epoger@google.com | ec3ed6a | 2011-07-28 14:26:00 +0000 | [diff] [blame] | 1 | /* |
| 2 | * Copyright 2006 The Android Open Source Project |
| 3 | * |
| 4 | * Use of this source code is governed by a BSD-style license that can be |
| 5 | * found in the LICENSE file. |
| 6 | */ |
| 7 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 8 | #include "SkGeometry.h" |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 9 | #include "SkMatrix.h" |
mtklein | c9adb05 | 2015-03-30 10:50:27 -0700 | [diff] [blame] | 10 | #include "SkNx.h" |
Cary Clark | e4442cb | 2017-10-18 11:46:18 -0400 | [diff] [blame] | 11 | #include "SkPoint3.h" |
Cary Clark | df429f3 | 2017-11-08 11:44:31 -0500 | [diff] [blame] | 12 | #include "SkPointPriv.h" |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 13 | |
Ben Wagner | f08d1d0 | 2018-06-18 15:11:00 -0400 | [diff] [blame] | 14 | #include <utility> |
| 15 | |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 16 | static SkVector to_vector(const Sk2s& x) { |
| 17 | SkVector vector; |
mtklein | 507ef6d | 2016-01-31 08:02:47 -0800 | [diff] [blame] | 18 | x.store(&vector); |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 19 | return vector; |
| 20 | } |
| 21 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 22 | //////////////////////////////////////////////////////////////////////// |
| 23 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 24 | static int is_not_monotonic(SkScalar a, SkScalar b, SkScalar c) { |
| 25 | SkScalar ab = a - b; |
| 26 | SkScalar bc = b - c; |
reed@google.com | 8f4d230 | 2013-12-17 16:44:46 +0000 | [diff] [blame] | 27 | if (ab < 0) { |
| 28 | bc = -bc; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 29 | } |
reed@google.com | 8f4d230 | 2013-12-17 16:44:46 +0000 | [diff] [blame] | 30 | return ab == 0 || bc < 0; |
| 31 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 32 | |
| 33 | //////////////////////////////////////////////////////////////////////// |
| 34 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 35 | static int valid_unit_divide(SkScalar numer, SkScalar denom, SkScalar* ratio) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 36 | SkASSERT(ratio); |
| 37 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 38 | if (numer < 0) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 39 | numer = -numer; |
| 40 | denom = -denom; |
| 41 | } |
| 42 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 43 | if (denom == 0 || numer == 0 || numer >= denom) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 44 | return 0; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 45 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 46 | |
reed | 80ea19c | 2015-05-12 10:37:34 -0700 | [diff] [blame] | 47 | SkScalar r = numer / denom; |
reed@android.com | 1516162 | 2010-03-08 17:44:42 +0000 | [diff] [blame] | 48 | if (SkScalarIsNaN(r)) { |
| 49 | return 0; |
| 50 | } |
Mike Klein | 11fca3f | 2014-09-12 12:17:25 -0400 | [diff] [blame] | 51 | SkASSERTF(r >= 0 && r < SK_Scalar1, "numer %f, denom %f, r %f", numer, denom, r); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 52 | if (r == 0) { // catch underflow if numer <<<< denom |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 53 | return 0; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 54 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 55 | *ratio = r; |
| 56 | return 1; |
| 57 | } |
| 58 | |
Mike Reed | 1e259cd | 2018-06-21 10:51:35 -0400 | [diff] [blame] | 59 | // Just returns its argument, but makes it easy to set a break-point to know when |
| 60 | // SkFindUnitQuadRoots is going to return 0 (an error). |
| 61 | static int return_check_zero(int value) { |
| 62 | if (value == 0) { |
| 63 | return 0; |
| 64 | } |
| 65 | return value; |
| 66 | } |
| 67 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 68 | /** From Numerical Recipes in C. |
| 69 | |
| 70 | Q = -1/2 (B + sign(B) sqrt[B*B - 4*A*C]) |
| 71 | x1 = Q / A |
| 72 | x2 = C / Q |
| 73 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 74 | int SkFindUnitQuadRoots(SkScalar A, SkScalar B, SkScalar C, SkScalar roots[2]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 75 | SkASSERT(roots); |
| 76 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 77 | if (A == 0) { |
Mike Reed | 1e259cd | 2018-06-21 10:51:35 -0400 | [diff] [blame] | 78 | return return_check_zero(valid_unit_divide(-C, B, roots)); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 79 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 80 | |
| 81 | SkScalar* r = roots; |
| 82 | |
Mike Reed | 1e259cd | 2018-06-21 10:51:35 -0400 | [diff] [blame] | 83 | // use doubles so we don't overflow temporarily trying to compute R |
| 84 | double dr = (double)B * B - 4 * (double)A * C; |
| 85 | if (dr < 0) { |
| 86 | return return_check_zero(0); |
reed@android.com | 1516162 | 2010-03-08 17:44:42 +0000 | [diff] [blame] | 87 | } |
Mike Reed | 1e259cd | 2018-06-21 10:51:35 -0400 | [diff] [blame] | 88 | dr = sqrt(dr); |
| 89 | SkScalar R = SkDoubleToScalar(dr); |
| 90 | if (!SkScalarIsFinite(R)) { |
| 91 | return return_check_zero(0); |
| 92 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 93 | |
| 94 | SkScalar Q = (B < 0) ? -(B-R)/2 : -(B+R)/2; |
| 95 | r += valid_unit_divide(Q, A, r); |
| 96 | r += valid_unit_divide(C, Q, r); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 97 | if (r - roots == 2) { |
Ben Wagner | f08d1d0 | 2018-06-18 15:11:00 -0400 | [diff] [blame] | 98 | if (roots[0] > roots[1]) { |
| 99 | using std::swap; |
| 100 | swap(roots[0], roots[1]); |
| 101 | } else if (roots[0] == roots[1]) { // nearly-equal? |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 102 | r -= 1; // skip the double root |
Ben Wagner | f08d1d0 | 2018-06-18 15:11:00 -0400 | [diff] [blame] | 103 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 104 | } |
Mike Reed | 1e259cd | 2018-06-21 10:51:35 -0400 | [diff] [blame] | 105 | return return_check_zero((int)(r - roots)); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 106 | } |
| 107 | |
reed@google.com | 8f4d230 | 2013-12-17 16:44:46 +0000 | [diff] [blame] | 108 | /////////////////////////////////////////////////////////////////////////////// |
| 109 | /////////////////////////////////////////////////////////////////////////////// |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 110 | |
reed | 65cb2cd | 2015-03-19 10:18:47 -0700 | [diff] [blame] | 111 | void SkEvalQuadAt(const SkPoint src[3], SkScalar t, SkPoint* pt, SkVector* tangent) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 112 | SkASSERT(src); |
| 113 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
mtklein | 950e986 | 2015-03-19 12:03:29 -0700 | [diff] [blame] | 114 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 115 | if (pt) { |
caryclark | 5ba2b96 | 2016-01-26 17:02:30 -0800 | [diff] [blame] | 116 | *pt = SkEvalQuadAt(src, t); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 117 | } |
| 118 | if (tangent) { |
caryclark | 45398df | 2015-08-25 13:19:06 -0700 | [diff] [blame] | 119 | *tangent = SkEvalQuadTangentAt(src, t); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 120 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 121 | } |
| 122 | |
reed | 65cb2cd | 2015-03-19 10:18:47 -0700 | [diff] [blame] | 123 | SkPoint SkEvalQuadAt(const SkPoint src[3], SkScalar t) { |
caryclark | 5ba2b96 | 2016-01-26 17:02:30 -0800 | [diff] [blame] | 124 | return to_point(SkQuadCoeff(src).eval(t)); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 125 | } |
| 126 | |
reed | 40b7dd5 | 2015-03-20 06:01:08 -0700 | [diff] [blame] | 127 | SkVector SkEvalQuadTangentAt(const SkPoint src[3], SkScalar t) { |
caryclark | 45398df | 2015-08-25 13:19:06 -0700 | [diff] [blame] | 128 | // The derivative equation is 2(b - a +(a - 2b +c)t). This returns a |
| 129 | // zero tangent vector when t is 0 or 1, and the control point is equal |
| 130 | // to the end point. In this case, use the quad end points to compute the tangent. |
| 131 | if ((t == 0 && src[0] == src[1]) || (t == 1 && src[1] == src[2])) { |
| 132 | return src[2] - src[0]; |
| 133 | } |
reed | 40b7dd5 | 2015-03-20 06:01:08 -0700 | [diff] [blame] | 134 | SkASSERT(src); |
| 135 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
| 136 | |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 137 | Sk2s P0 = from_point(src[0]); |
| 138 | Sk2s P1 = from_point(src[1]); |
| 139 | Sk2s P2 = from_point(src[2]); |
reed | 40b7dd5 | 2015-03-20 06:01:08 -0700 | [diff] [blame] | 140 | |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 141 | Sk2s B = P1 - P0; |
| 142 | Sk2s A = P2 - P1 - B; |
| 143 | Sk2s T = A * Sk2s(t) + B; |
reed | 40b7dd5 | 2015-03-20 06:01:08 -0700 | [diff] [blame] | 144 | |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 145 | return to_vector(T + T); |
reed | 40b7dd5 | 2015-03-20 06:01:08 -0700 | [diff] [blame] | 146 | } |
| 147 | |
reed | 40b7dd5 | 2015-03-20 06:01:08 -0700 | [diff] [blame] | 148 | static inline Sk2s interp(const Sk2s& v0, const Sk2s& v1, const Sk2s& t) { |
| 149 | return v0 + (v1 - v0) * t; |
| 150 | } |
| 151 | |
reed | c08330f | 2015-03-26 07:26:08 -0700 | [diff] [blame] | 152 | void SkChopQuadAt(const SkPoint src[3], SkPoint dst[5], SkScalar t) { |
reed | 40b7dd5 | 2015-03-20 06:01:08 -0700 | [diff] [blame] | 153 | SkASSERT(t > 0 && t < SK_Scalar1); |
| 154 | |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 155 | Sk2s p0 = from_point(src[0]); |
| 156 | Sk2s p1 = from_point(src[1]); |
| 157 | Sk2s p2 = from_point(src[2]); |
reed | ce6acc9 | 2015-03-20 13:46:08 -0700 | [diff] [blame] | 158 | Sk2s tt(t); |
mtklein | c9adb05 | 2015-03-30 10:50:27 -0700 | [diff] [blame] | 159 | |
reed | 40b7dd5 | 2015-03-20 06:01:08 -0700 | [diff] [blame] | 160 | Sk2s p01 = interp(p0, p1, tt); |
| 161 | Sk2s p12 = interp(p1, p2, tt); |
| 162 | |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 163 | dst[0] = to_point(p0); |
| 164 | dst[1] = to_point(p01); |
