1/*
2 * Copyright 2011 Google Inc.
3 *
4 * Use of this source code is governed by a BSD-style license that can be
5 * found in the LICENSE file.
6 */
7
8#ifndef GrPathUtils_DEFINED
9#define GrPathUtils_DEFINED
10
11#include "SkRect.h"
12#include "SkPath.h"
13#include "SkTArray.h"
14
15class SkMatrix;
16
17/**
18 *  Utilities for evaluating paths.
19 */
20namespace GrPathUtils {
21    SkScalar scaleToleranceToSrc(SkScalar devTol,
22                                 const SkMatrix& viewM,
23                                 const SkRect& pathBounds);
24
25    /// Since we divide by tol if we're computing exact worst-case bounds,
26    /// very small tolerances will be increased to gMinCurveTol.
27    int worstCasePointCount(const SkPath&,
28                            int* subpaths,
29                            SkScalar tol);
30
31    /// Since we divide by tol if we're computing exact worst-case bounds,
32    /// very small tolerances will be increased to gMinCurveTol.
33    uint32_t quadraticPointCount(const SkPoint points[], SkScalar tol);
34
35    uint32_t generateQuadraticPoints(const SkPoint& p0,
36                                     const SkPoint& p1,
37                                     const SkPoint& p2,
38                                     SkScalar tolSqd,
39                                     SkPoint** points,
40                                     uint32_t pointsLeft);
41
42    /// Since we divide by tol if we're computing exact worst-case bounds,
43    /// very small tolerances will be increased to gMinCurveTol.
44    uint32_t cubicPointCount(const SkPoint points[], SkScalar tol);
45
46    uint32_t generateCubicPoints(const SkPoint& p0,
47                                 const SkPoint& p1,
48                                 const SkPoint& p2,
49                                 const SkPoint& p3,
50                                 SkScalar tolSqd,
51                                 SkPoint** points,
52                                 uint32_t pointsLeft);
53
54    // A 2x3 matrix that goes from the 2d space coordinates to UV space where
55    // u^2-v = 0 specifies the quad. The matrix is determined by the control
56    // points of the quadratic.
57    class QuadUVMatrix {
58    public:
59        QuadUVMatrix() {};
60        // Initialize the matrix from the control pts
61        QuadUVMatrix(const SkPoint controlPts[3]) { this->set(controlPts); }
62        void set(const SkPoint controlPts[3]);
63
64        /**
65         * Applies the matrix to vertex positions to compute UV coords. This
66         * has been templated so that the compiler can easliy unroll the loop
67         * and reorder to avoid stalling for loads. The assumption is that a
68         * path renderer will have a small fixed number of vertices that it
69         * uploads for each quad.
70         *
71         * N is the number of vertices.
72         * STRIDE is the size of each vertex.
73         * UV_OFFSET is the offset of the UV values within each vertex.
74         * vertices is a pointer to the first vertex.
75         */
76        template <int N, size_t STRIDE, size_t UV_OFFSET>
77        void apply(const void* vertices) {
78            intptr_t xyPtr = reinterpret_cast<intptr_t>(vertices);
79            intptr_t uvPtr = reinterpret_cast<intptr_t>(vertices) + UV_OFFSET;
80            float sx = fM[0];
81            float kx = fM[1];
82            float tx = fM[2];
83            float ky = fM[3];
84            float sy = fM[4];
85            float ty = fM[5];
86            for (int i = 0; i < N; ++i) {
87                const SkPoint* xy = reinterpret_cast<const SkPoint*>(xyPtr);
88                SkPoint* uv = reinterpret_cast<SkPoint*>(uvPtr);
89                uv->fX = sx * xy->fX + kx * xy->fY + tx;
90                uv->fY = ky * xy->fX + sy * xy->fY + ty;
91                xyPtr += STRIDE;
92                uvPtr += STRIDE;
93            }
94        }
95    private:
96        float fM[6];
97    };
98
99    // Input is 3 control points and a weight for a bezier conic. Calculates the
100    // three linear functionals (K,L,M) that represent the implicit equation of the
101    // conic, K^2 - LM.
