michael@0: 
michael@0: /*
michael@0:  * Copyright 2009 The Android Open Source Project
michael@0:  *
michael@0:  * Use of this source code is governed by a BSD-style license that can be
michael@0:  * found in the LICENSE file.
michael@0:  */
michael@0: 
michael@0: 
michael@0: #include "SkCubicClipper.h"
michael@0: #include "SkGeometry.h"
michael@0: 
michael@0: SkCubicClipper::SkCubicClipper() {
michael@0:     fClip.setEmpty();
michael@0: }
michael@0: 
michael@0: void SkCubicClipper::setClip(const SkIRect& clip) {
michael@0:     // conver to scalars, since that's where we'll see the points
michael@0:     fClip.set(clip);
michael@0: }
michael@0: 
michael@0: 
michael@0: static bool chopMonoCubicAtY(SkPoint pts[4], SkScalar y, SkScalar* t) {
michael@0:     SkScalar ycrv[4];
michael@0:     ycrv[0] = pts[0].fY - y;
michael@0:     ycrv[1] = pts[1].fY - y;
michael@0:     ycrv[2] = pts[2].fY - y;
michael@0:     ycrv[3] = pts[3].fY - y;
michael@0: 
michael@0: #ifdef NEWTON_RAPHSON    // Quadratic convergence, typically <= 3 iterations.
michael@0:     // Initial guess.
michael@0:     // TODO(turk): Check for zero denominator? Shouldn't happen unless the curve
michael@0:     // is not only monotonic but degenerate.
michael@0:     SkScalar t1 = ycrv[0] / (ycrv[0] - ycrv[3]);
michael@0: 
michael@0:     // Newton's iterations.
michael@0:     const SkScalar tol = SK_Scalar1 / 16384;  // This leaves 2 fixed noise bits.
michael@0:     SkScalar t0;
michael@0:     const int maxiters = 5;
michael@0:     int iters = 0;
michael@0:     bool converged;
michael@0:     do {
michael@0:         t0 = t1;
michael@0:         SkScalar y01   = SkScalarInterp(ycrv[0], ycrv[1], t0);
michael@0:         SkScalar y12   = SkScalarInterp(ycrv[1], ycrv[2], t0);
michael@0:         SkScalar y23   = SkScalarInterp(ycrv[2], ycrv[3], t0);
michael@0:         SkScalar y012  = SkScalarInterp(y01,  y12,  t0);
michael@0:         SkScalar y123  = SkScalarInterp(y12,  y23,  t0);
michael@0:         SkScalar y0123 = SkScalarInterp(y012, y123, t0);
michael@0:         SkScalar yder  = (y123 - y012) * 3;
michael@0:         // TODO(turk): check for yder==0: horizontal.
michael@0:         t1 -= y0123 / yder;
michael@0:         converged = SkScalarAbs(t1 - t0) <= tol;  // NaN-safe
michael@0:         ++iters;
michael@0:     } while (!converged && (iters < maxiters));
michael@0:     *t = t1;                  // Return the result.
michael@0: 
michael@0:     // The result might be valid, even if outside of the range [0, 1], but
michael@0:     // we never evaluate a Bezier outside this interval, so we return false.
michael@0:     if (t1 < 0 || t1 > SK_Scalar1)
michael@0:         return false;         // This shouldn't happen, but check anyway.
michael@0:     return converged;
michael@0: 
michael@0: #else  // BISECTION    // Linear convergence, typically 16 iterations.
michael@0: 
michael@0:     // Check that the endpoints straddle zero.
michael@0:     SkScalar tNeg, tPos;    // Negative and positive function parameters.
