t (-1 + w)) - A (-1 + t) (t (-1 + w) - w) + B (1 - 2 t) w) 11560c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org// 11576862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org// t^2 : (2 P0 - 2 P2 - 2 P0 w + 2 P2 w) 11586862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org// t^1 : (-2 P0 + 2 P2 + 4 P0 w - 4 P1 w) 11596862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org// t^0 : -2 P0 w + 2 P1 w 11606862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org// 11616862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org// We disregard magnitude, so we can freely ignore the denominator of F', and 11626862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org// divide the numerator by 2 11630c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org// 116417a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// coeff[0] for t^2 11656862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org// coeff[1] for t^1 11666862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org// coeff[2] for t^0 116717a2c919d095797c364d407a5dbdb4d60533b953reed@google.com// 1168def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.orgstatic void conic_deriv_coeff(const SkScalar src[], 1169def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org SkScalar w, 1170def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org SkScalar coeff[3]) { 11716862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org const SkScalar P20 = src[4] - src[0]; 11726862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org const SkScalar P10 = src[2] - src[0]; 11736862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org const SkScalar wP10 = w * P10; 11746862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org coeff[0] = w * P20 - P20; 11756862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org coeff[1] = P20 - 2 * wP10; 11766862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org coeff[2] = wP10; 11776862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org} 11786862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org 11796862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.orgstatic SkScalar conic_eval_tan(const SkScalar coord[], SkScalar w, SkScalar t) { 11806862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org SkScalar coeff[3]; 11816862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org conic_deriv_coeff(coord, w, coeff); 11826862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org return t * (t * coeff[0] + coeff[1]) + coeff[2]; 11830c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org} 11840c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org 11856862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.orgstatic bool conic_find_extrema(const SkScalar src[], SkScalar w, SkScalar* t) { 11860c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar coeff[3]; 11876862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org conic_deriv_coeff(src, w, coeff); 11880c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org 11890c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar tValues[2]; 11900c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org int roots = SkFindUnitQuadRoots(coeff[0], coeff[1], coeff[2], tValues); 11910c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkASSERT(0 == roots || 1 == roots); 119245fb8b60137c65106b7903285672d0f8a8041f97skia.committer@gmail.com 11930c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org if (1 == roots) { 11940c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org *t = tValues[0]; 11950c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org return true; 11960c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org } 11970c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org return false; 119817a2c919d095797c364d407a5dbdb4d60533b953reed@google.com} 119917a2c919d095797c364d407a5dbdb4d60533b953reed@google.com 12000d099557feb99707c8f601746f46f5a295eb33b7reed@google.comstruct SkP3D { 12010d099557feb99707c8f601746f46f5a295eb33b7reed@google.com SkScalar fX, fY, fZ; 12024bb50b22fce5c4031549976cf7b04d63cc22e624skia.committer@gmail.com 12030d099557feb99707c8f601746f46f5a295eb33b7reed@google.com void set(SkScalar x, SkScalar y, SkScalar z) { 12040d099557feb99707c8f601746f46f5a295eb33b7reed@google.com fX = x; fY = y; fZ = z; 12050d099557feb99707c8f601746f46f5a295eb33b7reed@google.com } 12064bb50b22fce5c4031549976cf7b04d63cc22e624skia.committer@gmail.com 12070d099557feb99707c8f601746f46f5a295eb33b7reed@google.com void projectDown(SkPoint* dst) const { 12080d099557feb99707c8f601746f46f5a295eb33b7reed@google.com dst->set(fX / fZ, fY / fZ); 12090d099557feb99707c8f601746f46f5a295eb33b7reed@google.com } 12100d099557feb99707c8f601746f46f5a295eb33b7reed@google.com}; 12110d099557feb99707c8f601746f46f5a295eb33b7reed@google.com 1212d50d87a185d26a38d7100bbbb119be17947aa5e4commit-bot@chromium.org// We only interpolate one dimension at a time (the first, at +0, +3, +6). 