Chris Dalton | 419a94d | 2017-08-28 10:24:22 -0600 | [diff] [blame] | 1 | /* |
| 2 | * Copyright 2017 Google Inc. |
| 3 | * |
| 4 | * Use of this source code is governed by a BSD-style license that can be |
| 5 | * found in the LICENSE file. |
| 6 | */ |
| 7 | |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 8 | #include "GrCCGeometry.h" |
Chris Dalton | 419a94d | 2017-08-28 10:24:22 -0600 | [diff] [blame] | 9 | |
| 10 | #include "GrTypes.h" |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 11 | #include "GrPathUtils.h" |
Chris Dalton | 419a94d | 2017-08-28 10:24:22 -0600 | [diff] [blame] | 12 | #include <algorithm> |
| 13 | #include <cmath> |
| 14 | #include <cstdlib> |
| 15 | |
| 16 | // We convert between SkPoint and Sk2f freely throughout this file. |
| 17 | GR_STATIC_ASSERT(SK_SCALAR_IS_FLOAT); |
| 18 | GR_STATIC_ASSERT(2 * sizeof(float) == sizeof(SkPoint)); |
| 19 | GR_STATIC_ASSERT(0 == offsetof(SkPoint, fX)); |
| 20 | |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 21 | void GrCCGeometry::beginPath() { |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 22 | SkASSERT(!fBuildingContour); |
| 23 | fVerbs.push_back(Verb::kBeginPath); |
| 24 | } |
| 25 | |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 26 | void GrCCGeometry::beginContour(const SkPoint& pt) { |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 27 | SkASSERT(!fBuildingContour); |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 28 | // Store the current verb count in the fTriangles field for now. When we close the contour we |
| 29 | // will use this value to calculate the actual number of triangles in its fan. |
Chris Dalton | 84403d7 | 2018-02-13 21:46:17 -0500 | [diff] [blame] | 30 | fCurrContourTallies = {fVerbs.count(), 0, 0, 0}; |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 31 | |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 32 | fPoints.push_back(pt); |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 33 | fVerbs.push_back(Verb::kBeginContour); |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 34 | fCurrAnchorPoint = pt; |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 35 | |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 36 | SkDEBUGCODE(fBuildingContour = true); |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 37 | } |
| 38 | |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 39 | void GrCCGeometry::lineTo(const SkPoint& pt) { |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 40 | SkASSERT(fBuildingContour); |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 41 | fPoints.push_back(pt); |
| 42 | fVerbs.push_back(Verb::kLineTo); |
| 43 | } |
| 44 | |
| 45 | void GrCCGeometry::appendLine(const Sk2f& endpt) { |
| 46 | endpt.store(&fPoints.push_back()); |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 47 | fVerbs.push_back(Verb::kLineTo); |
| 48 | } |
| 49 | |
Chris Dalton | 419a94d | 2017-08-28 10:24:22 -0600 | [diff] [blame] | 50 | static inline Sk2f normalize(const Sk2f& n) { |
| 51 | Sk2f nn = n*n; |
| 52 | return n * (nn + SkNx_shuffle<1,0>(nn)).rsqrt(); |
| 53 | } |
| 54 | |
| 55 | static inline float dot(const Sk2f& a, const Sk2f& b) { |
| 56 | float product[2]; |
| 57 | (a * b).store(product); |
| 58 | return product[0] + product[1]; |
| 59 | } |
| 60 | |
Chris Dalton | 900cd05 | 2017-09-07 10:36:51 -0600 | [diff] [blame] | 61 | static inline bool are_collinear(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2) { |
Chris Dalton | 4364653 | 2017-12-07 12:47:02 -0700 | [diff] [blame] | 62 | static constexpr float kFlatnessTolerance = 4; // 1/4 of a pixel. |
Chris Dalton | 900cd05 | 2017-09-07 10:36:51 -0600 | [diff] [blame] | 63 | |
| 64 | // Area (times 2) of the triangle. |
| 65 | Sk2f a = (p0 - p1) * SkNx_shuffle<1,0>(p1 - p2); |
| 66 | a = (a - SkNx_shuffle<1,0>(a)).abs(); |
| 67 | |
| 68 | // Bounding box of the triangle. |
| 69 | Sk2f bbox0 = Sk2f::Min(Sk2f::Min(p0, p1), p2); |
| 70 | Sk2f bbox1 = Sk2f::Max(Sk2f::Max(p0, p1), p2); |
| 71 | |
| 72 | // The triangle is linear if its area is within a fraction of the largest bounding box |
| 73 | // dimension, or else if its area is within a fraction of a pixel. |