michael@0:     if (ycrv[0] < 0) {
michael@0:         if (ycrv[3] < 0)
michael@0:             return false;
michael@0:         tNeg = 0;
michael@0:         tPos = SK_Scalar1;
michael@0:     } else if (ycrv[0] > 0) {
michael@0:         if (ycrv[3] > 0)
michael@0:             return false;
michael@0:         tNeg = SK_Scalar1;
michael@0:         tPos = 0;
michael@0:     } else {
michael@0:         *t = 0;
michael@0:         return true;
michael@0:     }
michael@0: 
michael@0:     const SkScalar tol = SK_Scalar1 / 65536;  // 1 for fixed, 1e-5 for float.
michael@0:     int iters = 0;
michael@0:     do {
michael@0:         SkScalar tMid = (tPos + tNeg) / 2;
michael@0:         SkScalar y01   = SkScalarInterp(ycrv[0], ycrv[1], tMid);
michael@0:         SkScalar y12   = SkScalarInterp(ycrv[1], ycrv[2], tMid);
michael@0:         SkScalar y23   = SkScalarInterp(ycrv[2], ycrv[3], tMid);
michael@0:         SkScalar y012  = SkScalarInterp(y01,     y12,     tMid);
michael@0:         SkScalar y123  = SkScalarInterp(y12,     y23,     tMid);
michael@0:         SkScalar y0123 = SkScalarInterp(y012,    y123,    tMid);
michael@0:         if (y0123 == 0) {
michael@0:             *t = tMid;
michael@0:             return true;
michael@0:         }
michael@0:         if (y0123 < 0)  tNeg = tMid;
michael@0:         else            tPos = tMid;
michael@0:         ++iters;
michael@0:     } while (!(SkScalarAbs(tPos - tNeg) <= tol));   // Nan-safe
michael@0: 
michael@0:     *t = (tNeg + tPos) / 2;
michael@0:     return true;
michael@0: #endif  // BISECTION
michael@0: }
michael@0: 
michael@0: 
michael@0: bool SkCubicClipper::clipCubic(const SkPoint srcPts[4], SkPoint dst[4]) {
michael@0:     bool reverse;
michael@0: 
michael@0:     // we need the data to be monotonically descending in Y
michael@0:     if (srcPts[0].fY > srcPts[3].fY) {
michael@0:         dst[0] = srcPts[3];
michael@0:         dst[1] = srcPts[2];
michael@0:         dst[2] = srcPts[1];
michael@0:         dst[3] = srcPts[0];
michael@0:         reverse = true;
michael@0:     } else {
michael@0:         memcpy(dst, srcPts, 4 * sizeof(SkPoint));
michael@0:         reverse = false;
michael@0:     }
michael@0: 
michael@0:     // are we completely above or below
michael@0:     const SkScalar ctop = fClip.fTop;
michael@0:     const SkScalar cbot = fClip.fBottom;
michael@0:     if (dst[3].fY <= ctop || dst[0].fY >= cbot) {
michael@0:         return false;
michael@0:     }
michael@0: 
michael@0:     SkScalar t;
michael@0:     SkPoint tmp[7]; // for SkChopCubicAt
michael@0: 
michael@0:     // are we partially above
michael@0:     if (dst[0].fY < ctop && chopMonoCubicAtY(dst, ctop, &t)) {
michael@0:         SkChopCubicAt(dst, tmp, t);
michael@0:         dst[0] = tmp[3];
michael@0:         dst[1] = tmp[4];
michael@0:         dst[2] = tmp[5];
michael@0:     }
michael@0: 
michael@0:     // are we partially below
michael@0:     if (dst[3].fY > cbot && chopMonoCubicAtY(dst, cbot, &t)) {
michael@0:         SkChopCubicAt(dst, tmp, t);
michael@0:         dst[1] = tmp[1];
michael@0:         dst[2] = tmp[2];
michael@0:         dst[3] = tmp[3];
michael@0:     }
michael@0: 
michael@0:     if (reverse) {
michael@0:         SkTSwap<SkPoint>(dst[0], dst[3]);
michael@0:         SkTSwap<SkPoint>(dst[1], dst[2]);
michael@0:     }
michael@0:     return true;
michael@0: }