| 165 | dst[2] = to_point(interp(p01, p12, tt)); |
| 166 | dst[3] = to_point(p12); |
| 167 | dst[4] = to_point(p2); |
reed | 40b7dd5 | 2015-03-20 06:01:08 -0700 | [diff] [blame] | 168 | } |
| 169 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 170 | void SkChopQuadAtHalf(const SkPoint src[3], SkPoint dst[5]) { |
caryclark | b6474dd | 2016-01-19 08:07:49 -0800 | [diff] [blame] | 171 | SkChopQuadAt(src, dst, 0.5f); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 172 | } |
| 173 | |
| 174 | /** Quad'(t) = At + B, where |
| 175 | A = 2(a - 2b + c) |
| 176 | B = 2(b - a) |
| 177 | Solve for t, only if it fits between 0 < t < 1 |
| 178 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 179 | int SkFindQuadExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar tValue[1]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 180 | /* At + B == 0 |
| 181 | t = -B / A |
| 182 | */ |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 183 | return valid_unit_divide(a - b, a - b - b + c, tValue); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 184 | } |
| 185 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 186 | static inline void flatten_double_quad_extrema(SkScalar coords[14]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 187 | coords[2] = coords[6] = coords[4]; |
| 188 | } |
| 189 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 190 | /* Returns 0 for 1 quad, and 1 for two quads, either way the answer is |
reed@android.com | 77f0ef7 | 2009-11-17 18:47:52 +0000 | [diff] [blame] | 191 | stored in dst[]. Guarantees that the 1/2 quads will be monotonic. |
| 192 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 193 | int SkChopQuadAtYExtrema(const SkPoint src[3], SkPoint dst[5]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 194 | SkASSERT(src); |
| 195 | SkASSERT(dst); |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 196 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 197 | SkScalar a = src[0].fY; |
| 198 | SkScalar b = src[1].fY; |
| 199 | SkScalar c = src[2].fY; |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 200 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 201 | if (is_not_monotonic(a, b, c)) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 202 | SkScalar tValue; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 203 | if (valid_unit_divide(a - b, a - b - b + c, &tValue)) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 204 | SkChopQuadAt(src, dst, tValue); |
| 205 | flatten_double_quad_extrema(&dst[0].fY); |
| 206 | return 1; |
| 207 | } |
| 208 | // if we get here, we need to force dst to be monotonic, even though |
| 209 | // we couldn't compute a unit_divide value (probably underflow). |
| 210 | b = SkScalarAbs(a - b) < SkScalarAbs(b - c) ? a : c; |
| 211 | } |
| 212 | dst[0].set(src[0].fX, a); |
| 213 | dst[1].set(src[1].fX, b); |
| 214 | dst[2].set(src[2].fX, c); |
| 215 | return 0; |
| 216 | } |
| 217 | |
reed@android.com | 77f0ef7 | 2009-11-17 18:47:52 +0000 | [diff] [blame] | 218 | /* Returns 0 for 1 quad, and 1 for two quads, either way the answer is |
| 219 | stored in dst[]. Guarantees that the 1/2 quads will be monotonic. |
| 220 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 221 | int SkChopQuadAtXExtrema(const SkPoint src[3], SkPoint dst[5]) { |
reed@android.com | 77f0ef7 | 2009-11-17 18:47:52 +0000 | [diff] [blame] | 222 | SkASSERT(src); |
| 223 | SkASSERT(dst); |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 224 | |
reed@android.com | 77f0ef7 | 2009-11-17 18:47:52 +0000 | [diff] [blame] | 225 | SkScalar a = src[0].fX; |
| 226 | SkScalar b = src[1].fX; |
| 227 | SkScalar c = src[2].fX; |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 228 | |
reed@android.com | 77f0ef7 | 2009-11-17 18:47:52 +0000 | [diff] [blame] | 229 | if (is_not_monotonic(a, b, c)) { |
| 230 | SkScalar tValue; |
| 231 | if (valid_unit_divide(a - b, a - b - b + c, &tValue)) { |
| 232 | SkChopQuadAt(src, dst, tValue); |
| 233 | flatten_double_quad_extrema(&dst[0].fX); |
| 234 | return 1; |
| 235 | } |
| 236 | // if we get here, we need to force dst to be monotonic, even though |
| 237 | // we couldn't compute a unit_divide value (probably underflow). |
| 238 | b = SkScalarAbs(a - b) < SkScalarAbs(b - c) ? a : c; |
| 239 | } |
| 240 | dst[0].set(a, src[0].fY); |
| 241 | dst[1].set(b, src[1].fY); |
| 242 | dst[2].set(c, src[2].fY); |
| 243 | return 0; |
| 244 | } |
| 245 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 246 | // F(t) = a (1 - t) ^ 2 + 2 b t (1 - t) + c t ^ 2 |
| 247 | // F'(t) = 2 (b - a) + 2 (a - 2b + c) t |
| 248 | // F''(t) = 2 (a - 2b + c) |
| 249 | // |
| 250 | // A = 2 (b - a) |
| 251 | // B = 2 (a - 2b + c) |
| 252 | // |
| 253 | // Maximum curvature for a quadratic means solving |
| 254 | // Fx' Fx'' + Fy' Fy'' = 0 |
| 255 | // |
| 256 | // t = - (Ax Bx + Ay By) / (Bx ^ 2 + By ^ 2) |
| 257 | // |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 258 | SkScalar SkFindQuadMaxCurvature(const SkPoint src[3]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 259 | SkScalar Ax = src[1].fX - src[0].fX; |
| 260 | SkScalar Ay = src[1].fY - src[0].fY; |
| 261 | SkScalar Bx = src[0].fX - src[1].fX - src[1].fX + src[2].fX; |
| 262 | SkScalar By = src[0].fY - src[1].fY - src[1].fY + src[2].fY; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 263 | |
Chris Dalton | 1d474dd | 2018-07-24 01:08:31 -0600 | [diff] [blame^] | 264 | SkScalar numer = -(Ax * Bx + Ay * By); |
| 265 | SkScalar denom = Bx * Bx + By * By; |
| 266 | if (denom < 0) { |
| 267 | numer = -numer; |
| 268 | denom = -denom; |
| 269 | } |
| 270 | if (numer <= 0) { |
| 271 | return 0; |
| 272 | } |
| 273 | if (numer >= denom) { // Also catches denom=0. |
| 274 | return 1; |
| 275 | } |
| 276 | SkScalar t = numer / denom; |
| 277 | SkASSERT(0 <= t && t < 1); |
egdaniel@google.com | 5383a75 | 2013-07-12 20:15:34 +0000 | [diff] [blame] | 278 | return t; |
| 279 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 280 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 281 | int SkChopQuadAtMaxCurvature(const SkPoint src[3], SkPoint dst[5]) { |
egdaniel@google.com | 5383a75 | 2013-07-12 20:15:34 +0000 | [diff] [blame] | 282 | SkScalar t = SkFindQuadMaxCurvature(src); |
Chris Dalton | 1d474dd | 2018-07-24 01:08:31 -0600 | [diff] [blame^] | 283 | if (t == 0 || t == 1) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 284 | memcpy(dst, src, 3 * sizeof(SkPoint)); |
| 285 | return 1; |
egdaniel@google.com | 5383a75 | 2013-07-12 20:15:34 +0000 | [diff] [blame] | 286 | } else { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 287 | SkChopQuadAt(src, dst, t); |
| 288 | return 2; |
| 289 | } |
| 290 | } |
| 291 | |
reed@google.com | 6fc321a | 2011-07-27 13:54:36 +0000 | [diff] [blame] | 292 | void SkConvertQuadToCubic(const SkPoint src[3], SkPoint dst[4]) { |
reed | daee7ea | 2015-03-26 20:22:33 -0700 | [diff] [blame] | 293 | Sk2s scale(SkDoubleToScalar(2.0 / 3.0)); |
| 294 | Sk2s s0 = from_point(src[0]); |
| 295 | Sk2s s1 = from_point(src[1]); |
| 296 | Sk2s s2 = from_point(src[2]); |
| 297 | |
reed@google.com | 6fc321a | 2011-07-27 13:54:36 +0000 | [diff] [blame] | 298 | dst[0] = src[0]; |
reed | daee7ea | 2015-03-26 20:22:33 -0700 | [diff] [blame] | 299 | dst[1] = to_point(s0 + (s1 - s0) * scale); |
| 300 | dst[2] = to_point(s2 + (s1 - s2) * scale); |
reed@google.com | 6fc321a | 2011-07-27 13:54:36 +0000 | [diff] [blame] | 301 | dst[3] = src[2]; |
reed@android.com | 945a139 | 2010-02-05 20:41:02 +0000 | [diff] [blame] | 302 | } |
| 303 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 304 | ////////////////////////////////////////////////////////////////////////////// |
| 305 | ///// CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS ///// |
| 306 | ////////////////////////////////////////////////////////////////////////////// |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 307 | |
caryclark | 5ba2b96 | 2016-01-26 17:02:30 -0800 | [diff] [blame] | 308 | static SkVector eval_cubic_derivative(const SkPoint src[4], SkScalar t) { |
| 309 | SkQuadCoeff coeff; |
| 310 | Sk2s P0 = from_point(src[0]); |
| 311 | Sk2s P1 = from_point(src[1]); |
| 312 | Sk2s P2 = from_point(src[2]); |
| 313 | Sk2s P3 = from_point(src[3]); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 314 | |
caryclark | 5ba2b96 | 2016-01-26 17:02:30 -0800 | [diff] [blame] | 315 | coeff.fA = P3 + Sk2s(3) * (P1 - P2) - P0; |
| 316 | coeff.fB = times_2(P2 - times_2(P1) + P0); |
| 317 | coeff.fC = P1 - P0; |
| 318 | return to_vector(coeff.eval(t)); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 319 | } |
| 320 | |
caryclark | 5ba2b96 | 2016-01-26 17:02:30 -0800 | [diff] [blame] | 321 | static SkVector eval_cubic_2ndDerivative(const SkPoint src[4], SkScalar t) { |
| 322 | Sk2s P0 = from_point(src[0]); |
| 323 | Sk2s P1 = from_point(src[1]); |
| 324 | Sk2s P2 = from_point(src[2]); |
| 325 | Sk2s P3 = from_point(src[3]); |
| 326 | Sk2s A = P3 + Sk2s(3) * (P1 - P2) - P0; |
| 327 | Sk2s B = P2 - times_2(P1) + P0; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 328 | |
caryclark | 5ba2b96 | 2016-01-26 17:02:30 -0800 | [diff] [blame] | 329 | return to_vector(A * Sk2s(t) + B); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 330 | } |
| 331 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 332 | void SkEvalCubicAt(const SkPoint src[4], SkScalar t, SkPoint* loc, |
| 333 | SkVector* tangent, SkVector* curvature) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 334 | SkASSERT(src); |
| 335 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
| 336 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 337 | if (loc) { |
caryclark | 5ba2b96 | 2016-01-26 17:02:30 -0800 | [diff] [blame] | 338 | *loc = to_point(SkCubicCoeff(src).eval(t)); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 339 | } |
| 340 | if (tangent) { |
caryclark | 45398df | 2015-08-25 13:19:06 -0700 | [diff] [blame] | 341 | // The derivative equation returns a zero tangent vector when t is 0 or 1, and the |