| 74 | return (a * (kFlatnessTolerance/2) < Sk2f::Max(bbox1 - bbox0, 1)).anyTrue(); |
| 75 | } |
| 76 | |
Chris Dalton | 419a94d | 2017-08-28 10:24:22 -0600 | [diff] [blame] | 77 | // Returns whether the (convex) curve segment is monotonic with respect to [endPt - startPt]. |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 78 | static inline bool is_convex_curve_monotonic(const Sk2f& startPt, const Sk2f& tan0, |
| 79 | const Sk2f& endPt, const Sk2f& tan1) { |
Chris Dalton | 419a94d | 2017-08-28 10:24:22 -0600 | [diff] [blame] | 80 | Sk2f v = endPt - startPt; |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 81 | float dot0 = dot(tan0, v); |
| 82 | float dot1 = dot(tan1, v); |
Chris Dalton | 419a94d | 2017-08-28 10:24:22 -0600 | [diff] [blame] | 83 | |
| 84 | // A small, negative tolerance handles floating-point error in the case when one tangent |
| 85 | // approaches 0 length, meaning the (convex) curve segment is effectively a flat line. |
| 86 | float tolerance = -std::max(std::abs(dot0), std::abs(dot1)) * SK_ScalarNearlyZero; |
| 87 | return dot0 >= tolerance && dot1 >= tolerance; |
| 88 | } |
| 89 | |
| 90 | static inline Sk2f lerp(const Sk2f& a, const Sk2f& b, const Sk2f& t) { |
| 91 | return SkNx_fma(t, b - a, a); |
| 92 | } |
| 93 | |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 94 | void GrCCGeometry::quadraticTo(const SkPoint P[3]) { |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 95 | SkASSERT(fBuildingContour); |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 96 | SkASSERT(P[0] == fPoints.back()); |
| 97 | Sk2f p0 = Sk2f::Load(P); |
| 98 | Sk2f p1 = Sk2f::Load(P+1); |
| 99 | Sk2f p2 = Sk2f::Load(P+2); |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 100 | |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 101 | // Don't crunch on the curve if it is nearly flat (or just very small). Flat curves can break |
| 102 | // The monotonic chopping math. |
| 103 | if (are_collinear(p0, p1, p2)) { |
| 104 | this->appendLine(p2); |
| 105 | return; |
| 106 | } |
Chris Dalton | 419a94d | 2017-08-28 10:24:22 -0600 | [diff] [blame] | 107 | |
Chris Dalton | 29011a2 | 2017-09-28 12:08:33 -0600 | [diff] [blame] | 108 | this->appendMonotonicQuadratics(p0, p1, p2); |
| 109 | } |
| 110 | |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 111 | inline void GrCCGeometry::appendMonotonicQuadratics(const Sk2f& p0, const Sk2f& p1, |
| 112 | const Sk2f& p2) { |
Chris Dalton | 419a94d | 2017-08-28 10:24:22 -0600 | [diff] [blame] | 113 | Sk2f tan0 = p1 - p0; |
| 114 | Sk2f tan1 = p2 - p1; |
Chris Dalton | 29011a2 | 2017-09-28 12:08:33 -0600 | [diff] [blame] | 115 | |
Chris Dalton | 419a94d | 2017-08-28 10:24:22 -0600 | [diff] [blame] | 116 | // This should almost always be this case for well-behaved curves in the real world. |
Chris Dalton | 4364653 | 2017-12-07 12:47:02 -0700 | [diff] [blame] | 117 | if (is_convex_curve_monotonic(p0, tan0, p2, tan1)) { |
| 118 | this->appendSingleMonotonicQuadratic(p0, p1, p2); |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 119 | return; |
Chris Dalton | 419a94d | 2017-08-28 10:24:22 -0600 | [diff] [blame] | 120 | } |
| 121 | |
| 122 | // Chop the curve into two segments with equal curvature. To do this we find the T value whose |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 123 | // tangent angle is halfway between tan0 and tan1. |
Chris Dalton | 419a94d | 2017-08-28 10:24:22 -0600 | [diff] [blame] | 124 | Sk2f n = normalize(tan0) - normalize(tan1); |
| 125 | |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 126 | // The midtangent can be found where (dQ(t) dot n) = 0: |
Chris Dalton | 419a94d | 2017-08-28 10:24:22 -0600 | [diff] [blame] | 127 | // |
| 128 | // 0 = (dQ(t) dot n) = | 2*t 1 | * | p0 - 2*p1 + p2 | * | n | |
| 129 | // | -2*p0 + 2*p1 | | . | |
| 130 | // |
| 131 | // = | 2*t 1 | * | tan1 - tan0 | * | n | |
| 132 | // | 2*tan0 | | . | |
| 133 | // |
| 134 | // = 2*t * ((tan1 - tan0) dot n) + (2*tan0 dot n) |
| 135 | // |
| 136 | // t = (tan0 dot n) / ((tan0 - tan1) dot n) |
| 137 | Sk2f dQ1n = (tan0 - tan1) * n; |
| 138 | Sk2f dQ0n = tan0 * n; |