1213d50d87a185d26a38d7100bbbb119be17947aa5e4commit-bot@chromium.orgstatic void p3d_interp(const SkScalar src[7], SkScalar dst[7], SkScalar t) { 12140d099557feb99707c8f601746f46f5a295eb33b7reed@google.com SkScalar ab = SkScalarInterp(src[0], src[3], t); 12150d099557feb99707c8f601746f46f5a295eb33b7reed@google.com SkScalar bc = SkScalarInterp(src[3], src[6], t); 12160d099557feb99707c8f601746f46f5a295eb33b7reed@google.com dst[0] = ab; 12170d099557feb99707c8f601746f46f5a295eb33b7reed@google.com dst[3] = SkScalarInterp(ab, bc, t); 12180d099557feb99707c8f601746f46f5a295eb33b7reed@google.com dst[6] = bc; 12190d099557feb99707c8f601746f46f5a295eb33b7reed@google.com} 12200d099557feb99707c8f601746f46f5a295eb33b7reed@google.com 12210d099557feb99707c8f601746f46f5a295eb33b7reed@google.comstatic void ratquad_mapTo3D(const SkPoint src[3], SkScalar w, SkP3D dst[]) { 12220d099557feb99707c8f601746f46f5a295eb33b7reed@google.com dst[0].set(src[0].fX * 1, src[0].fY * 1, 1); 12230d099557feb99707c8f601746f46f5a295eb33b7reed@google.com dst[1].set(src[1].fX * w, src[1].fY * w, w); 12240d099557feb99707c8f601746f46f5a295eb33b7reed@google.com dst[2].set(src[2].fX * 1, src[2].fY * 1, 1); 12250d099557feb99707c8f601746f46f5a295eb33b7reed@google.com} 12260d099557feb99707c8f601746f46f5a295eb33b7reed@google.com 122724bd210f2e2cf66f356b4e98f7801631089b8aa3reed@google.comvoid SkConic::evalAt(SkScalar t, SkPoint* pt, SkVector* tangent) const { 1228c518710d9a99c4d0adf759a102f4a1cb582f5939reed@google.com SkASSERT(t >= 0 && t <= SK_Scalar1); 12294bb50b22fce5c4031549976cf7b04d63cc22e624skia.committer@gmail.com 1230c518710d9a99c4d0adf759a102f4a1cb582f5939reed@google.com if (pt) { 12316862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org pt->set(conic_eval_pos(&fPts[0].fX, fW, t), 12326862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org conic_eval_pos(&fPts[0].fY, fW, t)); 1233c518710d9a99c4d0adf759a102f4a1cb582f5939reed@google.com } 123424bd210f2e2cf66f356b4e98f7801631089b8aa3reed@google.com if (tangent) { 123524bd210f2e2cf66f356b4e98f7801631089b8aa3reed@google.com tangent->set(conic_eval_tan(&fPts[0].fX, fW, t), 123624bd210f2e2cf66f356b4e98f7801631089b8aa3reed@google.com conic_eval_tan(&fPts[0].fY, fW, t)); 123724bd210f2e2cf66f356b4e98f7801631089b8aa3reed@google.com } 1238c518710d9a99c4d0adf759a102f4a1cb582f5939reed@google.com} 1239c518710d9a99c4d0adf759a102f4a1cb582f5939reed@google.com 124028552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgvoid SkConic::chopAt(SkScalar t, SkConic dst[2]) const { 12410d099557feb99707c8f601746f46f5a295eb33b7reed@google.com SkP3D tmp[3], tmp2[3]; 12420d099557feb99707c8f601746f46f5a295eb33b7reed@google.com 12430d099557feb99707c8f601746f46f5a295eb33b7reed@google.com ratquad_mapTo3D(fPts, fW, tmp); 12444bb50b22fce5c4031549976cf7b04d63cc22e624skia.committer@gmail.com 12450d099557feb99707c8f601746f46f5a295eb33b7reed@google.com p3d_interp(&tmp[0].fX, &tmp2[0].fX, t); 12460d099557feb99707c8f601746f46f5a295eb33b7reed@google.com p3d_interp(&tmp[0].fY, &tmp2[0].fY, t); 12470d099557feb99707c8f601746f46f5a295eb33b7reed@google.com p3d_interp(&tmp[0].fZ, &tmp2[0].fZ, t); 12484bb50b22fce5c4031549976cf7b04d63cc22e624skia.committer@gmail.com 12490d099557feb99707c8f601746f46f5a295eb33b7reed@google.com dst[0].fPts[0] = fPts[0]; 12500d099557feb99707c8f601746f46f5a295eb33b7reed@google.com tmp2[0].projectDown(&dst[0].fPts[1]); 12510d099557feb99707c8f601746f46f5a295eb33b7reed@google.com tmp2[1].projectDown(&dst[0].fPts[2]); dst[1].fPts[0] = dst[0].fPts[2]; 12520d099557feb99707c8f601746f46f5a295eb33b7reed@google.com tmp2[2].projectDown(&dst[1].fPts[1]); 12530d099557feb99707c8f601746f46f5a295eb33b7reed@google.com dst[1].fPts[2] = fPts[2]; 12540d099557feb99707c8f601746f46f5a295eb33b7reed@google.com 12554af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org // to put in "standard form", where w0 and w2 are both 1, we compute the 12564af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org // new w1 as sqrt(w1*w1/w0*w2) 12574af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org // or 12584af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org // w1 /= sqrt(w0*w2) 12594af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org // 1260def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org // However, in our case, we know that for dst[0]: 1261def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org // w0 == 1, and for dst[1], w2 == 1 12624af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org // 12634af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org SkScalar root = SkScalarSqrt(tmp2[1].fZ); 12644af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org dst[0].fW = tmp2[0].fZ / root; 12654af6280aa366a02540f34c48f89ea73ce3d27974mike@reedtribe.org dst[1].fW = tmp2[2].fZ / root; 1266c518710d9a99c4d0adf759a102f4a1cb582f5939reed@google.com} 12678d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org 1268b640203cd5733aaf110277e28e22007c5b541565reedstatic Sk2s times_2(const Sk2s& value) { 1269b640203cd5733aaf110277e28e22007c5b541565reed return value + value; 1270b640203cd5733aaf110277e28e22007c5b541565reed} 1271b640203cd5733aaf110277e28e22007c5b541565reed 1272b640203cd5733aaf110277e28e22007c5b541565reedSkPoint SkConic::evalAt(SkScalar t) const { 1273b640203cd5733aaf110277e28e22007c5b541565reed Sk2s p0 = from_point(fPts[0]); 1274b640203cd5733aaf110277e28e22007c5b541565reed Sk2s p1 = from_point(fPts[1]); 1275b640203cd5733aaf110277e28e22007c5b541565reed Sk2s p2 = from_point(fPts[2]); 1276ce6acc91085c4b6d87d4bac84e66193908e648f9reed Sk2s tt(t); 1277ce6acc91085c4b6d87d4bac84e66193908e648f9reed Sk2s ww(fW); 1278ce6acc91085c4b6d87d4bac84e66193908e648f9reed Sk2s one(1); 1279b640203cd5733aaf110277e28e22007c5b541565reed 1280b640203cd5733aaf110277e28e22007c5b541565reed Sk2s p1w = p1 * ww; 1281b640203cd5733aaf110277e28e22007c5b541565reed Sk2s C = p0; 1282b640203cd5733aaf110277e28e22007c5b541565reed Sk2s A = p2 - times_2(p1w) + p0; 1283b640203cd5733aaf110277e28e22007c5b541565reed Sk2s B = times_2(p1w - C); 1284b640203cd5733aaf110277e28e22007c5b541565reed Sk2s numer = quad_poly_eval(A, B, C, tt); 1285b640203cd5733aaf110277e28e22007c5b541565reed 1286b640203cd5733aaf110277e28e22007c5b541565reed B = times_2(ww - one); 1287b640203cd5733aaf110277e28e22007c5b541565reed A = -B; 1288b640203cd5733aaf110277e28e22007c5b541565reed Sk2s denom = quad_poly_eval(A, B, one, tt); 1289b640203cd5733aaf110277e28e22007c5b541565reed 1290b640203cd5733aaf110277e28e22007c5b541565reed return to_point(numer / denom); 1291b640203cd5733aaf110277e28e22007c5b541565reed} 1292b640203cd5733aaf110277e28e22007c5b541565reed 1293b640203cd5733aaf110277e28e22007c5b541565reedSkVector SkConic::evalTangentAt(SkScalar t) const { 1294b640203cd5733aaf110277e28e22007c5b541565reed Sk2s p0 = from_point(fPts[0]); 1295b640203cd5733aaf110277e28e22007c5b541565reed Sk2s p1 = from_point(fPts[1]); 1296b640203cd5733aaf110277e28e22007c5b541565reed Sk2s p2 = from_point(fPts[2]); 1297ce6acc91085c4b6d87d4bac84e66193908e648f9reed Sk2s ww(fW); 1298b640203cd5733aaf110277e28e22007c5b541565reed 1299b640203cd5733aaf110277e28e22007c5b541565reed Sk2s p20 = p2 - p0; 1300b640203cd5733aaf110277e28e22007c5b541565reed Sk2s p10 = p1 - p0; 1301b640203cd5733aaf110277e28e22007c5b541565reed 1302b640203cd5733aaf110277e28e22007c5b541565reed Sk2s C = ww * p10; 1303b640203cd5733aaf110277e28e22007c5b541565reed Sk2s A = ww * p20 - p20; 1304b640203cd5733aaf110277e28e22007c5b541565reed Sk2s B = p20 - C - C; 1305b640203cd5733aaf110277e28e22007c5b541565reed 1306b640203cd5733aaf110277e28e22007c5b541565reed return to_vector(quad_poly_eval(A, B, C, Sk2s(t))); 1307b640203cd5733aaf110277e28e22007c5b541565reed} 1308b640203cd5733aaf110277e28e22007c5b541565reed 13093df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.orgstatic SkScalar subdivide_w_value(SkScalar w) { 13106862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org return SkScalarSqrt(SK_ScalarHalf + w * SK_ScalarHalf); 13113df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org} 13123df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org 131355011038816a3fc7f0c0a39d482fb85347cc2e78reedstatic Sk2s twice(const Sk2s& value) { 131455011038816a3fc7f0c0a39d482fb85347cc2e78reed return value + value; 13153df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org} 13163df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org 131755011038816a3fc7f0c0a39d482fb85347cc2e78reedvoid SkConic::chop(SkConic * SK_RESTRICT dst) const { 131855011038816a3fc7f0c0a39d482fb85347cc2e78reed Sk2s scale = Sk2s(SkScalarInvert(SK_Scalar1 + fW)); 1319b640203cd5733aaf110277e28e22007c5b541565reed SkScalar newW = subdivide_w_value(fW); 1320b640203cd5733aaf110277e28e22007c5b541565reed 1321b640203cd5733aaf110277e28e22007c5b541565reed Sk2s p0 = from_point(fPts[0]); 1322b640203cd5733aaf110277e28e22007c5b541565reed Sk2s p1 = from_point(fPts[1]); 1323b640203cd5733aaf110277e28e22007c5b541565reed Sk2s p2 = from_point(fPts[2]); 1324ce6acc91085c4b6d87d4bac84e66193908e648f9reed Sk2s ww(fW); 1325b640203cd5733aaf110277e28e22007c5b541565reed 1326b640203cd5733aaf110277e28e22007c5b541565reed Sk2s wp1 = ww * p1; 132755011038816a3fc7f0c0a39d482fb85347cc2e78reed Sk2s m = (p0 + twice(wp1) + p2) * scale * Sk2s(0.5f); 1328b640203cd5733aaf110277e28e22007c5b541565reed 1329b640203cd5733aaf110277e28e22007c5b541565reed dst[0].fPts[0] = fPts[0]; 1330b640203cd5733aaf110277e28e22007c5b541565reed dst[0].fPts[1] = to_point((p0 + wp1) * scale); 1331b640203cd5733aaf110277e28e22007c5b541565reed dst[0].fPts[2] = dst[1].fPts[0] = to_point(m); 1332b640203cd5733aaf110277e28e22007c5b541565reed dst[1].fPts[1] = to_point((wp1 + p2) * scale); 1333b640203cd5733aaf110277e28e22007c5b541565reed dst[1].fPts[2] = fPts[2]; 1334b640203cd5733aaf110277e28e22007c5b541565reed 1335b640203cd5733aaf110277e28e22007c5b541565reed dst[0].fW = dst[1].fW = newW; 1336b640203cd5733aaf110277e28e22007c5b541565reed} 1337b640203cd5733aaf110277e28e22007c5b541565reed 133897514f22e4cb85a0d79b089a1eecd54d4a952291mike@reedtribe.org/* 133997514f22e4cb85a0d79b089a1eecd54d4a952291mike@reedtribe.org * "High order approximation of conic sections by quadratic splines" 134097514f22e4cb85a0d79b089a1eecd54d4a952291mike@reedtribe.org * by Michael Floater, 1993 134197514f22e4cb85a0d79b089a1eecd54d4a952291mike@reedtribe.org */ 1342af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org#define AS_QUAD_ERROR_SETUP \ 1343af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org SkScalar a = fW - 1; \ 1344af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org SkScalar k = a / (4 * (2 + a)); \ 1345af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org SkScalar x = k * (fPts[0].fX - 2 * fPts[1].fX + fPts[2].fX); \ 1346af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org SkScalar y = k * (fPts[0].fY - 2 * fPts[1].fY + fPts[2].fY); 1347af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org 1348af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.orgvoid SkConic::computeAsQuadError(SkVector* err) const { 1349af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org AS_QUAD_ERROR_SETUP 1350af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org err->set(x, y); 1351af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org} 1352af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org 1353af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.orgbool SkConic::asQuadTol(SkScalar tol) const { 1354af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org AS_QUAD_ERROR_SETUP 1355af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org return (x * x + y * y) <= tol * tol; 135697514f22e4cb85a0d79b089a1eecd54d4a952291mike@reedtribe.org} 13577841c63136e8aa2d3aadbeab8432405abcd73c32skia.committer@gmail.com 1358f16c00e41b72daa81ed7efacbead06b387767841reed// Limit the number of suggested quads to approximate a conic 1359f16c00e41b72daa81ed7efacbead06b387767841reed#define kMaxConicToQuadPOW2 5 1360f16c00e41b72daa81ed7efacbead06b387767841reed 136197514f22e4cb85a0d79b089a1eecd54d4a952291mike@reedtribe.orgint SkConic::computeQuadPOW2(SkScalar tol) const { 1362f16c00e41b72daa81ed7efacbead06b387767841reed if (tol < 0 || !SkScalarIsFinite(tol)) { 1363f16c00e41b72daa81ed7efacbead06b387767841reed return 0; 1364f16c00e41b72daa81ed7efacbead06b387767841reed } 1365f16c00e41b72daa81ed7efacbead06b387767841reed 1366af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org AS_QUAD_ERROR_SETUP 1367f16c00e41b72daa81ed7efacbead06b387767841reed 1368f16c00e41b72daa81ed7efacbead06b387767841reed SkScalar error = SkScalarSqrt(x * x + y * y); 1369f16c00e41b72daa81ed7efacbead06b387767841reed int pow2; 1370f16c00e41b72daa81ed7efacbead06b387767841reed for (pow2 = 0; pow2 < kMaxConicToQuadPOW2; ++pow2) { 1371f16c00e41b72daa81ed7efacbead06b387767841reed if (error <= tol) { 1372f16c00e41b72daa81ed7efacbead06b387767841reed break; 1373f16c00e41b72daa81ed7efacbead06b387767841reed } 1374f16c00e41b72daa81ed7efacbead06b387767841reed error *= 0.25f; 1375f16c00e41b72daa81ed7efacbead06b387767841reed } 1376f16c00e41b72daa81ed7efacbead06b387767841reed // float version -- using ceil gives the same results as the above. 