| /* |
| * Copyright 2011 Google Inc. |
| * |
| * Use of this source code is governed by a BSD-style license that can be |
| * found in the LICENSE file. |
| */ |
| |
| #ifndef GrPathUtils_DEFINED |
| #define GrPathUtils_DEFINED |
| |
| #include "SkGeometry.h" |
| #include "SkRect.h" |
| #include "SkPathPriv.h" |
| #include "SkTArray.h" |
| |
| class SkMatrix; |
| |
| /** |
| * Utilities for evaluating paths. |
| */ |
| namespace GrPathUtils { |
| // Very small tolerances will be increased to a minimum threshold value, to avoid division |
| // problems in subsequent math. |
| SkScalar scaleToleranceToSrc(SkScalar devTol, |
| const SkMatrix& viewM, |
| const SkRect& pathBounds); |
| |
| int worstCasePointCount(const SkPath&, |
| int* subpaths, |
| SkScalar tol); |
| |
| uint32_t quadraticPointCount(const SkPoint points[], SkScalar tol); |
| |
| uint32_t generateQuadraticPoints(const SkPoint& p0, |
| const SkPoint& p1, |
| const SkPoint& p2, |
| SkScalar tolSqd, |
| SkPoint** points, |
| uint32_t pointsLeft); |
| |
| uint32_t cubicPointCount(const SkPoint points[], SkScalar tol); |
| |
| uint32_t generateCubicPoints(const SkPoint& p0, |
| const SkPoint& p1, |
| const SkPoint& p2, |
| const SkPoint& p3, |
| SkScalar tolSqd, |
| SkPoint** points, |
| uint32_t pointsLeft); |
| |
| // A 2x3 matrix that goes from the 2d space coordinates to UV space where |
| // u^2-v = 0 specifies the quad. The matrix is determined by the control |
| // points of the quadratic. |
| class QuadUVMatrix { |
| public: |
| QuadUVMatrix() {} |
| // Initialize the matrix from the control pts |
| QuadUVMatrix(const SkPoint controlPts[3]) { this->set(controlPts); } |
| void set(const SkPoint controlPts[3]); |
| |
| /** |
| * Applies the matrix to vertex positions to compute UV coords. This |
| * has been templated so that the compiler can easliy unroll the loop |
| * and reorder to avoid stalling for loads. The assumption is that a |
| * path renderer will have a small fixed number of vertices that it |
| * uploads for each quad. |
| * |
| * N is the number of vertices. |
| * STRIDE is the size of each vertex. |
| * UV_OFFSET is the offset of the UV values within each vertex. |
| * vertices is a pointer to the first vertex. |
| */ |
| template <int N, size_t STRIDE, size_t UV_OFFSET> |
| void apply(const void* vertices) const { |
| intptr_t xyPtr = reinterpret_cast<intptr_t>(vertices); |
| intptr_t uvPtr = reinterpret_cast<intptr_t>(vertices) + UV_OFFSET; |
| float sx = fM[0]; |
| float kx = fM[1]; |
| float tx = fM[2]; |
| float ky = fM[3]; |
| float sy = fM[4]; |
| float ty = fM[5]; |
| for (int i = 0; i < N; ++i) { |
| const SkPoint* xy = reinterpret_cast<const SkPoint*>(xyPtr); |
| SkPoint* uv = reinterpret_cast<SkPoint*>(uvPtr); |
| uv->fX = sx * xy->fX + kx * xy->fY + tx; |
| uv->fY = ky * xy->fX + sy * xy->fY + ty; |
| xyPtr += STRIDE; |
| uvPtr += STRIDE; |
| } |
| } |
| private: |
| float fM[6]; |
| }; |
| |
| // Input is 3 control points and a weight for a bezier conic. Calculates the |
| // three linear functionals (K,L,M) that represent the implicit equation of the |
| // conic, k^2 - lm. |
| // |
| // Output: klm holds the linear functionals K,L,M as row vectors: |
| // |
| // | ..K.. | | x | | k | |
| // | ..L.. | * | y | == | l | |
| // | ..M.. | | 1 | | m | |
| // |
| void getConicKLM(const SkPoint p[3], const SkScalar weight, SkMatrix* klm); |
| |
| // Converts a cubic into a sequence of quads. If working in device space |
| // use tolScale = 1, otherwise set based on stretchiness of the matrix. The |
| // result is sets of 3 points in quads. |
| void convertCubicToQuads(const SkPoint p[4], |
| SkScalar tolScale, |
| SkTArray<SkPoint, true>* quads); |
| |
| // When we approximate a cubic {a,b,c,d} with a quadratic we may have to |
| // ensure that the new control point lies between the lines ab and cd. The |
| // convex path renderer requires this. It starts with a path where all the |
| // control points taken together form a convex polygon. It relies on this |
| // property and the quadratic approximation of cubics step cannot alter it. |
| // This variation enforces this constraint. The cubic must be simple and dir |
| // must specify the orientation of the contour containing the cubic. |
| void convertCubicToQuadsConstrainToTangents(const SkPoint p[4], |