| 139 | Sk2f t = (dQ0n + SkNx_shuffle<1,0>(dQ0n)) / (dQ1n + SkNx_shuffle<1,0>(dQ1n)); |
| 140 | t = Sk2f::Min(Sk2f::Max(t, 0), 1); // Clamp for FP error. |
| 141 | |
| 142 | Sk2f p01 = SkNx_fma(t, tan0, p0); |
| 143 | Sk2f p12 = SkNx_fma(t, tan1, p1); |
| 144 | Sk2f p012 = lerp(p01, p12, t); |
| 145 | |
Chris Dalton | 4364653 | 2017-12-07 12:47:02 -0700 | [diff] [blame] | 146 | this->appendSingleMonotonicQuadratic(p0, p01, p012); |
| 147 | this->appendSingleMonotonicQuadratic(p012, p12, p2); |
| 148 | } |
| 149 | |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 150 | inline void GrCCGeometry::appendSingleMonotonicQuadratic(const Sk2f& p0, const Sk2f& p1, |
| 151 | const Sk2f& p2) { |
Chris Dalton | 4364653 | 2017-12-07 12:47:02 -0700 | [diff] [blame] | 152 | SkASSERT(fPoints.back() == SkPoint::Make(p0[0], p0[1])); |
| 153 | |
| 154 | // Don't send curves to the GPU if we know they are nearly flat (or just very small). |
| 155 | if (are_collinear(p0, p1, p2)) { |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 156 | this->appendLine(p2); |
Chris Dalton | 4364653 | 2017-12-07 12:47:02 -0700 | [diff] [blame] | 157 | return; |
| 158 | } |
| 159 | |
| 160 | p1.store(&fPoints.push_back()); |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 161 | p2.store(&fPoints.push_back()); |
Chris Dalton | 4364653 | 2017-12-07 12:47:02 -0700 | [diff] [blame] | 162 | fVerbs.push_back(Verb::kMonotonicQuadraticTo); |
| 163 | ++fCurrContourTallies.fQuadratics; |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 164 | } |
| 165 | |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 166 | using ExcludedTerm = GrPathUtils::ExcludedTerm; |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 167 | |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 168 | // Calculates the padding to apply around inflection points, in homogeneous parametric coordinates. |
| 169 | // |
| 170 | // More specifically, if the inflection point lies at C(t/s), then C((t +/- returnValue) / s) will |
| 171 | // be the two points on the curve at which a square box with radius "padRadius" will have a corner |
| 172 | // that touches the inflection point's tangent line. |
| 173 | // |
| 174 | // A serpentine cubic has two inflection points, so this method takes Sk2f and computes the padding |
| 175 | // for both in SIMD. |
| 176 | static inline Sk2f calc_inflect_homogeneous_padding(float padRadius, const Sk2f& t, const Sk2f& s, |
| 177 | const SkMatrix& CIT, ExcludedTerm skipTerm) { |
| 178 | SkASSERT(padRadius >= 0); |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 179 | |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 180 | Sk2f Clx = s*s*s; |
| 181 | Sk2f Cly = (ExcludedTerm::kLinearTerm == skipTerm) ? s*s*t*-3 : s*t*t*3; |
| 182 | |
| 183 | Sk2f Lx = CIT[0] * Clx + CIT[3] * Cly; |
| 184 | Sk2f Ly = CIT[1] * Clx + CIT[4] * Cly; |
| 185 | |
| 186 | float ret[2]; |
| 187 | Sk2f bloat = padRadius * (Lx.abs() + Ly.abs()); |
| 188 | (bloat * s >= 0).thenElse(bloat, -bloat).store(ret); |
| 189 | |
| 190 | ret[0] = cbrtf(ret[0]); |
| 191 | ret[1] = cbrtf(ret[1]); |
| 192 | return Sk2f::Load(ret); |
| 193 | } |
| 194 | |
| 195 | static inline void swap_if_greater(float& a, float& b) { |
| 196 | if (a > b) { |
| 197 | std::swap(a, b); |
| 198 | } |
| 199 | } |
| 200 | |
| 201 | // Calculates all parameter values for a loop at which points a square box with radius "padRadius" |
| 202 | // will have a corner that touches a tangent line from the intersection. |
| 203 | // |
| 204 | // T2 must contain the lesser parameter value of the loop intersection in its first component, and |
| 205 | // the greater in its second. |
| 206 | // |
| 207 | // roots[0] will be filled with 1 or 3 sorted parameter values, representing the padding points |
| 208 | // around the first tangent. roots[1] will be filled with the padding points for the second tangent. |
| 209 | static inline void calc_loop_intersect_padding_pts(float padRadius, const Sk2f& T2, |
| 210 | const SkMatrix& CIT, ExcludedTerm skipTerm, |
| 211 | SkSTArray<3, float, true> roots[2]) { |
| 212 | SkASSERT(padRadius >= 0); |
| 213 | SkASSERT(T2[0] <= T2[1]); |
| 214 | SkASSERT(roots[0].empty()); |