1377f16c00e41b72daa81ed7efacbead06b387767841reed if (false) { 1378f16c00e41b72daa81ed7efacbead06b387767841reed SkScalar err = SkScalarSqrt(x * x + y * y); 1379f16c00e41b72daa81ed7efacbead06b387767841reed if (err <= tol) { 1380f16c00e41b72daa81ed7efacbead06b387767841reed return 0; 1381f16c00e41b72daa81ed7efacbead06b387767841reed } 1382f16c00e41b72daa81ed7efacbead06b387767841reed SkScalar tol2 = tol * tol; 1383f16c00e41b72daa81ed7efacbead06b387767841reed if (tol2 == 0) { 1384f16c00e41b72daa81ed7efacbead06b387767841reed return kMaxConicToQuadPOW2; 1385f16c00e41b72daa81ed7efacbead06b387767841reed } 1386f16c00e41b72daa81ed7efacbead06b387767841reed SkScalar fpow2 = SkScalarLog2((x * x + y * y) / tol2) * 0.25f; 1387f16c00e41b72daa81ed7efacbead06b387767841reed int altPow2 = SkScalarCeilToInt(fpow2); 1388f16c00e41b72daa81ed7efacbead06b387767841reed if (altPow2 != pow2) { 1389f16c00e41b72daa81ed7efacbead06b387767841reed SkDebugf("pow2 %d altPow2 %d fbits %g err %g tol %g\n", pow2, altPow2, fpow2, err, tol); 1390f16c00e41b72daa81ed7efacbead06b387767841reed } 1391f16c00e41b72daa81ed7efacbead06b387767841reed pow2 = altPow2; 1392f16c00e41b72daa81ed7efacbead06b387767841reed } 1393f16c00e41b72daa81ed7efacbead06b387767841reed return pow2; 13943df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org} 13953df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org 139628552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgstatic SkPoint* subdivide(const SkConic& src, SkPoint pts[], int level) { 13973df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org SkASSERT(level >= 0); 1398af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org 13993df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org if (0 == level) { 14003df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org memcpy(pts, &src.fPts[1], 2 * sizeof(SkPoint)); 14013df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org return pts + 2; 14023df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org } else { 140328552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.org SkConic dst[2]; 14043df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org src.chop(dst); 14053df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org --level; 14063df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org pts = subdivide(dst[0], pts, level); 14073df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org return subdivide(dst[1], pts, level); 14083df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org } 14098d551011966a1bc14a654dbde704f343c0e222b6mike@reedtribe.org} 14103df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org 141128552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgint SkConic::chopIntoQuadsPOW2(SkPoint pts[], int pow2) const { 1412af5c506cd6b63f43a0ebee2fb171ea55ba98e09fmike@reedtribe.org SkASSERT(pow2 >= 0); 14133df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org *pts = fPts[0]; 1414aebfa7e1b1e94f693f3e7beb6ad43cfcb0f69e98reed@google.com SkDEBUGCODE(SkPoint* endPts =) subdivide(*this, pts + 1, pow2); 14153df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org SkASSERT(endPts - pts == (2 * (1 << pow2) + 1)); 14163df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org return 1 << pow2; 14173df87cb36e9f9d2e04d2f81ac64cf3d778c33847mike@reedtribe.org} 14180c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org 141928552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgbool SkConic::findXExtrema(SkScalar* t) const { 14206862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org return conic_find_extrema(&fPts[0].fX, fW, t); 14210c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org} 14220c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org 142328552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgbool SkConic::findYExtrema(SkScalar* t) const { 14246862cbad085729acb77825392c8c2a4f888a99cfmike@reedtribe.org return conic_find_extrema(&fPts[0].fY, fW, t); 14250c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org} 14260c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org 142728552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgbool SkConic::chopAtXExtrema(SkConic dst[2]) const { 14280c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar t; 14290c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org if (this->findXExtrema(&t)) { 14300c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org