1 /* 2 * Copyright (C) 2009 The Android Open Source Project 3 * 4 * Licensed under the Apache License, Version 2.0 (the "License"); 5 * you may not use this file except in compliance with the License. 6 * You may obtain a copy of the License at 7 * 8 * http://www.apache.org/licenses/LICENSE-2.0 9 * 10 * Unless required by applicable law or agreed to in writing, software 11 * distributed under the License is distributed on an "AS IS" BASIS, 12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 13 * See the License for the specific language governing permissions and 14 * limitations under the License. 15 */ 16 17 #include "SkCubicClipper.h" 18 #include "SkGeometry.h" 19 20 SkCubicClipper::SkCubicClipper() {} 21 22 void SkCubicClipper::setClip(const SkIRect& clip) { 23 // conver to scalars, since that's where we'll see the points 24 fClip.set(clip); 25 } 26 27 28 static bool chopMonoCubicAtY(SkPoint pts[4], SkScalar y, SkScalar* t) { 29 SkScalar ycrv[4]; 30 ycrv[0] = pts[0].fY - y; 31 ycrv[1] = pts[1].fY - y; 32 ycrv[2] = pts[2].fY - y; 33 ycrv[3] = pts[3].fY - y; 34 35 #ifdef NEWTON_RAPHSON // Quadratic convergence, typically <= 3 iterations. 36 // Initial guess. 37 // TODO(turk): Check for zero denominator? Shouldn't happen unless the curve 38 // is not only monotonic but degenerate. 39 #ifdef SK_SCALAR_IS_FLOAT 40 SkScalar t1 = ycrv[0] / (ycrv[0] - ycrv[3]); 41 #else // !SK_SCALAR_IS_FLOAT 42 SkScalar t1 = SkDivBits(ycrv[0], ycrv[0] - ycrv[3], 16); 43 #endif // !SK_SCALAR_IS_FLOAT 44 45 // Newton's iterations. 46 const SkScalar tol = SK_Scalar1 / 16384; // This leaves 2 fixed noise bits. 47 SkScalar t0; 48 const int maxiters = 5; 49 int iters = 0; 50 bool converged; 51 do { 52 t0 = t1; 53 SkScalar y01 = SkScalarInterp(ycrv[0], ycrv[1], t0); 54 SkScalar y12 = SkScalarInterp(ycrv[1], ycrv[2], t0); 55 SkScalar y23 = SkScalarInterp(ycrv[2], ycrv[3], t0); 56 SkScalar y012 = SkScalarInterp(y01, y12, t0); 57 SkScalar y123 = SkScalarInterp(y12, y23, t0); 58 SkScalar y0123 = SkScalarInterp(y012, y123, t0); 59 SkScalar yder = (y123 - y012) * 3; 60 // TODO(turk): check for yder==0: horizontal. 61 #ifdef SK_SCALAR_IS_FLOAT 62 t1 -= y0123 / yder; 63 #else // !SK_SCALAR_IS_FLOAT 64 t1 -= SkDivBits(y0123, yder, 16); 65 #endif // !SK_SCALAR_IS_FLOAT 66 converged = SkScalarAbs(t1 - t0) <= tol; // NaN-safe 67 ++iters; 68 } while (!converged && (iters < maxiters)); 69 *t = t1; // Return the result. 70 71 // The result might be valid, even if outside of the range [0, 1], but 72 // we never evaluate a Bezier outside this interval, so we return false. 73 if (t1 < 0 || t1 > SK_Scalar1) 74 return false; // This shouldn't happen, but check anyway. 75 return converged; 76 77 #else // BISECTION // Linear convergence, typically 16 iterations. 78 79 // Check that the endpoints straddle zero. 80 SkScalar tNeg, tPos; // Negative and positive function parameters. 81 if (ycrv[0] < 0) { 82 if (ycrv[3] < 0) 83 return false; 84 tNeg = 0; 85 tPos = SK_Scalar1; 86 } else if (ycrv[0] > 0) { 87 if (ycrv[3] > 0) 88 return false; 89 tNeg = SK_Scalar1; 90 tPos = 0; 91 } else { 92 *t = 0; 93 return true; 94 } 95 96 const SkScalar tol = SK_Scalar1 / 65536; // 1 for fixed, 1e-5 for float. 97 int iters = 0; 98 do { 99 SkScalar tMid = (tPos + tNeg) / 2; 100 SkScalar y01 = SkScalarInterp(ycrv[0], ycrv[1], tMid); 101 SkScalar y12 = SkScalarInterp(ycrv[1], ycrv[2], tMid); 102 SkScalar y23 = SkScalarInterp(ycrv[2], ycrv[3], tMid); 103 SkScalar y012 = SkScalarInterp(y01, y12, tMid); 104 SkScalar y123 = SkScalarInterp(y12, y23, tMid); 105 SkScalar y0123 = SkScalarInterp(y012, y123, tMid); 106 if (y0123 == 0) { 107 *t = tMid; 108 return true; 109 } 110 if (y0123 < 0) tNeg = tMid; 111 else tPos = tMid; 112 ++iters; 113 } while (!(SkScalarAbs(tPos - tNeg) <= tol)); // Nan-safe 114 115 *t = (tNeg + tPos) / 2; 116 return true; 117 #endif // BISECTION 118 } 119 120 121 bool SkCubicClipper::clipCubic(const SkPoint srcPts[4], SkPoint dst[4]) { 122 bool reverse; 123 124 // we need the data to be monotonically descending in Y 125 if (srcPts[0].fY > srcPts[3].fY) { 126 dst[0] = srcPts[3]; 127 dst[1] = srcPts[2]; 128 dst[2] = srcPts[1]; 129 dst[3] = srcPts[0]; 130 reverse = true; 131 } else { 132 memcpy(dst, srcPts, 4 * sizeof(SkPoint)); 133 reverse = false; 134 } 135 136 // are we completely above or below 137 const SkScalar ctop = fClip.fTop; 138 const SkScalar cbot = fClip.fBottom; 139 if (dst[3].fY <= ctop || dst[0].fY >= cbot) { 140 return false; 141 } 142 143 SkScalar t; 144 SkPoint tmp[7]; // for SkChopCubicAt 145 146 // are we partially above 147 if (dst[0].fY < ctop && chopMonoCubicAtY(dst, ctop, &t)) { 148 SkChopCubicAt(dst, tmp, t); 149 dst[0] = tmp[3]; 150 dst[1] = tmp[4]; 151 dst[2] = tmp[5]; 152 } 153 154 // are we partially below 155 if (dst[3].fY > cbot && chopMonoCubicAtY(dst, cbot, &t)) { 156 SkChopCubicAt(dst, tmp, t); 157 dst[1] = tmp[1]; 158 dst[2] = tmp[2]; 159 dst[3] = tmp[3]; 160 } 161 162 if (reverse) { 163 SkTSwap<SkPoint>(dst[0], dst[3]); 164 SkTSwap<SkPoint>(dst[1], dst[2]); 165 } 166 return true; 167 } 168 169