| 215 | SkASSERT(roots[1].empty()); |
| 216 | |
| 217 | Sk2f T1 = SkNx_shuffle<1,0>(T2); |
| 218 | Sk2f Cl = (ExcludedTerm::kLinearTerm == skipTerm) ? T2*-2 - T1 : T2*T2 + T2*T1*2; |
| 219 | Sk2f Lx = Cl * CIT[3] + CIT[0]; |
| 220 | Sk2f Ly = Cl * CIT[4] + CIT[1]; |
| 221 | |
| 222 | Sk2f bloat = Sk2f(+.5f * padRadius, -.5f * padRadius) * (Lx.abs() + Ly.abs()); |
| 223 | Sk2f q = (1.f/3) * (T2 - T1); |
| 224 | |
| 225 | Sk2f qqq = q*q*q; |
| 226 | Sk2f discr = qqq*bloat*2 + bloat*bloat; |
| 227 | |
| 228 | float numRoots[2], D[2]; |
| 229 | (discr < 0).thenElse(3, 1).store(numRoots); |
| 230 | (T2 - q).store(D); |
| 231 | |
| 232 | // Values for calculating one root. |
| 233 | float R[2], QQ[2]; |
| 234 | if ((discr >= 0).anyTrue()) { |
| 235 | Sk2f r = qqq + bloat; |
| 236 | Sk2f s = r.abs() + discr.sqrt(); |
| 237 | (r > 0).thenElse(-s, s).store(R); |
| 238 | (q*q).store(QQ); |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 239 | } |
| 240 | |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 241 | // Values for calculating three roots. |
| 242 | float P[2], cosTheta3[2]; |
| 243 | if ((discr < 0).anyTrue()) { |
| 244 | (q.abs() * -2).store(P); |
| 245 | ((q >= 0).thenElse(1, -1) + bloat / qqq.abs()).store(cosTheta3); |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 246 | } |
| 247 | |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 248 | for (int i = 0; i < 2; ++i) { |
| 249 | if (1 == numRoots[i]) { |
| 250 | float A = cbrtf(R[i]); |
| 251 | float B = A != 0 ? QQ[i]/A : 0; |
| 252 | roots[i].push_back(A + B + D[i]); |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 253 | continue; |
| 254 | } |
| 255 | |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 256 | static constexpr float k2PiOver3 = 2 * SK_ScalarPI / 3; |
| 257 | float theta = std::acos(cosTheta3[i]) * (1.f/3); |
| 258 | roots[i].push_back(P[i] * std::cos(theta) + D[i]); |
| 259 | roots[i].push_back(P[i] * std::cos(theta + k2PiOver3) + D[i]); |
| 260 | roots[i].push_back(P[i] * std::cos(theta - k2PiOver3) + D[i]); |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 261 | |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 262 | // Sort the three roots. |
| 263 | swap_if_greater(roots[i][0], roots[i][1]); |
| 264 | swap_if_greater(roots[i][1], roots[i][2]); |
| 265 | swap_if_greater(roots[i][0], roots[i][1]); |
| 266 | } |
| 267 | } |
| 268 | |
Chris Dalton | 29011a2 | 2017-09-28 12:08:33 -0600 | [diff] [blame] | 269 | static inline Sk2f first_unless_nearly_zero(const Sk2f& a, const Sk2f& b) { |
| 270 | Sk2f aa = a*a; |
| 271 | aa += SkNx_shuffle<1,0>(aa); |
| 272 | SkASSERT(aa[0] == aa[1]); |
| 273 | |
| 274 | Sk2f bb = b*b; |
| 275 | bb += SkNx_shuffle<1,0>(bb); |
| 276 | SkASSERT(bb[0] == bb[1]); |
| 277 | |
| 278 | return (aa > bb * SK_ScalarNearlyZero).thenElse(a, b); |
| 279 | } |
| 280 | |
| 281 | static inline bool is_cubic_nearly_quadratic(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2, |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 282 | const Sk2f& p3, Sk2f& tan0, Sk2f& tan1, Sk2f& c) { |
Chris Dalton | 29011a2 | 2017-09-28 12:08:33 -0600 | [diff] [blame] | 283 | tan0 = first_unless_nearly_zero(p1 - p0, p2 - p0); |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 284 | tan1 = first_unless_nearly_zero(p3 - p2, p3 - p1); |
Chris Dalton | 29011a2 | 2017-09-28 12:08:33 -0600 | [diff] [blame] | 285 | |
| 286 | Sk2f c1 = SkNx_fma(Sk2f(1.5f), tan0, p0); |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 287 | Sk2f c2 = SkNx_fma(Sk2f(-1.5f), tan1, p3); |
Chris Dalton | 29011a2 | 2017-09-28 12:08:33 -0600 | [diff] [blame] | 288 | c = (c1 + c2) * .5f; // Hopefully optimized out if not used? |
| 289 | |
| 290 | return ((c1 - c2).abs() <= 1).allTrue(); |
| 291 | } |
| 292 | |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 293 | void GrCCGeometry::cubicTo(const SkPoint P[4], float inflectPad, float loopIntersectPad) { |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 294 | SkASSERT(fBuildingContour); |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 295 | SkASSERT(P[0] == fPoints.back()); |
| 296 | Sk2f p0 = Sk2f::Load(P); |
| 297 | Sk2f p1 = Sk2f::Load(P+1); |