| 342 | // adjacent control point is equal to the end point. In this case, use the |
| 343 | // next control point or the end points to compute the tangent. |
| 344 | if ((t == 0 && src[0] == src[1]) || (t == 1 && src[2] == src[3])) { |
| 345 | if (t == 0) { |
| 346 | *tangent = src[2] - src[0]; |
| 347 | } else { |
| 348 | *tangent = src[3] - src[1]; |
| 349 | } |
| 350 | if (!tangent->fX && !tangent->fY) { |
| 351 | *tangent = src[3] - src[0]; |
| 352 | } |
| 353 | } else { |
caryclark | 5ba2b96 | 2016-01-26 17:02:30 -0800 | [diff] [blame] | 354 | *tangent = eval_cubic_derivative(src, t); |
caryclark | 45398df | 2015-08-25 13:19:06 -0700 | [diff] [blame] | 355 | } |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 356 | } |
| 357 | if (curvature) { |
caryclark | 5ba2b96 | 2016-01-26 17:02:30 -0800 | [diff] [blame] | 358 | *curvature = eval_cubic_2ndDerivative(src, t); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 359 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 360 | } |
| 361 | |
| 362 | /** Cubic'(t) = At^2 + Bt + C, where |
| 363 | A = 3(-a + 3(b - c) + d) |
| 364 | B = 6(a - 2b + c) |
| 365 | C = 3(b - a) |
| 366 | Solve for t, keeping only those that fit betwee 0 < t < 1 |
| 367 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 368 | int SkFindCubicExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar d, |
| 369 | SkScalar tValues[2]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 370 | // we divide A,B,C by 3 to simplify |
| 371 | SkScalar A = d - a + 3*(b - c); |
| 372 | SkScalar B = 2*(a - b - b + c); |
| 373 | SkScalar C = b - a; |
| 374 | |
| 375 | return SkFindUnitQuadRoots(A, B, C, tValues); |
| 376 | } |
| 377 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 378 | void SkChopCubicAt(const SkPoint src[4], SkPoint dst[7], SkScalar t) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 379 | SkASSERT(t > 0 && t < SK_Scalar1); |
| 380 | |
reed | 6b9ef90 | 2015-03-24 19:24:34 -0700 | [diff] [blame] | 381 | Sk2s p0 = from_point(src[0]); |
| 382 | Sk2s p1 = from_point(src[1]); |
| 383 | Sk2s p2 = from_point(src[2]); |
| 384 | Sk2s p3 = from_point(src[3]); |
| 385 | Sk2s tt(t); |
| 386 | |
| 387 | Sk2s ab = interp(p0, p1, tt); |
| 388 | Sk2s bc = interp(p1, p2, tt); |
| 389 | Sk2s cd = interp(p2, p3, tt); |
| 390 | Sk2s abc = interp(ab, bc, tt); |
| 391 | Sk2s bcd = interp(bc, cd, tt); |
| 392 | Sk2s abcd = interp(abc, bcd, tt); |
mtklein | c9adb05 | 2015-03-30 10:50:27 -0700 | [diff] [blame] | 393 | |
reed | 6b9ef90 | 2015-03-24 19:24:34 -0700 | [diff] [blame] | 394 | dst[0] = src[0]; |
| 395 | dst[1] = to_point(ab); |
| 396 | dst[2] = to_point(abc); |
| 397 | dst[3] = to_point(abcd); |
| 398 | dst[4] = to_point(bcd); |
| 399 | dst[5] = to_point(cd); |
| 400 | dst[6] = src[3]; |
| 401 | } |
| 402 | |
reed@android.com | a964028 | 2009-08-28 20:06:54 +0000 | [diff] [blame] | 403 | /* http://code.google.com/p/skia/issues/detail?id=32 |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 404 | |
reed@android.com | a964028 | 2009-08-28 20:06:54 +0000 | [diff] [blame] | 405 | This test code would fail when we didn't check the return result of |
| 406 | valid_unit_divide in SkChopCubicAt(... tValues[], int roots). The reason is |
| 407 | that after the first chop, the parameters to valid_unit_divide are equal |
| 408 | (thanks to finite float precision and rounding in the subtracts). Thus |
| 409 | even though the 2nd tValue looks < 1.0, after we renormalize it, we end |
| 410 | up with 1.0, hence the need to check and just return the last cubic as |
| 411 | a degenerate clump of 4 points in the sampe place. |
| 412 | |
| 413 | static void test_cubic() { |
| 414 | SkPoint src[4] = { |
| 415 | { 556.25000, 523.03003 }, |
| 416 | { 556.23999, 522.96002 }, |
| 417 | { 556.21997, 522.89001 }, |
| 418 | { 556.21997, 522.82001 } |
| 419 | }; |
| 420 | SkPoint dst[10]; |
| 421 | SkScalar tval[] = { 0.33333334f, 0.99999994f }; |
| 422 | SkChopCubicAt(src, dst, tval, 2); |
| 423 | } |
| 424 | */ |
| 425 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 426 | void SkChopCubicAt(const SkPoint src[4], SkPoint dst[], |
| 427 | const SkScalar tValues[], int roots) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 428 | #ifdef SK_DEBUG |
| 429 | { |
| 430 | for (int i = 0; i < roots - 1; i++) |
| 431 | { |
Chris Dalton | 1d474dd | 2018-07-24 01:08:31 -0600 | [diff] [blame^] | 432 | SkASSERT(0 < tValues[i] && tValues[i] < 1); |
| 433 | SkASSERT(0 < tValues[i+1] && tValues[i+1] < 1); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 434 | SkASSERT(tValues[i] < tValues[i+1]); |
| 435 | } |
| 436 | } |
| 437 | #endif |
| 438 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 439 | if (dst) { |
| 440 | if (roots == 0) { // nothing to chop |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 441 | memcpy(dst, src, 4*sizeof(SkPoint)); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 442 | } else { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 443 | SkScalar t = tValues[0]; |
| 444 | SkPoint tmp[4]; |
| 445 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 446 | for (int i = 0; i < roots; i++) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 447 | SkChopCubicAt(src, dst, t); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 448 | if (i == roots - 1) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 449 | break; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 450 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 451 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 452 | dst += 3; |
reed@android.com | a964028 | 2009-08-28 20:06:54 +0000 | [diff] [blame] | 453 | // have src point to the remaining cubic (after the chop) |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 454 | memcpy(tmp, dst, 4 * sizeof(SkPoint)); |
| 455 | src = tmp; |
reed@android.com | a964028 | 2009-08-28 20:06:54 +0000 | [diff] [blame] | 456 | |
| 457 | // watch out in case the renormalized t isn't in range |
| 458 | if (!valid_unit_divide(tValues[i+1] - tValues[i], |
| 459 | SK_Scalar1 - tValues[i], &t)) { |
| 460 | // if we can't, just create a degenerate cubic |
| 461 | dst[4] = dst[5] = dst[6] = src[3]; |
| 462 | break; |
| 463 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 464 | } |
| 465 | } |
| 466 | } |
| 467 | } |
| 468 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 469 | void SkChopCubicAtHalf(const SkPoint src[4], SkPoint dst[7]) { |
reed | c08330f | 2015-03-26 07:26:08 -0700 | [diff] [blame] | 470 | SkChopCubicAt(src, dst, 0.5f); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 471 | } |
| 472 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 473 | static void flatten_double_cubic_extrema(SkScalar coords[14]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 474 | coords[4] = coords[8] = coords[6]; |
| 475 | } |
| 476 | |
| 477 | /** Given 4 points on a cubic bezier, chop it into 1, 2, 3 beziers such that |
commit-bot@chromium.org | def6468 | 2014-02-21 19:49:10 +0000 | [diff] [blame] | 478 | the resulting beziers are monotonic in Y. This is called by the scan |
| 479 | converter. Depending on what is returned, dst[] is treated as follows: |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 480 | 0 dst[0..3] is the original cubic |
| 481 | 1 dst[0..3] and dst[3..6] are the two new cubics |
| 482 | 2 dst[0..3], dst[3..6], dst[6..9] are the three new cubics |
| 483 | If dst == null, it is ignored and only the count is returned. |
| 484 | */ |
reed@android.com | bb13586 | 2009-11-18 13:47:40 +0000 | [diff] [blame] | 485 | int SkChopCubicAtYExtrema(const SkPoint src[4], SkPoint dst[10]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 486 | SkScalar tValues[2]; |
reed@android.com | bb13586 | 2009-11-18 13:47:40 +0000 | [diff] [blame] | 487 | int roots = SkFindCubicExtrema(src[0].fY, src[1].fY, src[2].fY, |
| 488 | src[3].fY, tValues); |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 489 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 490 | SkChopCubicAt(src, dst, tValues, roots); |
reed@android.com | bb13586 | 2009-11-18 13:47:40 +0000 | [diff] [blame] | 491 | if (dst && roots > 0) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 492 | // we do some cleanup to ensure our Y extrema are flat |
| 493 | flatten_double_cubic_extrema(&dst[0].fY); |
reed@android.com | bb13586 | 2009-11-18 13:47:40 +0000 | [diff] [blame] | 494 | if (roots == 2) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 495 | flatten_double_cubic_extrema(&dst[3].fY); |
reed@android.com | bb13586 | 2009-11-18 13:47:40 +0000 | [diff] [blame] | 496 | } |
| 497 | } |
| 498 | return roots; |
| 499 | } |
| 500 | |
| 501 | int SkChopCubicAtXExtrema(const SkPoint src[4], SkPoint dst[10]) { |
| 502 | SkScalar tValues[2]; |
| 503 | int roots = SkFindCubicExtrema(src[0].fX, src[1].fX, src[2].fX, |
| 504 | src[3].fX, tValues); |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 505 | |
reed@android.com | bb13586 | 2009-11-18 13:47:40 +0000 | [diff] [blame] | 506 | SkChopCubicAt(src, dst, tValues, roots); |
| 507 | if (dst && roots > 0) { |
| 508 | // we do some cleanup to ensure our Y extrema are flat |
| 509 | flatten_double_cubic_extrema(&dst[0].fX); |
| 510 | if (roots == 2) { |
| 511 | flatten_double_cubic_extrema(&dst[3].fX); |
| 512 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 513 | } |
| 514 | return roots; |
| 515 | } |
| 516 | |
| 517 | /** http://www.faculty.idc.ac.il/arik/quality/appendixA.html |
| 518 | |
| 519 | Inflection means that curvature is zero. |
| 520 | Curvature is [F' x F''] / [F'^3] |
| 521 | So we solve F'x X F''y - F'y X F''y == 0 |
| 522 | After some canceling of the cubic term, we get |
| 523 | A = b - a |
| 524 | B = c - 2b + a |
| 525 | C = d - 3c + 3b - a |
| 526 | (BxCy - ByCx)t^2 + (AxCy - AyCx)t + AxBy - AyBx == 0 |
