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* tangent = NULL); 34 void SkEvalQuadAtHalf(const SkPoint src[3], SkPoint* pt, SkVector* tangent = NULL); 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 converter. 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, SkVector* 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 converter. 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 tValues[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, SkRotationDirection, 152 const SkMatrix* matrix, SkPoint quadPoints[]); 153 154 #endif 155