this->chopAt(t, dst); 14310c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org // now clean-up the middle, since we know t was meant to be at 14320c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org // an X-extrema 14330c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar value = dst[0].fPts[2].fX; 14340c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org dst[0].fPts[1].fX = value; 14350c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org dst[1].fPts[0].fX = value; 14360c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org dst[1].fPts[1].fX = value; 14370c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org return true; 14380c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org } 14390c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org return false; 14400c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org} 14410c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org 144228552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgbool SkConic::chopAtYExtrema(SkConic dst[2]) const { 14430c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar t; 14440c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org if (this->findYExtrema(&t)) { 14450c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org this->chopAt(t, dst); 14460c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org // now clean-up the middle, since we know t was meant to be at 14470c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org // an Y-extrema 14480c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org SkScalar value = dst[0].fPts[2].fY; 14490c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org dst[0].fPts[1].fY = value; 14500c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org dst[1].fPts[0].fY = value; 14510c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org dst[1].fPts[1].fY = value; 14520c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org return true; 14530c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org } 14540c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org return false; 14550c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org} 14560c5c3867bdbde1005a7bbb9de9df93cc10e27782mike@reedtribe.org 145728552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgvoid SkConic::computeTightBounds(SkRect* bounds) const { 14585c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org SkPoint pts[4]; 14595c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org pts[0] = fPts[0]; 14605c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org pts[1] = fPts[2]; 14615c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org int count = 2; 14625c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org 14635c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org SkScalar t; 14645c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org if (this->findXExtrema(&t)) { 14655c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org this->evalAt(t, &pts[count++]); 14665c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org } 14675c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org if (this->findYExtrema(&t)) { 14685c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org this->evalAt(t, &pts[count++]); 14695c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org } 14705c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org bounds->set(pts, count); 14715c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org} 14725c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org 147328552e12a019bf5ae55c9e8602bbe216562d7a3emike@reedtribe.orgvoid SkConic::computeFastBounds(SkRect* bounds) const { 14745c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org bounds->set(fPts, 3); 14755c082a14acbb70eec2fd6dc5a4c134799f3d8535mike@reedtribe.org} 1476def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org 1477def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.orgbool SkConic::findMaxCurvature(SkScalar* t) const { 1478def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org // TODO: Implement me 1479def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org return false; 1480def6468dd2daed36eced69098445aa99c90487d6commit-bot@chromium.org} 1481220f926d9d4b38a9018c922c095847bbd261f583reed 1482220f926d9d4b38a9018c922c095847bbd261f583reedSkScalar SkConic::TransformW(const SkPoint pts[], SkScalar w, 1483220f926d9d4b38a9018c922c095847bbd261f583reed const SkMatrix& matrix) { 1484220f926d9d4b38a9018c922c095847bbd261f583reed if (!matrix.hasPerspective()) { 