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 static bool chopMonoCubicAtY(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 #ifdef SK_SCALAR_IS_FLOAT 35 SkScalar t1 = ycrv[0] / (ycrv[0] - ycrv[3]); 36 #else // !SK_SCALAR_IS_FLOAT 37 SkScalar t1 = SkDivBits(ycrv[0], ycrv[0] - ycrv[3], 16); 38 #endif // !SK_SCALAR_IS_FLOAT 39 40 // Newton's iterations. 41 const SkScalar tol = SK_Scalar1 / 16384; // This leaves 2 fixed noise bits. 42 SkScalar t0; 43 const int maxiters = 5; 44 int iters = 0; 45 bool converged; 46 do { 47 t0 = t1; 48 SkScalar y01 = SkScalarInterp(ycrv[0], ycrv[1], t0); 49 SkScalar y12 = SkScalarInterp(ycrv[1], ycrv[2], t0); 50 SkScalar y23 = SkScalarInterp(ycrv[2], ycrv[3], t0); 51 SkScalar y012 = SkScalarInterp(y01, y12, t0); 52 SkScalar y123 = SkScalarInterp(y12, y23, t0); 53 SkScalar y0123 = SkScalarInterp(y012, y123, t0); 54 SkScalar yder = (y123 - y012) * 3; 55 // TODO(turk): check for yder==0: horizontal. 56 #ifdef SK_SCALAR_IS_FLOAT 57 t1 -= y0123 / yder; 58 #else // !SK_SCALAR_IS_FLOAT 59 t1 -= SkDivBits(y0123, yder, 16); 60 #endif // !SK_SCALAR_IS_FLOAT 61 converged = SkScalarAbs(t1 - t0) <= tol; // NaN-safe 62 ++iters; 63 } while (!converged && (iters < maxiters)); 64 *t = t1; // Return the result. 65 66 // The result might be valid, even if outside of the range [0, 1], but 67 // we never evaluate a Bezier outside this interval, so we return false. 68 if (t1 < 0 || t1 > SK_Scalar1) 69 return false; // This shouldn't happen, but check anyway. 70 return converged; 71 72 #else // BISECTION // Linear convergence, typically 16 iterations. 73 74 // Check that the endpoints straddle zero. 75 SkScalar tNeg, tPos; // Negative and positive function parameters. 76 if (ycrv[0] < 0) { 77 if (ycrv[3] < 0) 78 return false; 79 tNeg = 0; 80 tPos = SK_Scalar1; 81 } else if (ycrv[0] > 0) { 82 if (ycrv[3] > 0) 83 return false; 84 tNeg = SK_Scalar1; 85 tPos = 0; 86 } else { 87 *t = 0; 88 return true; 89 } 90 91 const SkScalar tol = SK_Scalar1 / 65536; // 1 for fixed, 1e-5 for float. 92 int iters = 0; 93 do { 94 SkScalar tMid = (tPos + tNeg) / 2; 95 SkScalar y01 = SkScalarInterp(ycrv[0], ycrv[1], tMid); 96 SkScalar y12 = SkScalarInterp(ycrv[1], ycrv[2], tMid); 97 SkScalar y23 = SkScalarInterp(ycrv[2], ycrv[3], tMid); 98 SkScalar y012 = SkScalarInterp(y01, y12, tMid); 99 SkScalar y123 = SkScalarInterp(y12, y23, tMid); 100 SkScalar y0123 = SkScalarInterp(y012, y123, tMid); 101 if (y0123 == 0) { 102 *t = tMid; 103 return true; 104 } 105 if (y0123 < 0) tNeg = tMid; 106 else tPos = tMid; 107 ++iters; 108 } while (!(SkScalarAbs(tPos - tNeg) <= tol)); // Nan-safe 109 110 *t = (tNeg + tPos) / 2; 111 return true; 112 #endif // BISECTION 113 } 114 115 116 bool SkCubicClipper::clipCubic(const SkPoint srcPts[4], SkPoint dst[4]) { 117 bool reverse; 118 119 // we need the data to be monotonically descending in Y 120 if (srcPts[0].fY > srcPts[3].fY) { 121 dst[0] = srcPts[3]; 122 dst[1] = srcPts[2]; 123 dst[2] = srcPts[1]; 124 dst[3] = srcPts[0]; 125 reverse = true; 126 } else { 127 memcpy(dst, srcPts, 4 * sizeof(SkPoint)); 128 reverse = false; 129 } 130 131 // are we completely above or below 132 const SkScalar ctop = fClip.fTop; 133 const SkScalar cbot = fClip.fBottom; 134 if (dst[3].fY <= ctop || dst[0].fY >= cbot) { 135 return false; 136 } 137 138 SkScalar t; 139 SkPoint tmp[7]; // for SkChopCubicAt 140 141 // are we partially above 142 if (dst[0].fY < ctop && chopMonoCubicAtY(dst, ctop, &t)) { 143 SkChopCubicAt(dst, tmp, t); 144 dst[0] = tmp[3]; 145 dst[1] = tmp[4]; 146 dst[2] = tmp[5]; 147 } 148 149 // are we partially below 150 if (dst[3].fY > cbot && chopMonoCubicAtY(dst, cbot, &t)) { 151 SkChopCubicAt(dst, tmp, t); 152 dst[1] = tmp[1]; 153 dst[2] = tmp[2]; 154 dst[3] = tmp[3]; 155 } 156 157 if (reverse) { 158 SkTSwap<SkPoint>(dst[0], dst[3]); 159 SkTSwap<SkPoint>(dst[1], dst[2]); 160 } 161 return true; 162 } 163