| SkScalar tolScale, |
| SkPathPriv::FirstDirection dir, |
| SkTArray<SkPoint, true>* quads); |
| |
| enum class ExcludedTerm { |
| kNonInvertible, |
| kQuadraticTerm, |
| kLinearTerm |
| }; |
| |
| // Computes the inverse-transpose of the cubic's power basis matrix, after removing a specific |
| // row of coefficients. |
| // |
| // E.g. if the cubic is defined in power basis form as follows: |
| // |
| // | x3 y3 0 | |
| // C(t,s) = [t^3 t^2*s t*s^2 s^3] * | x2 y2 0 | |
| // | x1 y1 0 | |
| // | x0 y0 1 | |
| // |
| // And the excluded term is "kQuadraticTerm", then the resulting inverse-transpose will be: |
| // |
| // | x3 y3 0 | -1 T |
| // | x1 y1 0 | |
| // | x0 y0 1 | |
| // |
| // (The term to exclude is chosen based on maximizing the resulting matrix determinant.) |
| // |
| // This can be used to find the KLM linear functionals: |
| // |
| // | ..K.. | | ..kcoeffs.. | |
| // | ..L.. | = | ..lcoeffs.. | * inverse_transpose_power_basis_matrix |
| // | ..M.. | | ..mcoeffs.. | |
| // |
| // NOTE: the same term that was excluded here must also be removed from the corresponding column |
| // of the klmcoeffs matrix. |
| // |
| // Returns which row of coefficients was removed, or kNonInvertible if the cubic was degenerate. |
| ExcludedTerm calcCubicInverseTransposePowerBasisMatrix(const SkPoint p[4], SkMatrix* out); |
| |
| // Computes the KLM linear functionals for the cubic implicit form. The "right" side of the |
| // curve (when facing in the direction of increasing parameter values) will be the area that |
| // satisfies: |
| // |
| // k^3 < l*m |
| // |
| // Output: |
| // |
| // klm: Holds the linear functionals K,L,M as row vectors: |
| // |
| // | ..K.. | | x | | k | |
| // | ..L.. | * | y | == | l | |
| // | ..M.. | | 1 | | m | |
| // |
| // NOTE: the KLM lines are calculated in the same space as the input control points. If you |
| // transform the points the lines will also need to be transformed. This can be done by mapping |
| // the lines with the inverse-transpose of the matrix used to map the points. |
| // |
| // t[],s[]: These are set to the two homogeneous parameter values at which points the lines L&M |
| // intersect with K (See SkClassifyCubic). |
| // |
| // Returns the cubic's classification. |
| SkCubicType getCubicKLM(const SkPoint src[4], SkMatrix* klm, double t[2], double s[2]); |
| |
| // Chops the cubic bezier passed in by src, at the double point (intersection point) |
| // if the curve is a cubic loop. If it is a loop, there will be two parametric values for |
| // the double point: t1 and t2. We chop the cubic at these values if they are between 0 and 1. |
| // Return value: |
| // Value of 3: t1 and t2 are both between (0,1), and dst will contain the three cubics, |
| // dst[0..3], dst[3..6], and dst[6..9] if dst is not nullptr |
| // Value of 2: Only one of t1 and t2 are between (0,1), and dst will contain the two cubics, |
| // dst[0..3] and dst[3..6] if dst is not nullptr |
| // Value of 1: Neither t1 nor t2 are between (0,1), and dst will contain the one original cubic, |
| // src[0..3] |
| // |
| // Output: |
| // |
| // klm: Holds the linear functionals K,L,M as row vectors. (See getCubicKLM().) |
| // |
| // loopIndex: This value will tell the caller which of the chopped sections (if any) are the |
| // actual loop. A value of -1 means there is no loop section. The caller can then use |
| // this value to decide how/if they want to flip the orientation of this section. |
| // The flip should be done by negating the k and l values as follows: |
| // |
| // KLM.postScale(-1, -1) |
| int chopCubicAtLoopIntersection(const SkPoint src[4], SkPoint dst[10], SkMatrix* klm, |
| int* loopIndex); |
| |
| // When tessellating curved paths into linear segments, this defines the maximum distance |
| // in screen space which a segment may deviate from the mathmatically correct value. |
| // Above this value, the segment will be subdivided. |
| // This value was chosen to approximate the supersampling accuracy of the raster path (16 |
| // samples, or one quarter pixel). |
| static const SkScalar kDefaultTolerance = SkDoubleToScalar(0.25); |
| |
| // We guarantee that no quad or cubic will ever produce more than this many points |
| static const int kMaxPointsPerCurve = 1 << 10; |
| }; |
| #endif |