1485220f926d9d4b38a9018c922c095847bbd261f583reed return w; 1486220f926d9d4b38a9018c922c095847bbd261f583reed } 1487220f926d9d4b38a9018c922c095847bbd261f583reed 1488220f926d9d4b38a9018c922c095847bbd261f583reed SkP3D src[3], dst[3]; 1489950e986b1bc127af1f484572d2494091957486f9mtklein 1490220f926d9d4b38a9018c922c095847bbd261f583reed ratquad_mapTo3D(pts, w, src); 1491220f926d9d4b38a9018c922c095847bbd261f583reed 1492220f926d9d4b38a9018c922c095847bbd261f583reed matrix.mapHomogeneousPoints(&dst[0].fX, &src[0].fX, 3); 1493220f926d9d4b38a9018c922c095847bbd261f583reed 1494220f926d9d4b38a9018c922c095847bbd261f583reed // w' = sqrt(w1*w1/w0*w2) 1495220f926d9d4b38a9018c922c095847bbd261f583reed SkScalar w0 = dst[0].fZ; 1496220f926d9d4b38a9018c922c095847bbd261f583reed SkScalar w1 = dst[1].fZ; 1497220f926d9d4b38a9018c922c095847bbd261f583reed SkScalar w2 = dst[2].fZ; 1498220f926d9d4b38a9018c922c095847bbd261f583reed w = SkScalarSqrt((w1 * w1) / (w0 * w2)); 1499220f926d9d4b38a9018c922c095847bbd261f583reed return w; 1500220f926d9d4b38a9018c922c095847bbd261f583reed} 1501d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed 1502d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reedint SkConic::BuildUnitArc(const SkVector& uStart, const SkVector& uStop, SkRotationDirection dir, 1503d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed const SkMatrix* userMatrix, SkConic dst[kMaxConicsForArc]) { 1504d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed // rotate by x,y so that uStart is (1.0) 1505d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed SkScalar x = SkPoint::DotProduct(uStart, uStop); 1506d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed SkScalar y = SkPoint::CrossProduct(uStart, uStop); 1507d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed 1508d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed SkScalar absY = SkScalarAbs(y); 1509d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed 1510d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed // check for (effectively) coincident vectors 1511d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed // this can happen if our angle is nearly 0 or nearly 180 (y == 0) 1512d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed // ... we use the dot-prod to distinguish between 0 and 180 (x > 0) 1513d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed if (absY <= SK_ScalarNearlyZero && x > 0 && ((y >= 0 && kCW_SkRotationDirection == dir) || 1514d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed (y <= 0 && kCCW_SkRotationDirection == dir))) { 1515d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed return 0; 1516d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed } 1517d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed 1518d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed if (dir == kCCW_SkRotationDirection) { 1519d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed y = -y; 1520d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed } 1521d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed 1522d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed // We decide to use 1-conic per quadrant of a circle. What quadrant does [xy] lie in? 1523d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed // 0 == [0 .. 90) 1524d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed // 1 == [90 ..180) 1525d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed // 2 == [180..270) 1526d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed // 3 == [270..360) 1527d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed // 1528d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed int quadrant = 0; 1529d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed if (0 == y) { 1530d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed quadrant = 2; // 180 1531d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed SkASSERT(SkScalarAbs(x + SK_Scalar1) <= SK_ScalarNearlyZero); 1532d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed } else if (0 == x) { 1533d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed SkASSERT(absY - SK_Scalar1 <= SK_ScalarNearlyZero); 1534d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed quadrant = y > 0 ? 