102    //
103    // Output:
104    //  K = (klm[0], klm[1], klm[2])
105    //  L = (klm[3], klm[4], klm[5])
106    //  M = (klm[6], klm[7], klm[8])
107    void getConicKLM(const SkPoint p[3], const SkScalar weight, SkScalar klm[9]);
108
109    // Converts a cubic into a sequence of quads. If working in device space
110    // use tolScale = 1, otherwise set based on stretchiness of the matrix. The
111    // result is sets of 3 points in quads (TODO: share endpoints in returned
112    // array)
113    // When we approximate a cubic {a,b,c,d} with a quadratic we may have to
114    // ensure that the new control point lies between the lines ab and cd. The
115    // convex path renderer requires this. It starts with a path where all the
116    // control points taken together form a convex polygon. It relies on this
117    // property and the quadratic approximation of cubics step cannot alter it.
118    // Setting constrainWithinTangents to true enforces this property. When this
119    // is true the cubic must be simple and dir must specify the orientation of
120    // the cubic. Otherwise, dir is ignored.
121    void convertCubicToQuads(const SkPoint p[4],
122                             SkScalar tolScale,
123                             bool constrainWithinTangents,
124                             SkPath::Direction dir,
125                             SkTArray<SkPoint, true>* quads);
126
127    // Chops the cubic bezier passed in by src, at the double point (intersection point)
128    // if the curve is a cubic loop. If it is a loop, there will be two parametric values for
129    // the double point: ls and ms. We chop the cubic at these values if they are between 0 and 1.
130    // Return value:
131    // Value of 3: ls and ms are both between (0,1), and dst will contain the three cubics,
132    //             dst[0..3], dst[3..6], and dst[6..9] if dst is not NULL
133    // Value of 2: Only one of ls and ms are between (0,1), and dst will contain the two cubics,
134    //             dst[0..3] and dst[3..6] if dst is not NULL
135    // Value of 1: Neither ls or ms are between (0,1), and dst will contain the one original cubic,
136    //             dst[0..3] if dst is not NULL
137    //
138    // Optional KLM Calculation:
139    // The function can also return the KLM linear functionals for the chopped cubic implicit form
140    // of K^3 - LM.
141    // It will calculate a single set of KLM values that can be shared by all sub cubics, except
142    // for the subsection that is "the loop" the K and L values need to be negated.
143    // Output:
144    // klm:     Holds the values for the linear functionals as:
145    //          K = (klm[0], klm[1], klm[2])
146    //          L = (klm[3], klm[4], klm[5])
147    //          M = (klm[6], klm[7], klm[8])
148    // klm_rev: These values are flags for the corresponding sub cubic saying whether or not
149    //          the K and L values need to be flipped. A value of -1.f means flip K and L and
150    //          a value of 1.f means do nothing.
151    //          *****DO NOT FLIP M, JUST K AND L*****
152    //
153    // Notice that the klm lines are calculated in the same space as the input control points.
154    // If you transform the points the lines will also need to be transformed. This can be done
155    // by mapping the lines with the inverse-transpose of the matrix used to map the points.
156    int chopCubicAtLoopIntersection(const SkPoint src[4], SkPoint dst[10] = NULL,
157                                    SkScalar klm[9] = NULL, SkScalar klm_rev[3] = NULL);
158
159    // Input is p which holds the 4 control points of a non-rational cubic Bezier curve.
160    // Output is the coefficients of the three linear functionals K, L, & M which
161    // represent the implicit form of the cubic as f(x,y,w) = K^3 - LM. The w term
162    // will always be 1. The output is stored in the array klm, where the values are:
163    // K = (klm[0], klm[1], klm[2])
164    // L = (klm[3], klm[4], klm[5])
165    // M = (klm[6], klm[7], klm[8])
166    //
167    // Notice that the klm lines are calculated in the same space as the input control points.
168    // If you transform the points the lines will also need to be transformed. This can be done
169    // by mapping the lines with the inverse-transpose of the matrix used to map the points.
170    void getCubicKLM(const SkPoint p[4], SkScalar klm[9]);
171};
172#endif
173