| 298 | Sk2f p2 = Sk2f::Load(P+2); |
| 299 | Sk2f p3 = Sk2f::Load(P+3); |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 300 | |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 301 | // Don't crunch on the curve or inflate geometry if it is nearly flat (or just very small). |
| 302 | // Flat curves can break the math below. |
Chris Dalton | 900cd05 | 2017-09-07 10:36:51 -0600 | [diff] [blame] | 303 | if (are_collinear(p0, p1, p2) && |
| 304 | are_collinear(p1, p2, p3) && |
| 305 | are_collinear(p0, (p1 + p2) * .5f, p3)) { |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 306 | this->appendLine(p3); |
Chris Dalton | 900cd05 | 2017-09-07 10:36:51 -0600 | [diff] [blame] | 307 | return; |
| 308 | } |
| 309 | |
Chris Dalton | 29011a2 | 2017-09-28 12:08:33 -0600 | [diff] [blame] | 310 | // Also detect near-quadratics ahead of time. |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 311 | Sk2f tan0, tan1, c; |
| 312 | if (is_cubic_nearly_quadratic(p0, p1, p2, p3, tan0, tan1, c)) { |
Chris Dalton | 29011a2 | 2017-09-28 12:08:33 -0600 | [diff] [blame] | 313 | this->appendMonotonicQuadratics(p0, c, p3); |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 314 | return; |
| 315 | } |
| 316 | |
Chris Dalton | 29011a2 | 2017-09-28 12:08:33 -0600 | [diff] [blame] | 317 | double tt[2], ss[2]; |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 318 | fCurrCubicType = SkClassifyCubic(P, tt, ss); |
Chris Dalton | 29011a2 | 2017-09-28 12:08:33 -0600 | [diff] [blame] | 319 | SkASSERT(!SkCubicIsDegenerate(fCurrCubicType)); // Should have been caught above. |
| 320 | |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 321 | SkMatrix CIT; |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 322 | ExcludedTerm skipTerm = GrPathUtils::calcCubicInverseTransposePowerBasisMatrix(P, &CIT); |
Chris Dalton | 29011a2 | 2017-09-28 12:08:33 -0600 | [diff] [blame] | 323 | SkASSERT(ExcludedTerm::kNonInvertible != skipTerm); // Should have been caught above. |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 324 | SkASSERT(0 == CIT[6]); |
| 325 | SkASSERT(0 == CIT[7]); |
| 326 | SkASSERT(1 == CIT[8]); |
| 327 | |
| 328 | // Each cubic has five different sections (not always inside t=[0..1]): |
| 329 | // |
| 330 | // 1. The section before the first inflection or loop intersection point, with padding. |
| 331 | // 2. The section that passes through the first inflection/intersection (aka the K,L |
| 332 | // intersection point or T=tt[0]/ss[0]). |
| 333 | // 3. The section between the two inflections/intersections, with padding. |
| 334 | // 4. The section that passes through the second inflection/intersection (aka the K,M |
| 335 | // intersection point or T=tt[1]/ss[1]). |
| 336 | // 5. The section after the second inflection/intersection, with padding. |
| 337 | // |
| 338 | // Sections 1,3,5 can be rendered directly using the CCPR cubic shader. |
| 339 | // |
| 340 | // Sections 2 & 4 must be approximated. For loop intersections we render them with |
| 341 | // quadratic(s), and when passing through an inflection point we use a plain old flat line. |
| 342 | // |
| 343 | // We find T0..T3 below to be the dividing points between these five sections. |
| 344 | float T0, T1, T2, T3; |
| 345 | if (SkCubicType::kLoop != fCurrCubicType) { |
| 346 | Sk2f t = Sk2f(static_cast<float>(tt[0]), static_cast<float>(tt[1])); |
| 347 | Sk2f s = Sk2f(static_cast<float>(ss[0]), static_cast<float>(ss[1])); |
| 348 | Sk2f pad = calc_inflect_homogeneous_padding(inflectPad, t, s, CIT, skipTerm); |
| 349 | |
| 350 | float T[2]; |
| 351 | ((t - pad) / s).store(T); |
| 352 | T0 = T[0]; |
| 353 | T2 = T[1]; |
| 354 | |
| 355 | ((t + pad) / s).store(T); |
| 356 | T1 = T[0]; |
| 357 | T3 = T[1]; |
| 358 | } else { |
| 359 | const float T[2] = {static_cast<float>(tt[0]/ss[0]), static_cast<float>(tt[1]/ss[1])}; |
| 360 | SkSTArray<3, float, true> roots[2]; |
| 361 | calc_loop_intersect_padding_pts(loopIntersectPad, Sk2f::Load(T), CIT, skipTerm, roots); |
| 362 | T0 = roots[0].front(); |
| 363 | if (1 == roots[0].count() || 1 == roots[1].count()) { |
| 364 | // The loop is tighter than our desired padding. Collapse the middle section to a point |
