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