| 527 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 528 | int SkFindCubicInflections(const SkPoint src[4], SkScalar tValues[]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 529 | SkScalar Ax = src[1].fX - src[0].fX; |
| 530 | SkScalar Ay = src[1].fY - src[0].fY; |
| 531 | SkScalar Bx = src[2].fX - 2 * src[1].fX + src[0].fX; |
| 532 | SkScalar By = src[2].fY - 2 * src[1].fY + src[0].fY; |
| 533 | SkScalar Cx = src[3].fX + 3 * (src[1].fX - src[2].fX) - src[0].fX; |
| 534 | SkScalar Cy = src[3].fY + 3 * (src[1].fY - src[2].fY) - src[0].fY; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 535 | |
commit-bot@chromium.org | def6468 | 2014-02-21 19:49:10 +0000 | [diff] [blame] | 536 | return SkFindUnitQuadRoots(Bx*Cy - By*Cx, |
| 537 | Ax*Cy - Ay*Cx, |
| 538 | Ax*By - Ay*Bx, |
| 539 | tValues); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 540 | } |
| 541 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 542 | int SkChopCubicAtInflections(const SkPoint src[], SkPoint dst[10]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 543 | SkScalar tValues[2]; |
| 544 | int count = SkFindCubicInflections(src, tValues); |
| 545 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 546 | if (dst) { |
| 547 | if (count == 0) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 548 | memcpy(dst, src, 4 * sizeof(SkPoint)); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 549 | } else { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 550 | SkChopCubicAt(src, dst, tValues, count); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 551 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 552 | } |
| 553 | return count + 1; |
| 554 | } |
| 555 | |
caryclark | 8dd31cf | 2014-12-12 09:11:23 -0800 | [diff] [blame] | 556 | // Assumes the third component of points is 1. |
| 557 | // Calcs p0 . (p1 x p2) |
Chris Dalton | 390f6cd | 2017-06-12 11:22:54 -0600 | [diff] [blame] | 558 | static double calc_dot_cross_cubic(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2) { |
Chris Dalton | fc31be4 | 2017-11-08 17:04:47 -0700 | [diff] [blame] | 559 | const double xComp = (double) p0.fX * ((double) p1.fY - (double) p2.fY); |
| 560 | const double yComp = (double) p0.fY * ((double) p2.fX - (double) p1.fX); |
Chris Dalton | 390f6cd | 2017-06-12 11:22:54 -0600 | [diff] [blame] | 561 | const double wComp = (double) p1.fX * (double) p2.fY - (double) p1.fY * (double) p2.fX; |
caryclark | 8dd31cf | 2014-12-12 09:11:23 -0800 | [diff] [blame] | 562 | return (xComp + yComp + wComp); |
| 563 | } |
| 564 | |
Chris Dalton | 6fdbf61 | 2018-04-15 21:58:19 -0600 | [diff] [blame] | 565 | // Returns a positive power of 2 that, when multiplied by n, and excepting the two edge cases listed |
| 566 | // below, shifts the exponent of n to yield a magnitude somewhere inside [1..2). |
| 567 | // Returns 2^1023 if abs(n) < 2^-1022 (including 0). |
| 568 | // Returns NaN if n is Inf or NaN. |
| 569 | inline static double previous_inverse_pow2(double n) { |
| 570 | uint64_t bits; |
| 571 | memcpy(&bits, &n, sizeof(double)); |
| 572 | bits = ((1023llu*2 << 52) + ((1llu << 52) - 1)) - bits; // exp=-exp |
| 573 | bits &= (0x7ffllu) << 52; // mantissa=1.0, sign=0 |
| 574 | memcpy(&n, &bits, sizeof(double)); |
| 575 | return n; |
caryclark | 8dd31cf | 2014-12-12 09:11:23 -0800 | [diff] [blame] | 576 | } |
| 577 | |
Chris Dalton | 6fdbf61 | 2018-04-15 21:58:19 -0600 | [diff] [blame] | 578 | inline static void write_cubic_inflection_roots(double t0, double s0, double t1, double s1, |
| 579 | double* t, double* s) { |
| 580 | t[0] = t0; |
| 581 | s[0] = s0; |
Chris Dalton | 4dbdc67 | 2017-10-31 12:35:54 -0600 | [diff] [blame] | 582 | |
Chris Dalton | febbffa | 2017-06-08 13:12:02 -0600 | [diff] [blame] | 583 | // This copysign/abs business orients the implicit function so positive values are always on the |
| 584 | // "left" side of the curve. |
Chris Dalton | 6fdbf61 | 2018-04-15 21:58:19 -0600 | [diff] [blame] | 585 | t[1] = -copysign(t1, t1 * s1); |
| 586 | s[1] = -fabs(s1); |
Chris Dalton | febbffa | 2017-06-08 13:12:02 -0600 | [diff] [blame] | 587 | |
| 588 | // Ensure t[0]/s[0] <= t[1]/s[1] (s[1] is negative from above). |
Chris Dalton | 390f6cd | 2017-06-12 11:22:54 -0600 | [diff] [blame] | 589 | if (copysign(s[1], s[0]) * t[0] > -fabs(s[0]) * t[1]) { |
Ben Wagner | f08d1d0 | 2018-06-18 15:11:00 -0400 | [diff] [blame] | 590 | using std::swap; |
| 591 | swap(t[0], t[1]); |
| 592 | swap(s[0], s[1]); |
Chris Dalton | febbffa | 2017-06-08 13:12:02 -0600 | [diff] [blame] | 593 | } |
| 594 | } |
| 595 | |
Chris Dalton | 6fdbf61 | 2018-04-15 21:58:19 -0600 | [diff] [blame] | 596 | SkCubicType SkClassifyCubic(const SkPoint P[4], double t[2], double s[2], double d[4]) { |
| 597 | // Find the cubic's inflection function, I = [T^3 -3T^2 3T -1] dot D. (D0 will always be 0 |
| 598 | // for integral cubics.) |
| 599 | // |
| 600 | // See "Resolution Independent Curve Rendering using Programmable Graphics Hardware", |
| 601 | // 4.2 Curve Categorization: |
| 602 | // |
| 603 | // https://www.microsoft.com/en-us/research/wp-content/uploads/2005/01/p1000-loop.pdf |
| 604 | double A1 = calc_dot_cross_cubic(P[0], P[3], P[2]); |
| 605 | double A2 = calc_dot_cross_cubic(P[1], P[0], P[3]); |
| 606 | double A3 = calc_dot_cross_cubic(P[2], P[1], P[0]); |
| 607 | |
| 608 | double D3 = 3 * A3; |
| 609 | double D2 = D3 - A2; |
| 610 | double D1 = D2 - A2 + A1; |
| 611 | |
| 612 | // Shift the exponents in D so the largest magnitude falls somewhere in 1..2. This protects us |
| 613 | // from overflow down the road while solving for roots and KLM functionals. |
| 614 | double Dmax = std::max(std::max(fabs(D1), fabs(D2)), fabs(D3)); |
| 615 | double norm = previous_inverse_pow2(Dmax); |
| 616 | D1 *= norm; |
| 617 | D2 *= norm; |
| 618 | D3 *= norm; |
| 619 | |
| 620 | if (d) { |
| 621 | d[3] = D3; |
| 622 | d[2] = D2; |
| 623 | d[1] = D1; |
| 624 | d[0] = 0; |
| 625 | } |
| 626 | |
| 627 | // Now use the inflection function to classify the cubic. |
| 628 | // |
| 629 | // See "Resolution Independent Curve Rendering using Programmable Graphics Hardware", |
| 630 | // 4.4 Integral Cubics: |
| 631 | // |
| 632 | // https://www.microsoft.com/en-us/research/wp-content/uploads/2005/01/p1000-loop.pdf |
| 633 | if (0 != D1) { |
| 634 | double discr = 3*D2*D2 - 4*D1*D3; |
| 635 | if (discr > 0) { // Serpentine. |
Chris Dalton | 29011a2 | 2017-09-28 12:08:33 -0600 | [diff] [blame] | 636 | if (t && s) { |
Chris Dalton | 6fdbf61 | 2018-04-15 21:58:19 -0600 | [diff] [blame] | 637 | double q = 3*D2 + copysign(sqrt(3*discr), D2); |
| 638 | write_cubic_inflection_roots(q, 6*D1, 2*D3, q, t, s); |
Chris Dalton | 29011a2 | 2017-09-28 12:08:33 -0600 | [diff] [blame] | 639 | } |
Chris Dalton | 6fdbf61 | 2018-04-15 21:58:19 -0600 | [diff] [blame] | 640 | return SkCubicType::kSerpentine; |
| 641 | } else if (discr < 0) { // Loop. |
| 642 | if (t && s) { |
| 643 | double q = D2 + copysign(sqrt(-discr), D2); |
| 644 | write_cubic_inflection_roots(q, 2*D1, 2*(D2*D2 - D3*D1), D1*q, t, s); |
| 645 | } |
| 646 | return SkCubicType::kLoop; |
| 647 | } else { // Cusp. |
| 648 | if (t && s) { |
| 649 | write_cubic_inflection_roots(D2, 2*D1, D2, 2*D1, t, s); |
| 650 | } |
| 651 | return SkCubicType::kLocalCusp; |
Chris Dalton | 29011a2 | 2017-09-28 12:08:33 -0600 | [diff] [blame] | 652 | } |
Chris Dalton | febbffa | 2017-06-08 13:12:02 -0600 | [diff] [blame] | 653 | } else { |
Chris Dalton | 6fdbf61 | 2018-04-15 21:58:19 -0600 | [diff] [blame] | 654 | if (0 != D2) { // Cusp at T=infinity. |
| 655 | if (t && s) { |
| 656 | write_cubic_inflection_roots(D3, 3*D2, 1, 0, t, s); // T1=infinity. |
| 657 | } |
| 658 | return SkCubicType::kCuspAtInfinity; |
| 659 | } else { // Degenerate. |
| 660 | if (t && s) { |
| 661 | write_cubic_inflection_roots(1, 0, 1, 0, t, s); // T0=T1=infinity. |
| 662 | } |
| 663 | return 0 != D3 ? SkCubicType::kQuadratic : SkCubicType::kLineOrPoint; |
Chris Dalton | febbffa | 2017-06-08 13:12:02 -0600 | [diff] [blame] | 664 | } |
| 665 | } |
| 666 | } |
| 667 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 668 | template <typename T> void bubble_sort(T array[], int count) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 669 | for (int i = count - 1; i > 0; --i) |
| 670 | for (int j = i; j > 0; --j) |
| 671 | if (array[j] < array[j-1]) |
| 672 | { |
| 673 | T tmp(array[j]); |
| 674 | array[j] = array[j-1]; |
| 675 | array[j-1] = tmp; |
| 676 | } |
| 677 | } |
| 678 | |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 679 | /** |
| 680 | * Given an array and count, remove all pair-wise duplicates from the array, |
| 681 | * keeping the existing sorting, and return the new count |
| 682 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 683 | static int collaps_duplicates(SkScalar array[], int count) { |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 684 | for (int n = count; n > 1; --n) { |
| 685 | if (array[0] == array[1]) { |
| 686 | for (int i = 1; i < n; ++i) { |
| 687 | array[i - 1] = array[i]; |
| 688 | } |
| 689 | count -= 1; |
| 690 | } else { |
| 691 | array += 1; |
| 692 | } |
| 693 | } |
| 694 | return count; |
| 695 | } |
| 696 | |
| 697 | #ifdef SK_DEBUG |
| 698 | |
| 699 | #define TEST_COLLAPS_ENTRY(array) array, SK_ARRAY_COUNT(array) |
| 700 | |
| 701 | static void test_collaps_duplicates() { |
| 702 | static bool gOnce; |
| 703 | if (gOnce) { return; } |
| 704 | gOnce = true; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 705 | const SkScalar src0[] = { 0 }; |
| 706 | const SkScalar src1[] = { 0, 0 }; |
| 707 | const SkScalar src2[] = { 0, 1 }; |
| 708 | const SkScalar src3[] = { 0, 0, 0 }; |
| 709 | const SkScalar src4[] = { 0, 0, 1 }; |
| 710 | const SkScalar src5[] = { 0, 1, 1 }; |
| 711 | const SkScalar src6[] = { 0, 1, 2 }; |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 712 | const struct { |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 713 | const SkScalar* fData; |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 714 | int fCount; |
