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- /*
- * 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 "include/core/SkRect.h"
- #include "include/private/SkTArray.h"
- #include "src/core/SkGeometry.h"
- #include "src/core/SkPathPriv.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.
- *
- * vertices is a pointer to the first vertex.
- * vertexCount is the number of vertices.
- * stride is the size of each vertex.
- * uvOffset is the offset of the UV values within each vertex.
- */
- void apply(void* vertices, int vertexCount, size_t stride, size_t uvOffset) const {
- intptr_t xyPtr = reinterpret_cast<intptr_t>(vertices);
- intptr_t uvPtr = reinterpret_cast<intptr_t>(vertices) + uvOffset;
- 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 < vertexCount; ++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. This will preserve the starting and
- // ending tangent vectors (modulo FP precision).
- 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
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