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 15 void SkCubicClipper::setClip(const SkIRect& clip) { 16 // conver to scalars, since that's where we'll see the points 17 fClip.set(clip); 18 } 19 20 21 static bool chopMonoCubicAtY(SkPoint pts[4], SkScalar y, SkScalar* t) { 22 SkScalar ycrv[4]; 23 ycrv[0] = pts[0].fY - y; 24 ycrv[1] = pts[1].fY - y; 25 ycrv[2] = pts[2].fY - y; 26 ycrv[3] = pts[3].fY - y; 27 28 #ifdef NEWTON_RAPHSON // Quadratic convergence, typically <= 3 iterations. 29 // Initial guess. 30 // TODO(turk): Check for zero denominator? Shouldn't happen unless the curve 31 // is not only monotonic but degenerate. 32 #ifdef SK_SCALAR_IS_FLOAT 33 SkScalar t1 = ycrv[0] / (ycrv[0] - ycrv[3]); 34 #else // !SK_SCALAR_IS_FLOAT 35 SkScalar t1 = SkDivBits(ycrv[0], ycrv[0] - ycrv[3], 16); 36 #endif // !SK_SCALAR_IS_FLOAT 37 38 // Newton's iterations. 39 const SkScalar tol = SK_Scalar1 / 16384; // This leaves 2 fixed noise bits. 40 SkScalar t0; 41 const int maxiters = 5; 42 int iters = 0; 43 bool converged; 44 do { 45 t0 = t1; 46 SkScalar y01 = SkScalarInterp(ycrv[0], ycrv[1], t0); 47 SkScalar y12 = SkScalarInterp(ycrv[1], ycrv[2], t0); 48 SkScalar y23 = SkScalarInterp(ycrv[2], ycrv[3], t0); 49 SkScalar y012 = SkScalarInterp(y01, y12, t0); 50 SkScalar y123 = SkScalarInterp(y12, y23, t0); 51 SkScalar y0123 = SkScalarInterp(y012, y123, t0); 52 SkScalar yder = (y123 - y012) * 3; 53 // TODO(turk): check for yder==0: horizontal. 54 #ifdef SK_SCALAR_IS_FLOAT 55 t1 -= y0123 / yder; 56 #else // !SK_SCALAR_IS_FLOAT 57 t1 -= SkDivBits(y0123, yder, 16); 58 #endif // !SK_SCALAR_IS_FLOAT 59 converged = SkScalarAbs(t1 - t0) <= tol; // NaN-safe 60 ++iters; 61 } while (!converged && (iters < maxiters)); 62 *t = t1; // Return the result. 63 64 // The result might be valid, even if outside of the range [0, 1], but 65 // we never evaluate a Bezier outside this interval, so we return false. 66 if (t1 < 0 || t1 > SK_Scalar1) 67 return false; // This shouldn't happen, but check anyway. 68 return converged; 69 70 #else // BISECTION // Linear convergence, typically 16 iterations. 71 72 // Check that the endpoints straddle zero. 73 SkScalar tNeg, tPos; // Negative and positive function parameters. 74 if (ycrv[0] < 0) { 75 if (ycrv[3] < 0) 76 return false; 77 tNeg = 0; 78 tPos = SK_Scalar1; 79 } else if (ycrv[0] > 0) { 80 if (ycrv[3] > 0) 81 return false; 82 tNeg = SK_Scalar1; 83 tPos = 0; 84 } else { 85 *t = 0; 86 return true; 87 } 88 89 const SkScalar tol = SK_Scalar1 / 65536; // 1 for fixed, 1e-5 for float. 90 int iters = 0; 91 do { 92 SkScalar tMid = (tPos + tNeg) / 2; 93 SkScalar y01 = SkScalarInterp(ycrv[0], ycrv[1], tMid); 94 SkScalar y12 = SkScalarInterp(ycrv[1], ycrv[2], tMid); 95 SkScalar y23 = SkScalarInterp(ycrv[2], ycrv[3], tMid); 96 SkScalar y012 = SkScalarInterp(y01, y12, tMid); 97 SkScalar y123 = SkScalarInterp(y12, y23, tMid); 98 SkScalar y0123 = SkScalarInterp(y012, y123, tMid); 99 if (y0123 == 0) { 100 *t = tMid; 101 return true; 102 } 103 if (y0123 < 0) tNeg = tMid; 104 else tPos = tMid; 105 ++iters; 106 } while (!(SkScalarAbs(tPos - tNeg) <= tol)); // Nan-safe 107 108 *t = (tNeg + tPos) / 2; 109 return true; 110 #endif // BISECTION 111 } 112 113 114 bool SkCubicClipper::clipCubic(const SkPoint srcPts[4], SkPoint dst[4]) { 115 bool reverse; 116 117 // we need the data to be monotonically descending in Y 118 if (srcPts[0].fY > srcPts[3].fY) { 119 dst[0] = srcPts[3]; 120 dst[1] = srcPts[2]; 121 dst[2] = srcPts[1]; 122 dst[3] = srcPts[0]; 123 reverse = true; 124 } else { 125 memcpy(dst, srcPts, 4 * sizeof(SkPoint)); 126 reverse = false; 127 } 128 129 // are we completely above or below 130 const SkScalar ctop = fClip.fTop; 131 const SkScalar cbot = fClip.fBottom; 132 if (dst[3].fY <= ctop || dst[0].fY >= cbot) { 133 return false; 134 } 135 136 SkScalar t; 137 SkPoint tmp[7]; // for SkChopCubicAt 138 139 // are we partially above 140 if (dst[0].fY < ctop && chopMonoCubicAtY(dst, ctop, &t)) { 141 SkChopCubicAt(dst, tmp, t); 142 dst[0] = tmp[3]; 143 dst[1] = tmp[4]; 144 dst[2] = tmp[5]; 145 } 146 147 // are we partially below 148 if (dst[3].fY > cbot && chopMonoCubicAtY(dst, cbot, &t)) { 149 SkChopCubicAt(dst, tmp, t); 150 dst[1] = tmp[1]; 151 dst[2] = tmp[2]; 152 dst[3] = tmp[3]; 153 } 154 155 if (reverse) { 156 SkTSwap<SkPoint>(dst[0], dst[3]); 157 SkTSwap<SkPoint>(dst[1], dst[2]); 158 } 159 return true; 160 } 161 162