| 715 | int fCollapsedCount; |
| 716 | } data[] = { |
| 717 | { TEST_COLLAPS_ENTRY(src0), 1 }, |
| 718 | { TEST_COLLAPS_ENTRY(src1), 1 }, |
| 719 | { TEST_COLLAPS_ENTRY(src2), 2 }, |
| 720 | { TEST_COLLAPS_ENTRY(src3), 1 }, |
| 721 | { TEST_COLLAPS_ENTRY(src4), 2 }, |
| 722 | { TEST_COLLAPS_ENTRY(src5), 2 }, |
| 723 | { TEST_COLLAPS_ENTRY(src6), 3 }, |
| 724 | }; |
| 725 | for (size_t i = 0; i < SK_ARRAY_COUNT(data); ++i) { |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 726 | SkScalar dst[3]; |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 727 | memcpy(dst, data[i].fData, data[i].fCount * sizeof(dst[0])); |
| 728 | int count = collaps_duplicates(dst, data[i].fCount); |
| 729 | SkASSERT(data[i].fCollapsedCount == count); |
| 730 | for (int j = 1; j < count; ++j) { |
| 731 | SkASSERT(dst[j-1] < dst[j]); |
| 732 | } |
| 733 | } |
| 734 | } |
| 735 | #endif |
| 736 | |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 737 | static SkScalar SkScalarCubeRoot(SkScalar x) { |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 738 | return SkScalarPow(x, 0.3333333f); |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 739 | } |
| 740 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 741 | /* Solve coeff(t) == 0, returning the number of roots that |
| 742 | lie withing 0 < t < 1. |
| 743 | coeff[0]t^3 + coeff[1]t^2 + coeff[2]t + coeff[3] |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 744 | |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 745 | Eliminates repeated roots (so that all tValues are distinct, and are always |
| 746 | in increasing order. |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 747 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 748 | static int solve_cubic_poly(const SkScalar coeff[4], SkScalar tValues[3]) { |
| 749 | if (SkScalarNearlyZero(coeff[0])) { // we're just a quadratic |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 750 | return SkFindUnitQuadRoots(coeff[1], coeff[2], coeff[3], tValues); |
| 751 | } |
| 752 | |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 753 | SkScalar a, b, c, Q, R; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 754 | |
| 755 | { |
| 756 | SkASSERT(coeff[0] != 0); |
| 757 | |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 758 | SkScalar inva = SkScalarInvert(coeff[0]); |
| 759 | a = coeff[1] * inva; |
| 760 | b = coeff[2] * inva; |
| 761 | c = coeff[3] * inva; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 762 | } |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 763 | Q = (a*a - b*3) / 9; |
| 764 | R = (2*a*a*a - 9*a*b + 27*c) / 54; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 765 | |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 766 | SkScalar Q3 = Q * Q * Q; |
| 767 | SkScalar R2MinusQ3 = R * R - Q3; |
| 768 | SkScalar adiv3 = a / 3; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 769 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 770 | if (R2MinusQ3 < 0) { // we have 3 real roots |
caryclark | 93ca884 | 2016-05-27 05:24:37 -0700 | [diff] [blame] | 771 | // the divide/root can, due to finite precisions, be slightly outside of -1...1 |
| 772 | SkScalar theta = SkScalarACos(SkScalarPin(R / SkScalarSqrt(Q3), -1, 1)); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 773 | SkScalar neg2RootQ = -2 * SkScalarSqrt(Q); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 774 | |
Chris Dalton | 1d474dd | 2018-07-24 01:08:31 -0600 | [diff] [blame^] | 775 | tValues[0] = SkScalarPin(neg2RootQ * SkScalarCos(theta/3) - adiv3, 0, 1); |
| 776 | tValues[1] = SkScalarPin(neg2RootQ * SkScalarCos((theta + 2*SK_ScalarPI)/3) - adiv3, 0, 1); |
| 777 | tValues[2] = SkScalarPin(neg2RootQ * SkScalarCos((theta - 2*SK_ScalarPI)/3) - adiv3, 0, 1); |
reed@google.com | 087d5aa | 2012-02-29 20:59:24 +0000 | [diff] [blame] | 778 | SkDEBUGCODE(test_collaps_duplicates();) |
| 779 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 780 | // now sort the roots |
Chris Dalton | 1d474dd | 2018-07-24 01:08:31 -0600 | [diff] [blame^] | 781 | bubble_sort(tValues, 3); |
| 782 | return collaps_duplicates(tValues, 3); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 783 | } else { // we have 1 real root |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 784 | SkScalar A = SkScalarAbs(R) + SkScalarSqrt(R2MinusQ3); |
| 785 | A = SkScalarCubeRoot(A); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 786 | if (R > 0) { |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 787 | A = -A; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 788 | } |
| 789 | if (A != 0) { |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 790 | A += Q / A; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 791 | } |
Chris Dalton | 1d474dd | 2018-07-24 01:08:31 -0600 | [diff] [blame^] | 792 | tValues[0] = SkScalarPin(A - adiv3, 0, 1); |
| 793 | return 1; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 794 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 795 | } |
| 796 | |
| 797 | /* Looking for F' dot F'' == 0 |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 798 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 799 | A = b - a |
| 800 | B = c - 2b + a |
| 801 | C = d - 3c + 3b - a |
| 802 | |
| 803 | F' = 3Ct^2 + 6Bt + 3A |
| 804 | F'' = 6Ct + 6B |
| 805 | |
| 806 | F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB |
| 807 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 808 | static void formulate_F1DotF2(const SkScalar src[], SkScalar coeff[4]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 809 | SkScalar a = src[2] - src[0]; |
| 810 | SkScalar b = src[4] - 2 * src[2] + src[0]; |
| 811 | SkScalar c = src[6] + 3 * (src[2] - src[4]) - src[0]; |
| 812 | |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 813 | coeff[0] = c * c; |
| 814 | coeff[1] = 3 * b * c; |
| 815 | coeff[2] = 2 * b * b + c * a; |
| 816 | coeff[3] = a * b; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 817 | } |
| 818 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 819 | /* Looking for F' dot F'' == 0 |
rmistry@google.com | fbfcd56 | 2012-08-23 18:09:54 +0000 | [diff] [blame] | 820 | |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 821 | A = b - a |
| 822 | B = c - 2b + a |
| 823 | C = d - 3c + 3b - a |
| 824 | |
| 825 | F' = 3Ct^2 + 6Bt + 3A |
| 826 | F'' = 6Ct + 6B |
| 827 | |
| 828 | F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB |
| 829 | */ |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 830 | int SkFindCubicMaxCurvature(const SkPoint src[4], SkScalar tValues[3]) { |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 831 | SkScalar coeffX[4], coeffY[4]; |
| 832 | int i; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 833 | |
| 834 | formulate_F1DotF2(&src[0].fX, coeffX); |
| 835 | formulate_F1DotF2(&src[0].fY, coeffY); |
| 836 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 837 | for (i = 0; i < 4; i++) { |
reed@google.com | 3c12840 | 2013-12-16 14:17:40 +0000 | [diff] [blame] | 838 | coeffX[i] += coeffY[i]; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 839 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 840 | |
Chris Dalton | 1d474dd | 2018-07-24 01:08:31 -0600 | [diff] [blame^] | 841 | int numRoots = solve_cubic_poly(coeffX, tValues); |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 842 | // now remove extrema where the curvature is zero (mins) |
| 843 | // !!!! need a test for this !!!! |
Chris Dalton | 1d474dd | 2018-07-24 01:08:31 -0600 | [diff] [blame^] | 844 | return numRoots; |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 845 | } |
| 846 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 847 | int SkChopCubicAtMaxCurvature(const SkPoint src[4], SkPoint dst[13], |
| 848 | SkScalar tValues[3]) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 849 | SkScalar t_storage[3]; |
| 850 | |
halcanary | 96fcdcc | 2015-08-27 07:41:13 -0700 | [diff] [blame] | 851 | if (tValues == nullptr) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 852 | tValues = t_storage; |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 853 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 854 | |
Chris Dalton | 1d474dd | 2018-07-24 01:08:31 -0600 | [diff] [blame^] | 855 | SkScalar roots[3]; |
| 856 | int rootCount = SkFindCubicMaxCurvature(src, roots); |
| 857 | |
| 858 | // Throw out values not inside 0..1. |
| 859 | int count = 0; |
| 860 | for (int i = 0; i < rootCount; ++i) { |
| 861 | if (0 < roots[i] && roots[i] < 1) { |
| 862 | tValues[count++] = roots[i]; |
| 863 | } |
| 864 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 865 | |
egdaniel@google.com | 5383a75 | 2013-07-12 20:15:34 +0000 | [diff] [blame] | 866 | if (dst) { |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 867 | if (count == 0) { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 868 | memcpy(dst, src, 4 * sizeof(SkPoint)); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 869 | } else { |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 870 | SkChopCubicAt(src, dst, tValues, count); |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 871 | } |
reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame] | 872 | } |
| 873 | return count + 1; |
| 874 | } |
| 875 | |
reed | dc30885 | 2015-04-30 07:47:13 -0700 | [diff] [blame] | 876 | #include "../pathops/SkPathOpsCubic.h" |
| 877 | |
| 878 | typedef int (SkDCubic::*InterceptProc)(double intercept, double roots[3]) const; |
| 879 | |
| 880 | static bool cubic_dchop_at_intercept(const SkPoint src[4], SkScalar intercept, SkPoint dst[7], |
| 881 | InterceptProc method) { |
| 882 | SkDCubic cubic; |
| 883 | double roots[3]; |
| 884 | int count = (cubic.set(src).*method)(intercept, roots); |
| 885 | if (count > 0) { |
| 886 | SkDCubicPair pair = cubic.chopAt(roots[0]); |
| 887 | for (int i = 0; i < 7; ++i) { |
| 888 | dst[i] = pair.pts[i].asSkPoint(); |
| 889 | } |
| 890 | return true; |
| 891 | } |
| 892 | return false; |
| 893 | } |
| 894 | |
