reed@android.com | 8a1c16f | 2008-12-17 15:59:43 +0000 | [diff] [blame^] | 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 | ////////////////////////////////////////////////////////////////////////////// |
| 155 | |
| 156 | #ifdef SK_DEBUG |
| 157 | class SkGeometry { |
| 158 | public: |
| 159 | static void UnitTest(); |
| 160 | }; |
| 161 | #endif |
| 162 | |
| 163 | #endif |