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      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