| 895 | bool SkChopMonoCubicAtY(SkPoint src[4], SkScalar y, SkPoint dst[7]) { |
| 896 | return cubic_dchop_at_intercept(src, y, dst, &SkDCubic::horizontalIntersect); |
| 897 | } |
| 898 | |
| 899 | bool SkChopMonoCubicAtX(SkPoint src[4], SkScalar x, SkPoint dst[7]) { |
| 900 | return cubic_dchop_at_intercept(src, x, dst, &SkDCubic::verticalIntersect); |
| 901 | } |
| 902 | |
commit-bot@chromium.org | b39d561 | 2014-02-21 12:17:34 +0000 | [diff] [blame] | 903 | /////////////////////////////////////////////////////////////////////////////// |
commit-bot@chromium.org | def6468 | 2014-02-21 19:49:10 +0000 | [diff] [blame] | 904 | // |
| 905 | // NURB representation for conics. Helpful explanations at: |
| 906 | // |
| 907 | // http://citeseerx.ist.psu.edu/viewdoc/ |
| 908 | // download?doi=10.1.1.44.5740&rep=rep1&type=ps |
| 909 | // and |
| 910 | // http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/NURBS/RB-conics.html |
| 911 | // |
reed@google.com | 17a2c91 | 2013-04-16 21:07:27 +0000 | [diff] [blame] | 912 | // F = (A (1 - t)^2 + C t^2 + 2 B (1 - t) t w) |
| 913 | // ------------------------------------------ |
| 914 | // ((1 - t)^2 + t^2 + 2 (1 - t) t w) |
| 915 | // |
| 916 | // = {t^2 (P0 + P2 - 2 P1 w), t (-2 P0 + 2 P1 w), P0} |
| 917 | // ------------------------------------------------ |
| 918 | // {t^2 (2 - 2 w), t (-2 + 2 w), 1} |
| 919 | // |
reed@google.com | 17a2c91 | 2013-04-16 21:07:27 +0000 | [diff] [blame] | 920 | |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 921 | // F' = 2 (C t (1 + t (-1 + w)) - A (-1 + t) (t (-1 + w) - w) + B (1 - 2 t) w) |
| 922 | // |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 923 | // t^2 : (2 P0 - 2 P2 - 2 P0 w + 2 P2 w) |
| 924 | // t^1 : (-2 P0 + 2 P2 + 4 P0 w - 4 P1 w) |
| 925 | // t^0 : -2 P0 w + 2 P1 w |
| 926 | // |
| 927 | // We disregard magnitude, so we can freely ignore the denominator of F', and |
| 928 | // divide the numerator by 2 |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 929 | // |
reed@google.com | 17a2c91 | 2013-04-16 21:07:27 +0000 | [diff] [blame] | 930 | // coeff[0] for t^2 |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 931 | // coeff[1] for t^1 |
| 932 | // coeff[2] for t^0 |
reed@google.com | 17a2c91 | 2013-04-16 21:07:27 +0000 | [diff] [blame] | 933 | // |
commit-bot@chromium.org | def6468 | 2014-02-21 19:49:10 +0000 | [diff] [blame] | 934 | static void conic_deriv_coeff(const SkScalar src[], |
| 935 | SkScalar w, |
| 936 | SkScalar coeff[3]) { |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 937 | const SkScalar P20 = src[4] - src[0]; |
| 938 | const SkScalar P10 = src[2] - src[0]; |
| 939 | const SkScalar wP10 = w * P10; |
| 940 | coeff[0] = w * P20 - P20; |
| 941 | coeff[1] = P20 - 2 * wP10; |
| 942 | coeff[2] = wP10; |
reed@google.com | 17a2c91 | 2013-04-16 21:07:27 +0000 | [diff] [blame] | 943 | } |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 944 | |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 945 | static bool conic_find_extrema(const SkScalar src[], SkScalar w, SkScalar* t) { |
| 946 | SkScalar coeff[3]; |
| 947 | conic_deriv_coeff(src, w, coeff); |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 948 | |
| 949 | SkScalar tValues[2]; |
| 950 | int roots = SkFindUnitQuadRoots(coeff[0], coeff[1], coeff[2], tValues); |
| 951 | SkASSERT(0 == roots || 1 == roots); |
skia.committer@gmail.com | 45fb8b6 | 2013-04-17 07:00:56 +0000 | [diff] [blame] | 952 | |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 953 | if (1 == roots) { |
| 954 | *t = tValues[0]; |
| 955 | return true; |
| 956 | } |
| 957 | return false; |
| 958 | } |
reed@google.com | 17a2c91 | 2013-04-16 21:07:27 +0000 | [diff] [blame] | 959 | |
commit-bot@chromium.org | d50d87a | 2014-01-28 14:36:52 +0000 | [diff] [blame] | 960 | // We only interpolate one dimension at a time (the first, at +0, +3, +6). |
| 961 | static void p3d_interp(const SkScalar src[7], SkScalar dst[7], SkScalar t) { |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 962 | SkScalar ab = SkScalarInterp(src[0], src[3], t); |
| 963 | SkScalar bc = SkScalarInterp(src[3], src[6], t); |
| 964 | dst[0] = ab; |
| 965 | dst[3] = SkScalarInterp(ab, bc, t); |
| 966 | dst[6] = bc; |
| 967 | } |
| 968 | |
Cary Clark | e4442cb | 2017-10-18 11:46:18 -0400 | [diff] [blame] | 969 | static void ratquad_mapTo3D(const SkPoint src[3], SkScalar w, SkPoint3 dst[3]) { |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 970 | dst[0].set(src[0].fX * 1, src[0].fY * 1, 1); |
| 971 | dst[1].set(src[1].fX * w, src[1].fY * w, w); |
| 972 | dst[2].set(src[2].fX * 1, src[2].fY * 1, 1); |
| 973 | } |
| 974 | |
Cary Clark | e4442cb | 2017-10-18 11:46:18 -0400 | [diff] [blame] | 975 | static SkPoint project_down(const SkPoint3& src) { |
| 976 | return {src.fX / src.fZ, src.fY / src.fZ}; |
| 977 | } |
| 978 | |
caryclark | 414c429 | 2016-09-26 11:03:54 -0700 | [diff] [blame] | 979 | // return false if infinity or NaN is generated; caller must check |
| 980 | bool SkConic::chopAt(SkScalar t, SkConic dst[2]) const { |
Cary Clark | e4442cb | 2017-10-18 11:46:18 -0400 | [diff] [blame] | 981 | SkPoint3 tmp[3], tmp2[3]; |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 982 | |
| 983 | ratquad_mapTo3D(fPts, fW, tmp); |
skia.committer@gmail.com | 4bb50b2 | 2013-04-13 07:01:15 +0000 | [diff] [blame] | 984 | |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 985 | p3d_interp(&tmp[0].fX, &tmp2[0].fX, t); |
| 986 | p3d_interp(&tmp[0].fY, &tmp2[0].fY, t); |
| 987 | p3d_interp(&tmp[0].fZ, &tmp2[0].fZ, t); |
skia.committer@gmail.com | 4bb50b2 | 2013-04-13 07:01:15 +0000 | [diff] [blame] | 988 | |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 989 | dst[0].fPts[0] = fPts[0]; |
Cary Clark | e4442cb | 2017-10-18 11:46:18 -0400 | [diff] [blame] | 990 | dst[0].fPts[1] = project_down(tmp2[0]); |
| 991 | dst[0].fPts[2] = project_down(tmp2[1]); dst[1].fPts[0] = dst[0].fPts[2]; |
| 992 | dst[1].fPts[1] = project_down(tmp2[2]); |
reed@google.com | 0d09955 | 2013-04-12 21:55:26 +0000 | [diff] [blame] | 993 | dst[1].fPts[2] = fPts[2]; |
| 994 | |
mike@reedtribe.org | 4af6280 | 2013-04-13 10:51:51 +0000 | [diff] [blame] | 995 | // to put in "standard form", where w0 and w2 are both 1, we compute the |
| 996 | // new w1 as sqrt(w1*w1/w0*w2) |
| 997 | // or |
| 998 | // w1 /= sqrt(w0*w2) |
| 999 | // |
commit-bot@chromium.org | def6468 | 2014-02-21 19:49:10 +0000 | [diff] [blame] | 1000 | // However, in our case, we know that for dst[0]: |
| 1001 | // w0 == 1, and for dst[1], w2 == 1 |
mike@reedtribe.org | 4af6280 | 2013-04-13 10:51:51 +0000 | [diff] [blame] | 1002 | // |
| 1003 | SkScalar root = SkScalarSqrt(tmp2[1].fZ); |
| 1004 | dst[0].fW = tmp2[0].fZ / root; |
| 1005 | dst[1].fW = tmp2[2].fZ / root; |
caryclark | 414c429 | 2016-09-26 11:03:54 -0700 | [diff] [blame] | 1006 | SkASSERT(sizeof(dst[0]) == sizeof(SkScalar) * 7); |
| 1007 | SkASSERT(0 == offsetof(SkConic, fPts[0].fX)); |
| 1008 | return SkScalarsAreFinite(&dst[0].fPts[0].fX, 7 * 2); |
reed@google.com | c518710 | 2013-04-12 19:11:10 +0000 | [diff] [blame] | 1009 | } |
mike@reedtribe.org | 8d55101 | 2013-04-14 02:40:50 +0000 | [diff] [blame] | 1010 | |
caryclark | b6474dd | 2016-01-19 08:07:49 -0800 | [diff] [blame] | 1011 | void SkConic::chopAt(SkScalar t1, SkScalar t2, SkConic* dst) const { |
| 1012 | if (0 == t1 || 1 == t2) { |
| 1013 | if (0 == t1 && 1 == t2) { |
| 1014 | *dst = *this; |
caryclark | 414c429 | 2016-09-26 11:03:54 -0700 | [diff] [blame] | 1015 | return; |
caryclark | b6474dd | 2016-01-19 08:07:49 -0800 | [diff] [blame] | 1016 | } else { |
| 1017 | SkConic pair[2]; |
caryclark | 414c429 | 2016-09-26 11:03:54 -0700 | [diff] [blame] | 1018 | if (this->chopAt(t1 ? t1 : t2, pair)) { |
| 1019 | *dst = pair[SkToBool(t1)]; |
| 1020 | return; |
| 1021 | } |
caryclark | b6474dd | 2016-01-19 08:07:49 -0800 | [diff] [blame] | 1022 | } |
caryclark | b6474dd | 2016-01-19 08:07:49 -0800 | [diff] [blame] | 1023 | } |
| 1024 | SkConicCoeff coeff(*this); |
| 1025 | Sk2s tt1(t1); |
| 1026 | Sk2s aXY = coeff.fNumer.eval(tt1); |
| 1027 | Sk2s aZZ = coeff.fDenom.eval(tt1); |
| 1028 | Sk2s midTT((t1 + t2) / 2); |
| 1029 | Sk2s dXY = coeff.fNumer.eval(midTT); |
| 1030 | Sk2s dZZ = coeff.fDenom.eval(midTT); |
| 1031 | Sk2s tt2(t2); |
| 1032 | Sk2s cXY = coeff.fNumer.eval(tt2); |
| 1033 | Sk2s cZZ = coeff.fDenom.eval(tt2); |
| 1034 | Sk2s bXY = times_2(dXY) - (aXY + cXY) * Sk2s(0.5f); |
| 1035 | Sk2s bZZ = times_2(dZZ) - (aZZ + cZZ) * Sk2s(0.5f); |
| 1036 | dst->fPts[0] = to_point(aXY / aZZ); |
| 1037 | dst->fPts[1] = to_point(bXY / bZZ); |
| 1038 | dst->fPts[2] = to_point(cXY / cZZ); |
| 1039 | Sk2s ww = bZZ / (aZZ * cZZ).sqrt(); |
mtklein | 7c249e5 | 2016-02-21 10:54:19 -0800 | [diff] [blame] | 1040 | dst->fW = ww[0]; |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 1041 | } |
| 1042 | |
| 1043 | SkPoint SkConic::evalAt(SkScalar t) const { |
caryclark | 5ba2b96 | 2016-01-26 17:02:30 -0800 | [diff] [blame] | 1044 | return to_point(SkConicCoeff(*this).eval(t)); |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 1045 | } |
| 1046 | |
| 1047 | SkVector SkConic::evalTangentAt(SkScalar t) const { |
caryclark | 45398df | 2015-08-25 13:19:06 -0700 | [diff] [blame] | 1048 | // The derivative equation returns a zero tangent vector when t is 0 or 1, |
| 1049 | // and the control point is equal to the end point. |
| 1050 | // In this case, use the conic endpoints to compute the tangent. |
| 1051 | if ((t == 0 && fPts[0] == fPts[1]) || (t == 1 && fPts[1] == fPts[2])) { |
| 1052 | return fPts[2] - fPts[0]; |
| 1053 | } |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 1054 | Sk2s p0 = from_point(fPts[0]); |
| 1055 | Sk2s p1 = from_point(fPts[1]); |
| 1056 | Sk2s p2 = from_point(fPts[2]); |
reed | ce6acc9 | 2015-03-20 13:46:08 -0700 | [diff] [blame] | 1057 | Sk2s ww(fW); |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 1058 | |
| 1059 | Sk2s p20 = p2 - p0; |
