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