| 365 | // somewhere in the middle-ish of the loop and Sections 2 & 4 will approximate the the |
| 366 | // whole thing with quadratics. |
| 367 | T1 = T2 = (T[0] + T[1]) * .5f; |
| 368 | } else { |
| 369 | T1 = roots[0][1]; |
| 370 | T2 = roots[1][1]; |
| 371 | } |
| 372 | T3 = roots[1].back(); |
| 373 | } |
| 374 | |
| 375 | // Guarantee that T0..T3 are monotonic. |
| 376 | if (T0 > T3) { |
| 377 | // This is not a mathematically valid scenario. The only reason it would happen is if |
| 378 | // padding is very small and we have encountered FP rounding error. |
| 379 | T0 = T1 = T2 = T3 = (T0 + T3) / 2; |
| 380 | } else if (T1 > T2) { |
| 381 | // This just means padding before the middle section overlaps the padding after it. We |
| 382 | // collapse the middle section to a single point that splits the difference between the |
| 383 | // overlap in padding. |
| 384 | T1 = T2 = (T1 + T2) / 2; |
| 385 | } |
| 386 | // Clamp T1 & T2 inside T0..T3. The only reason this would be necessary is if we have |
| 387 | // encountered FP rounding error. |
| 388 | T1 = std::max(T0, std::min(T1, T3)); |
| 389 | T2 = std::max(T0, std::min(T2, T3)); |
| 390 | |
| 391 | // Next we chop the cubic up at all T0..T3 inside 0..1 and store the resulting segments. |
| 392 | if (T1 >= 1) { |
| 393 | // Only sections 1 & 2 can be in 0..1. |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 394 | this->chopCubic<&GrCCGeometry::appendMonotonicCubics, |
| 395 | &GrCCGeometry::appendCubicApproximation>(p0, p1, p2, p3, T0); |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 396 | return; |
| 397 | } |
| 398 | |
| 399 | if (T2 <= 0) { |
| 400 | // Only sections 4 & 5 can be in 0..1. |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 401 | this->chopCubic<&GrCCGeometry::appendCubicApproximation, |
| 402 | &GrCCGeometry::appendMonotonicCubics>(p0, p1, p2, p3, T3); |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 403 | return; |
| 404 | } |
| 405 | |
| 406 | Sk2f midp0, midp1; // These hold the first two bezier points of the middle section, if needed. |
| 407 | |
| 408 | if (T1 > 0) { |
| 409 | Sk2f T1T1 = Sk2f(T1); |
| 410 | Sk2f ab1 = lerp(p0, p1, T1T1); |
| 411 | Sk2f bc1 = lerp(p1, p2, T1T1); |
| 412 | Sk2f cd1 = lerp(p2, p3, T1T1); |
| 413 | Sk2f abc1 = lerp(ab1, bc1, T1T1); |
| 414 | Sk2f bcd1 = lerp(bc1, cd1, T1T1); |
| 415 | Sk2f abcd1 = lerp(abc1, bcd1, T1T1); |
| 416 | |
| 417 | // Sections 1 & 2. |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 418 | this->chopCubic<&GrCCGeometry::appendMonotonicCubics, |
| 419 | &GrCCGeometry::appendCubicApproximation>(p0, ab1, abc1, abcd1, T0/T1); |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 420 | |
| 421 | if (T2 >= 1) { |
| 422 | // The rest of the curve is Section 3 (middle section). |
| 423 | this->appendMonotonicCubics(abcd1, bcd1, cd1, p3); |
| 424 | return; |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 425 | } |
| 426 | |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 427 | // Now calculate the first two bezier points of the middle section. The final two will come |
| 428 | // from when we chop the other side, as that is numerically more stable. |
| 429 | midp0 = abcd1; |
| 430 | midp1 = lerp(abcd1, bcd1, Sk2f((T2 - T1) / (1 - T1))); |
| 431 | } else if (T2 >= 1) { |
| 432 | // The entire cubic is Section 3 (middle section). |
| 433 | this->appendMonotonicCubics(p0, p1, p2, p3); |
| 434 | return; |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 435 | } |
| 436 | |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 437 | SkASSERT(T2 > 0 && T2 < 1); |
| 438 | |
| 439 | Sk2f T2T2 = Sk2f(T2); |
| 440 | Sk2f ab2 = lerp(p0, p1, T2T2); |
| 441 | Sk2f bc2 = lerp(p1, p2, T2T2); |
| 442 | Sk2f cd2 = lerp(p2, p3, T2T2); |
| 443 | Sk2f abc2 = lerp(ab2, bc2, T2T2); |
| 444 | Sk2f bcd2 = lerp(bc2, cd2, T2T2); |
| 445 | Sk2f abcd2 = lerp(abc2, bcd2, T2T2); |
| 446 | |
| 447 | if (T1 <= 0) { |
| 448 | // The curve begins at Section 3 (middle section). |
| 449 | this->appendMonotonicCubics(p0, ab2, abc2, abcd2); |
| 450 | } else if (T2 > T1) { |
| 451 | // Section 3 (middle section). |
| 452 | Sk2f midp2 = lerp(abc2, abcd2, T1/T2); |