| 1060 | Sk2s p10 = p1 - p0; |
| 1061 | |
| 1062 | Sk2s C = ww * p10; |
| 1063 | Sk2s A = ww * p20 - p20; |
| 1064 | Sk2s B = p20 - C - C; |
| 1065 | |
caryclark | 5ba2b96 | 2016-01-26 17:02:30 -0800 | [diff] [blame] | 1066 | return to_vector(SkQuadCoeff(A, B, C).eval(t)); |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 1067 | } |
| 1068 | |
reed | f0b6c55 | 2016-01-01 13:05:10 -0800 | [diff] [blame] | 1069 | void SkConic::evalAt(SkScalar t, SkPoint* pt, SkVector* tangent) const { |
| 1070 | SkASSERT(t >= 0 && t <= SK_Scalar1); |
mtklein | 507ef6d | 2016-01-31 08:02:47 -0800 | [diff] [blame] | 1071 | |
reed | f0b6c55 | 2016-01-01 13:05:10 -0800 | [diff] [blame] | 1072 | if (pt) { |
| 1073 | *pt = this->evalAt(t); |
| 1074 | } |
| 1075 | if (tangent) { |
| 1076 | *tangent = this->evalTangentAt(t); |
| 1077 | } |
| 1078 | } |
| 1079 | |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1080 | static SkScalar subdivide_w_value(SkScalar w) { |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1081 | return SkScalarSqrt(SK_ScalarHalf + w * SK_ScalarHalf); |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1082 | } |
| 1083 | |
reed | 5501103 | 2015-03-26 09:10:22 -0700 | [diff] [blame] | 1084 | void SkConic::chop(SkConic * SK_RESTRICT dst) const { |
| 1085 | Sk2s scale = Sk2s(SkScalarInvert(SK_Scalar1 + fW)); |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 1086 | SkScalar newW = subdivide_w_value(fW); |
| 1087 | |
| 1088 | Sk2s p0 = from_point(fPts[0]); |
| 1089 | Sk2s p1 = from_point(fPts[1]); |
| 1090 | Sk2s p2 = from_point(fPts[2]); |
reed | ce6acc9 | 2015-03-20 13:46:08 -0700 | [diff] [blame] | 1091 | Sk2s ww(fW); |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 1092 | |
| 1093 | Sk2s wp1 = ww * p1; |
caryclark | 5ba2b96 | 2016-01-26 17:02:30 -0800 | [diff] [blame] | 1094 | Sk2s m = (p0 + times_2(wp1) + p2) * scale * Sk2s(0.5f); |
Cary Clark | a0e30b1 | 2018-02-02 11:02:46 -0500 | [diff] [blame] | 1095 | SkPoint mPt = to_point(m); |
| 1096 | if (!mPt.isFinite()) { |
| 1097 | double w_d = fW; |
| 1098 | double w_2 = w_d * 2; |
| 1099 | double scale_half = 1 / (1 + w_d) * 0.5; |
| 1100 | mPt.fX = SkDoubleToScalar((fPts[0].fX + w_2 * fPts[1].fX + fPts[2].fX) * scale_half); |
| 1101 | mPt.fY = SkDoubleToScalar((fPts[0].fY + w_2 * fPts[1].fY + fPts[2].fY) * scale_half); |
| 1102 | } |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 1103 | dst[0].fPts[0] = fPts[0]; |
| 1104 | dst[0].fPts[1] = to_point((p0 + wp1) * scale); |
Cary Clark | a0e30b1 | 2018-02-02 11:02:46 -0500 | [diff] [blame] | 1105 | dst[0].fPts[2] = dst[1].fPts[0] = mPt; |
reed | b640203 | 2015-03-20 13:23:43 -0700 | [diff] [blame] | 1106 | dst[1].fPts[1] = to_point((wp1 + p2) * scale); |
| 1107 | dst[1].fPts[2] = fPts[2]; |
| 1108 | |
| 1109 | dst[0].fW = dst[1].fW = newW; |
| 1110 | } |
| 1111 | |
mike@reedtribe.org | 97514f2 | 2013-04-27 18:23:16 +0000 | [diff] [blame] | 1112 | /* |
| 1113 | * "High order approximation of conic sections by quadratic splines" |
| 1114 | * by Michael Floater, 1993 |
| 1115 | */ |
mike@reedtribe.org | af5c506 | 2013-04-30 02:14:58 +0000 | [diff] [blame] | 1116 | #define AS_QUAD_ERROR_SETUP \ |
| 1117 | SkScalar a = fW - 1; \ |
| 1118 | SkScalar k = a / (4 * (2 + a)); \ |
| 1119 | SkScalar x = k * (fPts[0].fX - 2 * fPts[1].fX + fPts[2].fX); \ |
| 1120 | SkScalar y = k * (fPts[0].fY - 2 * fPts[1].fY + fPts[2].fY); |
| 1121 | |
| 1122 | void SkConic::computeAsQuadError(SkVector* err) const { |
| 1123 | AS_QUAD_ERROR_SETUP |
| 1124 | err->set(x, y); |
| 1125 | } |
| 1126 | |
| 1127 | bool SkConic::asQuadTol(SkScalar tol) const { |
| 1128 | AS_QUAD_ERROR_SETUP |
| 1129 | return (x * x + y * y) <= tol * tol; |
mike@reedtribe.org | 97514f2 | 2013-04-27 18:23:16 +0000 | [diff] [blame] | 1130 | } |
| 1131 | |
reed | f16c00e | 2015-02-12 17:56:21 -0800 | [diff] [blame] | 1132 | // Limit the number of suggested quads to approximate a conic |
| 1133 | #define kMaxConicToQuadPOW2 5 |
| 1134 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1135 | int SkConic::computeQuadPOW2(SkScalar tol) const { |
Cary Clark | df429f3 | 2017-11-08 11:44:31 -0500 | [diff] [blame] | 1136 | if (tol < 0 || !SkScalarIsFinite(tol) || !SkPointPriv::AreFinite(fPts, 3)) { |
reed | f16c00e | 2015-02-12 17:56:21 -0800 | [diff] [blame] | 1137 | return 0; |
| 1138 | } |
| 1139 | |
mike@reedtribe.org | af5c506 | 2013-04-30 02:14:58 +0000 | [diff] [blame] | 1140 | AS_QUAD_ERROR_SETUP |
reed | f16c00e | 2015-02-12 17:56:21 -0800 | [diff] [blame] | 1141 | |
reed | f16c00e | 2015-02-12 17:56:21 -0800 | [diff] [blame] | 1142 | SkScalar error = SkScalarSqrt(x * x + y * y); |
| 1143 | int pow2; |
| 1144 | for (pow2 = 0; pow2 < kMaxConicToQuadPOW2; ++pow2) { |
| 1145 | if (error <= tol) { |
| 1146 | break; |
| 1147 | } |
| 1148 | error *= 0.25f; |
| 1149 | } |
| 1150 | // float version -- using ceil gives the same results as the above. |
| 1151 | if (false) { |
| 1152 | SkScalar err = SkScalarSqrt(x * x + y * y); |
| 1153 | if (err <= tol) { |
| 1154 | return 0; |
| 1155 | } |
| 1156 | SkScalar tol2 = tol * tol; |
| 1157 | if (tol2 == 0) { |
| 1158 | return kMaxConicToQuadPOW2; |
| 1159 | } |
| 1160 | SkScalar fpow2 = SkScalarLog2((x * x + y * y) / tol2) * 0.25f; |
| 1161 | int altPow2 = SkScalarCeilToInt(fpow2); |
| 1162 | if (altPow2 != pow2) { |
| 1163 | SkDebugf("pow2 %d altPow2 %d fbits %g err %g tol %g\n", pow2, altPow2, fpow2, err, tol); |
| 1164 | } |
| 1165 | pow2 = altPow2; |
| 1166 | } |
| 1167 | return pow2; |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1168 | } |
| 1169 | |
Ben Wagner | 63fd760 | 2017-10-09 15:45:33 -0400 | [diff] [blame] | 1170 | // This was originally developed and tested for pathops: see SkOpTypes.h |
caryclark | bac1046 | 2016-09-22 10:24:59 -0700 | [diff] [blame] | 1171 | // returns true if (a <= b <= c) || (a >= b >= c) |
| 1172 | static bool between(SkScalar a, SkScalar b, SkScalar c) { |
| 1173 | return (a - b) * (c - b) <= 0; |
| 1174 | } |
| 1175 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1176 | static SkPoint* subdivide(const SkConic& src, SkPoint pts[], int level) { |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1177 | SkASSERT(level >= 0); |
mike@reedtribe.org | af5c506 | 2013-04-30 02:14:58 +0000 | [diff] [blame] | 1178 | |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1179 | if (0 == level) { |
| 1180 | memcpy(pts, &src.fPts[1], 2 * sizeof(SkPoint)); |
| 1181 | return pts + 2; |
| 1182 | } else { |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1183 | SkConic dst[2]; |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1184 | src.chop(dst); |
caryclark | bac1046 | 2016-09-22 10:24:59 -0700 | [diff] [blame] | 1185 | const SkScalar startY = src.fPts[0].fY; |
Cary Clark | a0e30b1 | 2018-02-02 11:02:46 -0500 | [diff] [blame] | 1186 | SkScalar endY = src.fPts[2].fY; |
caryclark | bac1046 | 2016-09-22 10:24:59 -0700 | [diff] [blame] | 1187 | if (between(startY, src.fPts[1].fY, endY)) { |
| 1188 | // If the input is monotonic and the output is not, the scan converter hangs. |
| 1189 | // Ensure that the chopped conics maintain their y-order. |
| 1190 | SkScalar midY = dst[0].fPts[2].fY; |
| 1191 | if (!between(startY, midY, endY)) { |
| 1192 | // If the computed midpoint is outside the ends, move it to the closer one. |
| 1193 | SkScalar closerY = SkTAbs(midY - startY) < SkTAbs(midY - endY) ? startY : endY; |
| 1194 | dst[0].fPts[2].fY = dst[1].fPts[0].fY = closerY; |
| 1195 | } |
| 1196 | if (!between(startY, dst[0].fPts[1].fY, dst[0].fPts[2].fY)) { |
| 1197 | // If the 1st control is not between the start and end, put it at the start. |
| 1198 | // This also reduces the quad to a line. |
| 1199 | dst[0].fPts[1].fY = startY; |
| 1200 | } |
| 1201 | if (!between(dst[1].fPts[0].fY, dst[1].fPts[1].fY, endY)) { |
| 1202 | // If the 2nd control is not between the start and end, put it at the end. |
| 1203 | // This also reduces the quad to a line. |
| 1204 | dst[1].fPts[1].fY = endY; |
| 1205 | } |
| 1206 | // Verify that all five points are in order. |
| 1207 | SkASSERT(between(startY, dst[0].fPts[1].fY, dst[0].fPts[2].fY)); |
| 1208 | SkASSERT(between(dst[0].fPts[1].fY, dst[0].fPts[2].fY, dst[1].fPts[1].fY)); |
| 1209 | SkASSERT(between(dst[0].fPts[2].fY, dst[1].fPts[1].fY, endY)); |
| 1210 | } |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1211 | --level; |
| 1212 | pts = subdivide(dst[0], pts, level); |
| 1213 | return subdivide(dst[1], pts, level); |
| 1214 | } |
| 1215 | } |
| 1216 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1217 | int SkConic::chopIntoQuadsPOW2(SkPoint pts[], int pow2) const { |
mike@reedtribe.org | af5c506 | 2013-04-30 02:14:58 +0000 | [diff] [blame] | 1218 | SkASSERT(pow2 >= 0); |
caryclark | 3cebe24 | 2016-08-23 09:41:00 -0700 | [diff] [blame] | 1219 | *pts = fPts[0]; |
| 1220 | SkDEBUGCODE(SkPoint* endPts); |
| 1221 | if (pow2 == kMaxConicToQuadPOW2) { // If an extreme weight generates many quads ... |
| 1222 | SkConic dst[2]; |
| 1223 | this->chop(dst); |
| 1224 | // check to see if the first chop generates a pair of lines |
Cary Clark | df429f3 | 2017-11-08 11:44:31 -0500 | [diff] [blame] | 1225 | if (SkPointPriv::EqualsWithinTolerance(dst[0].fPts[1], dst[0].fPts[2]) && |
| 1226 | SkPointPriv::EqualsWithinTolerance(dst[1].fPts[0], dst[1].fPts[1])) { |
caryclark | 3cebe24 | 2016-08-23 09:41:00 -0700 | [diff] [blame] | 1227 | pts[1] = pts[2] = pts[3] = dst[0].fPts[1]; // set ctrl == end to make lines |
| 1228 | pts[4] = dst[1].fPts[2]; |
| 1229 | pow2 = 1; |
| 1230 | SkDEBUGCODE(endPts = &pts[5]); |
| 1231 | goto commonFinitePtCheck; |
| 1232 | } |
| 1233 | } |
| 1234 | SkDEBUGCODE(endPts = ) subdivide(*this, pts + 1, pow2); |
| 1235 | commonFinitePtCheck: |
reed | b1b12f8 | 2016-07-13 10:56:53 -0700 | [diff] [blame] | 1236 | const int quadCount = 1 << pow2; |
| 1237 | const int ptCount = 2 * quadCount + 1; |
reed | b1b12f8 | 2016-07-13 10:56:53 -0700 | [diff] [blame] | 1238 | SkASSERT(endPts - pts == ptCount); |
