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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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