| 453 | this->appendMonotonicCubics(midp0, midp1, midp2, abcd2); |
| 454 | } |
| 455 | |
| 456 | // Sections 4 & 5. |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 457 | this->chopCubic<&GrCCGeometry::appendCubicApproximation, |
| 458 | &GrCCGeometry::appendMonotonicCubics>(abcd2, bcd2, cd2, p3, (T3-T2) / (1-T2)); |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 459 | } |
| 460 | |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 461 | template<GrCCGeometry::AppendCubicFn AppendLeftRight> |
| 462 | inline void GrCCGeometry::chopCubicAtMidTangent(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2, |
| 463 | const Sk2f& p3, const Sk2f& tan0, |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 464 | const Sk2f& tan1, int maxFutureSubdivisions) { |
| 465 | // Find the T value whose tangent is perpendicular to the vector that bisects tan0 and -tan1. |
| 466 | Sk2f n = normalize(tan0) - normalize(tan1); |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 467 | |
| 468 | float a = 3 * dot(p3 + (p1 - p2)*3 - p0, n); |
| 469 | float b = 6 * dot(p0 - p1*2 + p2, n); |
| 470 | float c = 3 * dot(p1 - p0, n); |
| 471 | |
| 472 | float discr = b*b - 4*a*c; |
| 473 | if (discr < 0) { |
| 474 | // If this is the case then the cubic must be nearly flat. |
| 475 | (this->*AppendLeftRight)(p0, p1, p2, p3, maxFutureSubdivisions); |
| 476 | return; |
| 477 | } |
| 478 | |
| 479 | float q = -.5f * (b + copysignf(std::sqrt(discr), b)); |
| 480 | float m = .5f*q*a; |
| 481 | float T = std::abs(q*q - m) < std::abs(a*c - m) ? q/a : c/q; |
| 482 | |
| 483 | this->chopCubic<AppendLeftRight, AppendLeftRight>(p0, p1, p2, p3, T, maxFutureSubdivisions); |
| 484 | } |
| 485 | |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 486 | template<GrCCGeometry::AppendCubicFn AppendLeft, GrCCGeometry::AppendCubicFn AppendRight> |
| 487 | inline void GrCCGeometry::chopCubic(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2, |
| 488 | const Sk2f& p3, float T, int maxFutureSubdivisions) { |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 489 | if (T >= 1) { |
| 490 | (this->*AppendLeft)(p0, p1, p2, p3, maxFutureSubdivisions); |
| 491 | return; |
| 492 | } |
| 493 | |
| 494 | if (T <= 0) { |
| 495 | (this->*AppendRight)(p0, p1, p2, p3, maxFutureSubdivisions); |
| 496 | return; |
| 497 | } |
| 498 | |
| 499 | Sk2f TT = T; |
| 500 | Sk2f ab = lerp(p0, p1, TT); |
| 501 | Sk2f bc = lerp(p1, p2, TT); |
| 502 | Sk2f cd = lerp(p2, p3, TT); |
| 503 | Sk2f abc = lerp(ab, bc, TT); |
| 504 | Sk2f bcd = lerp(bc, cd, TT); |
| 505 | Sk2f abcd = lerp(abc, bcd, TT); |
| 506 | (this->*AppendLeft)(p0, ab, abc, abcd, maxFutureSubdivisions); |
| 507 | (this->*AppendRight)(abcd, bcd, cd, p3, maxFutureSubdivisions); |
| 508 | } |
| 509 | |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 510 | void GrCCGeometry::appendMonotonicCubics(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2, |
| 511 | const Sk2f& p3, int maxSubdivisions) { |
Chris Dalton | 29011a2 | 2017-09-28 12:08:33 -0600 | [diff] [blame] | 512 | SkASSERT(maxSubdivisions >= 0); |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 513 | if ((p0 == p3).allTrue()) { |
| 514 | return; |
| 515 | } |
| 516 | |
| 517 | if (maxSubdivisions) { |
| 518 | Sk2f tan0 = first_unless_nearly_zero(p1 - p0, p2 - p0); |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 519 | Sk2f tan1 = first_unless_nearly_zero(p3 - p2, p3 - p1); |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 520 | |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 521 | if (!is_convex_curve_monotonic(p0, tan0, p3, tan1)) { |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 522 | this->chopCubicAtMidTangent<&GrCCGeometry::appendMonotonicCubics>(p0, p1, p2, p3, |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 523 | tan0, tan1, |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 524 | maxSubdivisions - 1); |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 525 | return; |
| 526 | } |
| 527 | } |
| 528 | |
| 529 | SkASSERT(fPoints.back() == SkPoint::Make(p0[0], p0[1])); |
Chris Dalton | 4364653 | 2017-12-07 12:47:02 -0700 | [diff] [blame] | 530 | |