Cary Clark | df429f3 | 2017-11-08 11:44:31 -0500 | [diff] [blame] | 1239 | if (!SkPointPriv::AreFinite(pts, ptCount)) { |
reed | b1b12f8 | 2016-07-13 10:56:53 -0700 | [diff] [blame] | 1240 | // if we generated a non-finite, pin ourselves to the middle of the hull, |
| 1241 | // as our first and last are already on the first/last pts of the hull. |
| 1242 | for (int i = 1; i < ptCount - 1; ++i) { |
| 1243 | pts[i] = fPts[1]; |
| 1244 | } |
| 1245 | } |
mike@reedtribe.org | 3df87cb | 2013-04-15 15:20:52 +0000 | [diff] [blame] | 1246 | return 1 << pow2; |
| 1247 | } |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1248 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1249 | bool SkConic::findXExtrema(SkScalar* t) const { |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1250 | return conic_find_extrema(&fPts[0].fX, fW, t); |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1251 | } |
| 1252 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1253 | bool SkConic::findYExtrema(SkScalar* t) const { |
mike@reedtribe.org | 6862cba | 2013-05-08 01:55:49 +0000 | [diff] [blame] | 1254 | return conic_find_extrema(&fPts[0].fY, fW, t); |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1255 | } |
| 1256 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1257 | bool SkConic::chopAtXExtrema(SkConic dst[2]) const { |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1258 | SkScalar t; |
| 1259 | if (this->findXExtrema(&t)) { |
caryclark | 414c429 | 2016-09-26 11:03:54 -0700 | [diff] [blame] | 1260 | if (!this->chopAt(t, dst)) { |
| 1261 | // if chop can't return finite values, don't chop |
| 1262 | return false; |
| 1263 | } |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1264 | // now clean-up the middle, since we know t was meant to be at |
| 1265 | // an X-extrema |
| 1266 | SkScalar value = dst[0].fPts[2].fX; |
| 1267 | dst[0].fPts[1].fX = value; |
| 1268 | dst[1].fPts[0].fX = value; |
| 1269 | dst[1].fPts[1].fX = value; |
| 1270 | return true; |
| 1271 | } |
| 1272 | return false; |
| 1273 | } |
| 1274 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1275 | bool SkConic::chopAtYExtrema(SkConic dst[2]) const { |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1276 | SkScalar t; |
| 1277 | if (this->findYExtrema(&t)) { |
caryclark | 414c429 | 2016-09-26 11:03:54 -0700 | [diff] [blame] | 1278 | if (!this->chopAt(t, dst)) { |
| 1279 | // if chop can't return finite values, don't chop |
| 1280 | return false; |
| 1281 | } |
mike@reedtribe.org | 0c5c386 | 2013-04-17 01:21:01 +0000 | [diff] [blame] | 1282 | // now clean-up the middle, since we know t was meant to be at |
| 1283 | // an Y-extrema |
| 1284 | SkScalar value = dst[0].fPts[2].fY; |
| 1285 | dst[0].fPts[1].fY = value; |
| 1286 | dst[1].fPts[0].fY = value; |
| 1287 | dst[1].fPts[1].fY = value; |
| 1288 | return true; |
| 1289 | } |
| 1290 | return false; |
| 1291 | } |
| 1292 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1293 | void SkConic::computeTightBounds(SkRect* bounds) const { |
mike@reedtribe.org | 5c082a1 | 2013-04-17 02:25:33 +0000 | [diff] [blame] | 1294 | SkPoint pts[4]; |
| 1295 | pts[0] = fPts[0]; |
| 1296 | pts[1] = fPts[2]; |
| 1297 | int count = 2; |
| 1298 | |
| 1299 | SkScalar t; |
| 1300 | if (this->findXExtrema(&t)) { |
| 1301 | this->evalAt(t, &pts[count++]); |
| 1302 | } |
| 1303 | if (this->findYExtrema(&t)) { |
| 1304 | this->evalAt(t, &pts[count++]); |
| 1305 | } |
| 1306 | bounds->set(pts, count); |
| 1307 | } |
| 1308 | |
mike@reedtribe.org | 28552e1 | 2013-04-26 00:58:29 +0000 | [diff] [blame] | 1309 | void SkConic::computeFastBounds(SkRect* bounds) const { |
mike@reedtribe.org | 5c082a1 | 2013-04-17 02:25:33 +0000 | [diff] [blame] | 1310 | bounds->set(fPts, 3); |
| 1311 | } |
commit-bot@chromium.org | def6468 | 2014-02-21 19:49:10 +0000 | [diff] [blame] | 1312 | |
caryclark | 612f70d | 2015-05-19 11:05:37 -0700 | [diff] [blame] | 1313 | #if 0 // unimplemented |
commit-bot@chromium.org | def6468 | 2014-02-21 19:49:10 +0000 | [diff] [blame] | 1314 | bool SkConic::findMaxCurvature(SkScalar* t) const { |
| 1315 | // TODO: Implement me |
| 1316 | return false; |
| 1317 | } |
caryclark | 612f70d | 2015-05-19 11:05:37 -0700 | [diff] [blame] | 1318 | #endif |
reed | 220f926 | 2014-12-17 08:21:04 -0800 | [diff] [blame] | 1319 | |
Mike Reed | 0a78e1e | 2018-02-22 14:13:21 -0500 | [diff] [blame] | 1320 | SkScalar SkConic::TransformW(const SkPoint pts[], SkScalar w, const SkMatrix& matrix) { |
reed | 220f926 | 2014-12-17 08:21:04 -0800 | [diff] [blame] | 1321 | if (!matrix.hasPerspective()) { |
| 1322 | return w; |
| 1323 | } |
| 1324 | |
Cary Clark | e4442cb | 2017-10-18 11:46:18 -0400 | [diff] [blame] | 1325 | SkPoint3 src[3], dst[3]; |
mtklein | 950e986 | 2015-03-19 12:03:29 -0700 | [diff] [blame] | 1326 | |
reed | 220f926 | 2014-12-17 08:21:04 -0800 | [diff] [blame] | 1327 | ratquad_mapTo3D(pts, w, src); |
| 1328 | |
Cary Clark | e4442cb | 2017-10-18 11:46:18 -0400 | [diff] [blame] | 1329 | matrix.mapHomogeneousPoints(dst, src, 3); |
reed | 220f926 | 2014-12-17 08:21:04 -0800 | [diff] [blame] | 1330 | |
| 1331 | // w' = sqrt(w1*w1/w0*w2) |
Mike Reed | 0a78e1e | 2018-02-22 14:13:21 -0500 | [diff] [blame] | 1332 | // use doubles temporarily, to handle small numer/denom |
| 1333 | double w0 = dst[0].fZ; |
| 1334 | double w1 = dst[1].fZ; |
| 1335 | double w2 = dst[2].fZ; |
Mike Reed | 5a5e084 | 2018-05-24 14:12:47 -0400 | [diff] [blame] | 1336 | return sk_double_to_float(sqrt(sk_ieee_double_divide(w1 * w1, w0 * w2))); |
reed | 220f926 | 2014-12-17 08:21:04 -0800 | [diff] [blame] | 1337 | } |
reed | d5d27d9 | 2015-02-09 13:54:43 -0800 | [diff] [blame] | 1338 | |
| 1339 | int SkConic::BuildUnitArc(const SkVector& uStart, const SkVector& uStop, SkRotationDirection dir, |
| 1340 | const SkMatrix* userMatrix, SkConic dst[kMaxConicsForArc]) { |
| 1341 | // rotate by x,y so that uStart is (1.0) |
| 1342 | SkScalar x = SkPoint::DotProduct(uStart, uStop); |
| 1343 | SkScalar y = SkPoint::CrossProduct(uStart, uStop); |
| 1344 | |
| 1345 | SkScalar absY = SkScalarAbs(y); |
| 1346 | |
| 1347 | // check for (effectively) coincident vectors |
| 1348 | // this can happen if our angle is nearly 0 or nearly 180 (y == 0) |
| 1349 | // ... we use the dot-prod to distinguish between 0 and 180 (x > 0) |
| 1350 | if (absY <= SK_ScalarNearlyZero && x > 0 && ((y >= 0 && kCW_SkRotationDirection == dir) || |
| 1351 | (y <= 0 && kCCW_SkRotationDirection == dir))) { |
| 1352 | return 0; |
| 1353 | } |
| 1354 | |
| 1355 | if (dir == kCCW_SkRotationDirection) { |
| 1356 | y = -y; |
| 1357 | } |
| 1358 | |
| 1359 | // We decide to use 1-conic per quadrant of a circle. What quadrant does [xy] lie in? |
| 1360 | // 0 == [0 .. 90) |
| 1361 | // 1 == [90 ..180) |
| 1362 | // 2 == [180..270) |
| 1363 | // 3 == [270..360) |
| 1364 | // |
| 1365 | int quadrant = 0; |
| 1366 | if (0 == y) { |
| 1367 | quadrant = 2; // 180 |
| 1368 | SkASSERT(SkScalarAbs(x + SK_Scalar1) <= SK_ScalarNearlyZero); |
| 1369 | } else if (0 == x) { |
| 1370 | SkASSERT(absY - SK_Scalar1 <= SK_ScalarNearlyZero); |
| 1371 | quadrant = y > 0 ? 1 : 3; // 90 : 270 |
| 1372 | } else { |
| 1373 | if (y < 0) { |
| 1374 | quadrant += 2; |
| 1375 | } |
| 1376 | if ((x < 0) != (y < 0)) { |
| 1377 | quadrant += 1; |
| 1378 | } |
| 1379 | } |
| 1380 | |
| 1381 | const SkPoint quadrantPts[] = { |
| 1382 | { 1, 0 }, { 1, 1 }, { 0, 1 }, { -1, 1 }, { -1, 0 }, { -1, -1 }, { 0, -1 }, { 1, -1 } |
| 1383 | }; |
| 1384 | const SkScalar quadrantWeight = SK_ScalarRoot2Over2; |
| 1385 | |
| 1386 | int conicCount = quadrant; |
| 1387 | for (int i = 0; i < conicCount; ++i) { |
| 1388 | dst[i].set(&quadrantPts[i * 2], quadrantWeight); |
| 1389 | } |
| 1390 | |
| 1391 | // Now compute any remaing (sub-90-degree) arc for the last conic |
| 1392 | const SkPoint finalP = { x, y }; |
| 1393 | const SkPoint& lastQ = quadrantPts[quadrant * 2]; // will already be a unit-vector |
| 1394 | const SkScalar dot = SkVector::DotProduct(lastQ, finalP); |
reed | 88f0a99 | 2015-02-10 08:45:06 -0800 | [diff] [blame] | 1395 | SkASSERT(0 <= dot && dot <= SK_Scalar1 + SK_ScalarNearlyZero); |
reed | d5d27d9 | 2015-02-09 13:54:43 -0800 | [diff] [blame] | 1396 | |
caryclark | c6325cd | 2015-05-11 14:36:33 -0700 | [diff] [blame] | 1397 | if (dot < 1) { |
reed | d5d27d9 | 2015-02-09 13:54:43 -0800 | [diff] [blame] | 1398 | SkVector offCurve = { lastQ.x() + x, lastQ.y() + y }; |
| 1399 | // compute the bisector vector, and then rescale to be the off-curve point. |
| 1400 | // we compute its length from cos(theta/2) = length / 1, using half-angle identity we get |
| 1401 | // length = sqrt(2 / (1 + cos(theta)). We already have cos() when to computed the dot. |
| 1402 | // This is nice, since our computed weight is cos(theta/2) as well! |
| 1403 | // |
| 1404 | const SkScalar cosThetaOver2 = SkScalarSqrt((1 + dot) / 2); |
| 1405 | offCurve.setLength(SkScalarInvert(cosThetaOver2)); |
Cary Clark | df429f3 | 2017-11-08 11:44:31 -0500 | [diff] [blame] | 1406 | if (!SkPointPriv::EqualsWithinTolerance(lastQ, offCurve)) { |
caryclark | f71ab8f | 2016-08-26 09:54:25 -0700 | [diff] [blame] | 1407 | dst[conicCount].set(lastQ, offCurve, finalP, cosThetaOver2); |
| 1408 | conicCount += 1; |
Ben Wagner | 63fd760 | 2017-10-09 15:45:33 -0400 | [diff] [blame] | 1409 | } |
reed | d5d27d9 | 2015-02-09 13:54:43 -0800 | [diff] [blame] | 1410 | } |
| 1411 | |
| 1412 | // now handle counter-clockwise and the initial unitStart rotation |
| 1413 | SkMatrix matrix; |
| 1414 | matrix.setSinCos(uStart.fY, uStart.fX); |
| 1415 | if (dir == kCCW_SkRotationDirection) { |
| 1416 | matrix.preScale(SK_Scalar1, -SK_Scalar1); |
| 1417 | } |
| 1418 | if (userMatrix) { |
| 1419 | matrix.postConcat(*userMatrix); |
| 1420 | } |
| 1421 | for (int i = 0; i < conicCount; ++i) { |
| 1422 | matrix.mapPoints(dst[i].fPts, 3); |
| 1423 | } |
| 1424 | return conicCount; |
| 1425 | } |