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1 /* libs/graphics/sgl/SkGeometry.h | |
2 ** | |
3 ** Copyright 2006, The Android Open Source Project | |
4 ** | |
5 ** Licensed under the Apache License, Version 2.0 (the "License"); | |
6 ** you may not use this file except in compliance with the License. | |
7 ** You may obtain a copy of the License at | |
8 ** | |
9 ** http://www.apache.org/licenses/LICENSE-2.0 | |
10 ** | |
11 ** Unless required by applicable law or agreed to in writing, software | |
12 ** distributed under the License is distributed on an "AS IS" BASIS, | |
13 ** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | |
14 ** See the License for the specific language governing permissions and | |
15 ** limitations under the License. | |
16 */ | |
17 | |
18 #ifndef SkGeometry_DEFINED | |
19 #define SkGeometry_DEFINED | |
20 | |
21 #include "SkMatrix.h" | |
22 | |
23 /** Given a quadratic equation Ax^2 + Bx + C = 0, return 0, 1, 2 roots for the | |
24 equation. | |
25 */ | |
26 int SkFindUnitQuadRoots(SkScalar A, SkScalar B, SkScalar C, SkScalar roots[2]); | |
27 | |
28 /////////////////////////////////////////////////////////////////////////////// | |
29 | |
30 /** Set pt to the point on the src quadratic specified by t. t must be | |
31 0 <= t <= 1.0 | |
32 */ | |
33 void SkEvalQuadAt(const SkPoint src[3], SkScalar t, SkPoint* pt, SkVector* tange
nt = NULL); | |
34 void SkEvalQuadAtHalf(const SkPoint src[3], SkPoint* pt, SkVector* tangent = NUL
L); | |
35 | |
36 /** Given a src quadratic bezier, chop it at the specified t value, | |
37 where 0 < t < 1, and return the two new quadratics in dst: | |
38 dst[0..2] and dst[2..4] | |
39 */ | |
40 void SkChopQuadAt(const SkPoint src[3], SkPoint dst[5], SkScalar t); | |
41 | |
42 /** Given a src quadratic bezier, chop it at the specified t == 1/2, | |
43 The new quads are returned in dst[0..2] and dst[2..4] | |
44 */ | |
45 void SkChopQuadAtHalf(const SkPoint src[3], SkPoint dst[5]); | |
46 | |
47 /** Given the 3 coefficients for a quadratic bezier (either X or Y values), look | |
48 for extrema, and return the number of t-values that are found that represent | |
49 these extrema. If the quadratic has no extrema betwee (0..1) exclusive, the | |
50 function returns 0. | |
51 Returned count tValues[] | |
52 0 ignored | |
53 1 0 < tValues[0] < 1 | |
54 */ | |
55 int SkFindQuadExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar tValues[1]); | |
56 | |
57 /** Given 3 points on a quadratic bezier, chop it into 1, 2 beziers such that | |
58 the resulting beziers are monotonic in Y. This is called by the scan convert
er. | |
59 Depending on what is returned, dst[] is treated as follows | |
60 1 dst[0..2] is the original quad | |
61 2 dst[0..2] and dst[2..4] are the two new quads | |
62 If dst == null, it is ignored and only the count is returned. | |
63 */ | |
64 int SkChopQuadAtYExtrema(const SkPoint src[3], SkPoint dst[5]); | |
65 | |
66 /** Given 3 points on a quadratic bezier, divide it into 2 quadratics | |
67 if the point of maximum curvature exists on the quad segment. | |
68 Depending on what is returned, dst[] is treated as follows | |
69 1 dst[0..2] is the original quad | |
70 2 dst[0..2] and dst[2..4] are the two new quads | |
71 If dst == null, it is ignored and only the count is returned. | |
72 */ | |
73 int SkChopQuadAtMaxCurvature(const SkPoint src[3], SkPoint dst[5]); | |
74 | |
75 ////////////////////////////////////////////////////////////////////////////////
//////// | |
76 | |
77 /** Convert from parametric from (pts) to polynomial coefficients | |
78 coeff[0]*T^3 + coeff[1]*T^2 + coeff[2]*T + coeff[3] | |
79 */ | |
80 void SkGetCubicCoeff(const SkPoint pts[4], SkScalar cx[4], SkScalar cy[4]); | |