| 531 | // Don't send curves to the GPU if we know they are nearly flat (or just very small). |
| 532 | // Since the cubic segment is known to be convex at this point, our flatness check is simple. |
| 533 | if (are_collinear(p0, (p1 + p2) * .5f, p3)) { |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 534 | this->appendLine(p3); |
Chris Dalton | 4364653 | 2017-12-07 12:47:02 -0700 | [diff] [blame] | 535 | return; |
| 536 | } |
| 537 | |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 538 | p1.store(&fPoints.push_back()); |
| 539 | p2.store(&fPoints.push_back()); |
| 540 | p3.store(&fPoints.push_back()); |
Chris Dalton | be4ffab | 2017-12-08 10:59:58 -0700 | [diff] [blame] | 541 | fVerbs.push_back(Verb::kMonotonicCubicTo); |
| 542 | ++fCurrContourTallies.fCubics; |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 543 | } |
| 544 | |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 545 | void GrCCGeometry::appendCubicApproximation(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2, |
| 546 | const Sk2f& p3, int maxSubdivisions) { |
Chris Dalton | 29011a2 | 2017-09-28 12:08:33 -0600 | [diff] [blame] | 547 | SkASSERT(maxSubdivisions >= 0); |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 548 | if ((p0 == p3).allTrue()) { |
| 549 | return; |
| 550 | } |
| 551 | |
| 552 | if (SkCubicType::kLoop != fCurrCubicType && SkCubicType::kQuadratic != fCurrCubicType) { |
| 553 | // This section passes through an inflection point, so we can get away with a flat line. |
| 554 | // This can cause some curves to feel slightly more flat when inspected rigorously back and |
| 555 | // forth against another renderer, but for now this seems acceptable given the simplicity. |
| 556 | SkASSERT(fPoints.back() == SkPoint::Make(p0[0], p0[1])); |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 557 | this->appendLine(p3); |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 558 | return; |
| 559 | } |
| 560 | |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 561 | Sk2f tan0, tan1, c; |
| 562 | if (!is_cubic_nearly_quadratic(p0, p1, p2, p3, tan0, tan1, c) && maxSubdivisions) { |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 563 | this->chopCubicAtMidTangent<&GrCCGeometry::appendCubicApproximation>(p0, p1, p2, p3, |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 564 | tan0, tan1, |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 565 | maxSubdivisions - 1); |
Chris Dalton | 29011a2 | 2017-09-28 12:08:33 -0600 | [diff] [blame] | 566 | return; |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 567 | } |
| 568 | |
Chris Dalton | 4364653 | 2017-12-07 12:47:02 -0700 | [diff] [blame] | 569 | if (maxSubdivisions) { |
| 570 | this->appendMonotonicQuadratics(p0, c, p3); |
| 571 | } else { |
| 572 | this->appendSingleMonotonicQuadratic(p0, c, p3); |
| 573 | } |
Chris Dalton | 7f578bf | 2017-09-05 16:46:48 -0600 | [diff] [blame] | 574 | } |
| 575 | |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 576 | GrCCGeometry::PrimitiveTallies GrCCGeometry::endContour() { |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 577 | SkASSERT(fBuildingContour); |
| 578 | SkASSERT(fVerbs.count() >= fCurrContourTallies.fTriangles); |
| 579 | |
| 580 | // The fTriangles field currently contains this contour's starting verb index. We can now |
| 581 | // use it to calculate the size of the contour's fan. |
| 582 | int fanSize = fVerbs.count() - fCurrContourTallies.fTriangles; |
Chris Dalton | 7ca3b7b | 2018-04-10 00:21:19 -0600 | [diff] [blame^] | 583 | if (fPoints.back() == fCurrAnchorPoint) { |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 584 | --fanSize; |
| 585 | fVerbs.push_back(Verb::kEndClosedContour); |
| 586 | } else { |
| 587 | fVerbs.push_back(Verb::kEndOpenContour); |
| 588 | } |
| 589 | |
| 590 | fCurrContourTallies.fTriangles = SkTMax(fanSize - 2, 0); |
| 591 | |
Chris Dalton | 383a2ef | 2018-01-08 17:21:41 -0500 | [diff] [blame] | 592 | SkDEBUGCODE(fBuildingContour = false); |
Chris Dalton | c1e5963 | 2017-09-05 00:30:07 -0600 | [diff] [blame] | 593 | return fCurrContourTallies; |
Chris Dalton | 419a94d | 2017-08-28 10:24:22 -0600 | [diff] [blame] | 594 | } |