1 : 3; // 90 : 270 1535d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed } else { 1536d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed if (y < 0) { 1537d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed quadrant += 2; 1538d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed } 1539d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed if ((x < 0) != (y < 0)) { 1540d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed quadrant += 1; 1541d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed } 1542d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed } 1543d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed 1544d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed const SkPoint quadrantPts[] = { 1545d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed { 1, 0 }, { 1, 1 }, { 0, 1 }, { -1, 1 }, { -1, 0 }, { -1, -1 }, { 0, -1 }, { 1, -1 } 1546d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed }; 1547d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed const SkScalar quadrantWeight = SK_ScalarRoot2Over2; 1548d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed 1549d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed int conicCount = quadrant; 1550d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed for (int i = 0; i < conicCount; ++i) { 1551d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed dst[i].set(&quadrantPts[i * 2], quadrantWeight); 1552d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed } 1553d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed 1554d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed // Now compute any remaing (sub-90-degree) arc for the last conic 1555d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed const SkPoint finalP = { x, y }; 1556d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed const SkPoint& lastQ = quadrantPts[quadrant * 2]; // will already be a unit-vector 1557d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed const SkScalar dot = SkVector::DotProduct(lastQ, finalP); 155888f0a99fd48cfb30ca5596182f8932d76cd76f17reed SkASSERT(0 <= dot && dot <= SK_Scalar1 + SK_ScalarNearlyZero); 1559d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed 1560c6325cde797baeedebc515bc8610f96eacbd36c9caryclark if (dot < 1) { 1561d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed SkVector offCurve = { lastQ.x() + x, lastQ.y() + y }; 1562d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed // compute the bisector vector, and then rescale to be the off-curve point. 1563d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed // we compute its length from cos(theta/2) = length / 1, using half-angle identity we get 1564d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed // length = sqrt(2 / (1 + cos(theta)). We already have cos() when to computed the dot. 1565d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed // This is nice, since our computed weight is cos(theta/2) as well! 1566d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed // 1567d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed const SkScalar cosThetaOver2 = SkScalarSqrt((1 + dot) / 2); 1568d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed offCurve.setLength(SkScalarInvert(cosThetaOver2)); 1569d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed dst[conicCount].set(lastQ, offCurve, finalP, cosThetaOver2); 1570d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed conicCount += 1; 1571d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed } 1572d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed 1573d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed // now handle counter-clockwise and the initial unitStart rotation 1574d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed SkMatrix matrix; 1575d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed matrix.setSinCos(uStart.fY, uStart.fX); 1576d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed if (dir == kCCW_SkRotationDirection) { 1577d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed matrix.preScale(SK_Scalar1, -SK_Scalar1); 1578d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed } 1579d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed if (userMatrix) { 1580d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed matrix.postConcat(*userMatrix); 1581d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed } 1582d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed for (int i = 0; i < conicCount; ++i) { 1583d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed matrix.mapPoints(dst[i].fPts, 3); 1584d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed } 1585d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed return conicCount; 1586d5d27d9b146731b871b1bcc6d6de36fba2d5ea44reed} 1587