81 | |
82 /** Set pt to the point on the src cubic specified by t. t must be | |
83 0 <= t <= 1.0 | |
84 */ | |
85 void SkEvalCubicAt(const SkPoint src[4], SkScalar t, SkPoint* locOrNull, SkVecto
r* tangentOrNull, SkVector* curvatureOrNull); | |
86 | |
87 /** Given a src cubic bezier, chop it at the specified t value, | |
88 where 0 < t < 1, and return the two new cubics in dst: | |
89 dst[0..3] and dst[3..6] | |
90 */ | |
91 void SkChopCubicAt(const SkPoint src[4], SkPoint dst[7], SkScalar t); | |
92 void SkChopCubicAt(const SkPoint src[4], SkPoint dst[7], const SkScalar t[], int
t_count); | |
93 | |
94 /** Given a src cubic bezier, chop it at the specified t == 1/2, | |
95 The new cubics are returned in dst[0..3] and dst[3..6] | |
96 */ | |
97 void SkChopCubicAtHalf(const SkPoint src[4], SkPoint dst[7]); | |
98 | |
99 /** Given the 4 coefficients for a cubic bezier (either X or Y values), look | |
100 for extrema, and return the number of t-values that are found that represent | |
101 these extrema. If the cubic has no extrema betwee (0..1) exclusive, the | |
102 function returns 0. | |
103 Returned count tValues[] | |
104 0 ignored | |
105 1 0 < tValues[0] < 1 | |
106 2 0 < tValues[0] < tValues[1] < 1 | |
107 */ | |
108 int SkFindCubicExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar d, SkScalar
tValues[2]); | |
109 | |
110 /** Given 4 points on a cubic bezier, chop it into 1, 2, 3 beziers such that | |
111 the resulting beziers are monotonic in Y. This is called by the scan convert
er. | |
112 Depending on what is returned, dst[] is treated as follows | |
113 1 dst[0..3] is the original cubic | |
114 2 dst[0..3] and dst[3..6] are the two new cubics | |
115 3 dst[0..3], dst[3..6], dst[6..9] are the three new cubics | |
116 If dst == null, it is ignored and only the count is returned. | |
117 */ | |
118 int SkChopCubicAtYExtrema(const SkPoint src[4], SkPoint dst[10]); | |
119 | |
120 /** Given a cubic bezier, return 0, 1, or 2 t-values that represent the | |
121 inflection points. | |
122 */ | |
123 int SkFindCubicInflections(const SkPoint src[4], SkScalar tValues[2]); | |
124 | |
125 /** Return 1 for no chop, or 2 for having chopped the cubic at its | |
126 inflection point. | |
127 */ | |
128 int SkChopCubicAtInflections(const SkPoint src[4], SkPoint dst[10]); | |
129 | |
130 int SkFindCubicMaxCurvature(const SkPoint src[4], SkScalar tValues[3]); | |
131 int SkChopCubicAtMaxCurvature(const SkPoint src[4], SkPoint dst[13], SkScalar tV
alues[3] = NULL); | |
132 | |
133 ////////////////////////////////////////////////////////////////////////////////
/////////// | |
134 | |
135 enum SkRotationDirection { | |
136 kCW_SkRotationDirection, | |
137 kCCW_SkRotationDirection | |
138 }; | |
139 | |
140 /** Maximum number of points needed in the quadPoints[] parameter for | |
141 SkBuildQuadArc() | |
142 */ | |
143 #define kSkBuildQuadArcStorage 17 | |
144 | |
145 /** Given 2 unit vectors and a rotation direction, fill out the specified | |
146 array of points with quadratic segments. Return is the number of points | |
147 written to, which will be { 0, 3, 5, 7, ... kSkBuildQuadArcStorage } | |
148 | |
149 matrix, if not null, is appled to the points before they are returned. | |
150 */ | |
151 int SkBuildQuadArc(const SkVector& unitStart, const SkVector& unitStop, SkRotati
onDirection, | |
152 const SkMatrix* matrix, SkPoint quadPoints[]); | |
153 | |
154 ////////////////////////////////////////////////////////////////////////////// | |
155 | |
156 #ifdef SK_DEBUG | |
157 class SkGeometry { | |
158 public: | |
159 static void UnitTest(); | |
160 }; | |
161 #endif | |
162 | |
163 #endif | |
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