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 #include <utility>
13
SkCubicClipper()14 SkCubicClipper::SkCubicClipper() {
15 fClip.setEmpty();
16 }
17
setClip(const SkIRect & clip)18 void SkCubicClipper::setClip(const SkIRect& clip) {
19 // conver to scalars, since that's where we'll see the points
20 fClip.set(clip);
21 }
22
23
ChopMonoAtY(const SkPoint pts[4],SkScalar y,SkScalar * t)24 bool SkCubicClipper::ChopMonoAtY(const SkPoint pts[4], SkScalar y, SkScalar* t) {
25 SkScalar ycrv[4];
26 ycrv[0] = pts[0].fY - y;
27 ycrv[1] = pts[1].fY - y;
28 ycrv[2] = pts[2].fY - y;
29 ycrv[3] = pts[3].fY - y;
30
31 #ifdef NEWTON_RAPHSON // Quadratic convergence, typically <= 3 iterations.
32 // Initial guess.
33 // TODO(turk): Check for zero denominator? Shouldn't happen unless the curve
34 // is not only monotonic but degenerate.
35 SkScalar t1 = ycrv[0] / (ycrv[0] - ycrv[3]);
36
37 // Newton's iterations.
38 const SkScalar tol = SK_Scalar1 / 16384; // This leaves 2 fixed noise bits.
39 SkScalar t0;
40 const int maxiters = 5;
41 int iters = 0;
42 bool converged;
43 do {
44 t0 = t1;
45 SkScalar y01 = SkScalarInterp(ycrv[0], ycrv[1], t0);
46 SkScalar y12 = SkScalarInterp(ycrv[1], ycrv[2], t0);
47 SkScalar y23 = SkScalarInterp(ycrv[2], ycrv[3], t0);
48 SkScalar y012 = SkScalarInterp(y01, y12, t0);
49 SkScalar y123 = SkScalarInterp(y12, y23, t0);
50 SkScalar y0123 = SkScalarInterp(y012, y123, t0);
51 SkScalar yder = (y123 - y012) * 3;
52 // TODO(turk): check for yder==0: horizontal.
53 t1 -= y0123 / yder;
54 converged = SkScalarAbs(t1 - t0) <= tol; // NaN-safe
55 ++iters;
56 } while (!converged && (iters < maxiters));
57 *t = t1; // Return the result.
58
59 // The result might be valid, even if outside of the range [0, 1], but
60 // we never evaluate a Bezier outside this interval, so we return false.
61 if (t1 < 0 || t1 > SK_Scalar1)
62 return false; // This shouldn't happen, but check anyway.
63 return converged;
64
65 #else // BISECTION // Linear convergence, typically 16 iterations.
66
67 // Check that the endpoints straddle zero.
68 SkScalar tNeg, tPos; // Negative and positive function parameters.
69 if (ycrv[0] < 0) {
70 if (ycrv[3] < 0)
71 return false;
72 tNeg = 0;
73 tPos = SK_Scalar1;
74 } else if (ycrv[0] > 0) {
75 if (ycrv[3] > 0)
76 return false;
77 tNeg = SK_Scalar1;
78 tPos = 0;
79 } else {
80 *t = 0;
81 return true;
82 }
83
84 const SkScalar tol = SK_Scalar1 / 65536; // 1 for fixed, 1e-5 for float.
85 int iters = 0;
86 do {
87 SkScalar tMid = (tPos + tNeg) / 2;
88 SkScalar y01 = SkScalarInterp(ycrv[0], ycrv[1], tMid);
89 SkScalar y12 = SkScalarInterp(ycrv[1], ycrv[2], tMid);
90 SkScalar y23 = SkScalarInterp(ycrv[2], ycrv[3], tMid);
91 SkScalar y012 = SkScalarInterp(y01, y12, tMid);
92 SkScalar y123 = SkScalarInterp(y12, y23, tMid);
93 SkScalar y0123 = SkScalarInterp(y012, y123, tMid);
94 if (y0123 == 0) {
95 *t = tMid;
96 return true;
97 }
98 if (y0123 < 0) tNeg = tMid;
99 else tPos = tMid;
100 ++iters;
101 } while (!(SkScalarAbs(tPos - tNeg) <= tol)); // Nan-safe
102
103 *t = (tNeg + tPos) / 2;
104 return true;
105 #endif // BISECTION
106 }
107
108
clipCubic(const SkPoint srcPts[4],SkPoint dst[4])109 bool SkCubicClipper::clipCubic(const SkPoint srcPts[4], SkPoint dst[4]) {
110 bool reverse;
111
112 // we need the data to be monotonically descending in Y
113 if (srcPts[0].fY > srcPts[3].fY) {
114 dst[0] = srcPts[3];
115 dst[1] = srcPts[2];
116 dst[2] = srcPts[1];
117 dst[3] = srcPts[0];
118 reverse = true;
119 } else {
120 memcpy(dst, srcPts, 4 * sizeof(SkPoint));
121 reverse = false;
122 }
123
124 // are we completely above or below
125 const SkScalar ctop = fClip.fTop;
126 const SkScalar cbot = fClip.fBottom;
127 if (dst[3].fY <= ctop || dst[0].fY >= cbot) {
128 return false;
129 }
130
131 SkScalar t;
132 SkPoint tmp[7]; // for SkChopCubicAt
133
134 // are we partially above
135 if (dst[0].fY < ctop && ChopMonoAtY(dst, ctop, &t)) {
136 SkChopCubicAt(dst, tmp, t);
137 dst[0] = tmp[3];
138 dst[1] = tmp[4];
139 dst[2] = tmp[5];
140 }
141
142 // are we partially below
143 if (dst[3].fY > cbot && ChopMonoAtY(dst, cbot, &t)) {
144 SkChopCubicAt(dst, tmp, t);
145 dst[1] = tmp[1];
146 dst[2] = tmp[2];
147 dst[3] = tmp[3];
148 }
149
150 if (reverse) {
151 using std::swap;
152 swap(dst[0], dst[3]);
153 swap(dst[1], dst[2]);
154 }
155 return true;
156 }
157