1 2 /* 3 * Copyright 2009 The Android Open Source Project 4 * 5 * Use of this source code is governed by a BSD-style license that can be 6 * found in the LICENSE file. 7 */ 8 9 10 #include "SkCubicClipper.h" 11 #include "SkGeometry.h" 12 13 SkCubicClipper::SkCubicClipper() { 14 fClip.setEmpty(); 15 } 16 17 void SkCubicClipper::setClip(const SkIRect& clip) { 18 // conver to scalars, since that's where we'll see the points 19 fClip.set(clip); 20 } 21 22 23 bool SkCubicClipper::ChopMonoAtY(const SkPoint pts[4], SkScalar y, SkScalar* t) { 24 SkScalar ycrv[4]; 25 ycrv[0] = pts[0].fY - y; 26 ycrv[1] = pts[1].fY - y; 27 ycrv[2] = pts[2].fY - y; 28 ycrv[3] = pts[3].fY - y; 29 30 #ifdef NEWTON_RAPHSON // Quadratic convergence, typically <= 3 iterations. 31 // Initial guess. 32 // TODO(turk): Check for zero denominator? Shouldn't happen unless the curve 33 // is not only monotonic but degenerate. 34 SkScalar t1 = ycrv[0] / (ycrv[0] - ycrv[3]); 35 36 // Newton's iterations. 37 const SkScalar tol = SK_Scalar1 / 16384; // This leaves 2 fixed noise bits. 38 SkScalar t0; 39 const int maxiters = 5; 40 int iters = 0; 41 bool converged; 42 do { 43 t0 = t1; 44 SkScalar y01 = SkScalarInterp(ycrv[0], ycrv[1], t0); 45 SkScalar y12 = SkScalarInterp(ycrv[1], ycrv[2], t0); 46 SkScalar y23 = SkScalarInterp(ycrv[2], ycrv[3], t0); 47 SkScalar y012 = SkScalarInterp(y01, y12, t0); 48 SkScalar y123 = SkScalarInterp(y12, y23, t0); 49 SkScalar y0123 = SkScalarInterp(y012, y123, t0); 50 SkScalar yder = (y123 - y012) * 3; 51 // TODO(turk): check for yder==0: horizontal. 52 t1 -= y0123 / yder; 53 converged = SkScalarAbs(t1 - t0) <= tol; // NaN-safe 54 ++iters; 55 } while (!converged && (iters < maxiters)); 56 *t = t1; // Return the result. 57 58 // The result might be valid, even if outside of the range [0, 1], but 59 // we never evaluate a Bezier outside this interval, so we return false. 60 if (t1 < 0 || t1 > SK_Scalar1) 61 return false; // This shouldn't happen, but check anyway. 62 return converged; 63 64 #else // BISECTION // Linear convergence, typically 16 iterations. 65 66 // Check that the endpoints straddle zero. 67 SkScalar tNeg, tPos; // Negative and positive function parameters. 68 if (ycrv[0] < 0) { 69 if (ycrv[3] < 0) 70 return false; 71 tNeg = 0; 72 tPos = SK_Scalar1; 73 } else if (ycrv[0] > 0) { 74 if (ycrv[3] > 0) 75 return false; 76 tNeg = SK_Scalar1; 77 tPos = 0; 78 } else { 79 *t = 0; 80 return true; 81 } 82 83 const SkScalar tol = SK_Scalar1 / 65536; // 1 for fixed, 1e-5 for float. 84 int iters = 0; 85 do { 86 SkScalar tMid = (tPos + tNeg) / 2; 87 SkScalar y01 = SkScalarInterp(ycrv[0], ycrv[1], tMid); 88 SkScalar y12 = SkScalarInterp(ycrv[1], ycrv[2], tMid); 89 SkScalar y23 = SkScalarInterp(ycrv[2], ycrv[3], tMid); 90 SkScalar y012 = SkScalarInterp(y01, y12, tMid); 91 SkScalar y123 = SkScalarInterp(y12, y23, tMid); 92 SkScalar y0123 = SkScalarInterp(y012, y123, tMid); 93 if (y0123 == 0) { 94 *t = tMid; 95 return true; 96 } 97 if (y0123 < 0) tNeg = tMid; 98 else tPos = tMid; 99 ++iters; 100 } while (!(SkScalarAbs(tPos - tNeg) <= tol)); // Nan-safe 101 102 *t = (tNeg + tPos) / 2; 103 return true; 104 #endif // BISECTION 105 } 106 107 108 bool SkCubicClipper::clipCubic(const SkPoint srcPts[4], SkPoint dst[4]) { 109 bool reverse; 110 111 // we need the data to be monotonically descending in Y 112 if (srcPts[0].fY > srcPts[3].fY) { 113 dst[0] = srcPts[3]; 114 dst[1] = srcPts[2]; 115 dst[2] = srcPts[1]; 116 dst[3] = srcPts[0]; 117 reverse = true; 118 } else { 119 memcpy(dst, srcPts, 4 * sizeof(SkPoint)); 120 reverse = false; 121 } 122 123 // are we completely above or below 124 const SkScalar ctop = fClip.fTop; 125 const SkScalar cbot = fClip.fBottom; 126 if (dst[3].fY <= ctop || dst[0].fY >= cbot) { 127 return false; 128 } 129 130 SkScalar t; 131 SkPoint tmp[7]; // for SkChopCubicAt 132 133 // are we partially above 134 if (dst[0].fY < ctop && ChopMonoAtY(dst, ctop, &t)) { 135 SkChopCubicAt(dst, tmp, t); 136 dst[0] = tmp[3]; 137 dst[1] = tmp[4]; 138 dst[2] = tmp[5]; 139 } 140 141 // are we partially below 142 if (dst[3].fY > cbot && ChopMonoAtY(dst, cbot, &t)) { 143 SkChopCubicAt(dst, tmp, t); 144 dst[1] = tmp[1]; 145 dst[2] = tmp[2]; 146 dst[3] = tmp[3]; 147 } 148 149 if (reverse) { 150 SkTSwap<SkPoint>(dst[0], dst[3]); 151 SkTSwap<SkPoint>(dst[1], dst[2]); 152 } 153 return true; 154 } 155