src/pathops/SkPathOpsCubic.h

/*
 * Copyright 2012 Google Inc.
 *
 * Use of this source code is governed by a BSD-style license that can be
 * found in the LICENSE file.
 */

#ifndef SkPathOpsCubic_DEFINED
#define SkPathOpsCubic_DEFINED

#include "SkPath.h"
#include "SkPathOpsPoint.h"

struct SkDCubicPair {
    const SkDCubic& first() const { return (const SkDCubic&) pts[0]; }
    const SkDCubic& second() const { return (const SkDCubic&) pts[3]; }
    SkDPoint pts[7];
};

struct SkDCubic {
    static const int kPointCount = 4;
    static const int kPointLast = kPointCount - 1;
    static const int kMaxIntersections = 9;

    enum SearchAxis {
        kXAxis,
        kYAxis
    };

    enum CubicType {
        kUnsplit_SkDCubicType,
        kSplitAtLoop_SkDCubicType,
        kSplitAtInflection_SkDCubicType,
        kSplitAtMaxCurvature_SkDCubicType,
    };

    bool collapsed() const {
        return fPts[0].approximatelyEqual(fPts[1]) && fPts[0].approximatelyEqual(fPts[2])
                && fPts[0].approximatelyEqual(fPts[3]);
    }

    bool controlsInside() const {
        SkDVector v01 = fPts[0] - fPts[1];
        SkDVector v02 = fPts[0] - fPts[2];
        SkDVector v03 = fPts[0] - fPts[3];
        SkDVector v13 = fPts[1] - fPts[3];
        SkDVector v23 = fPts[2] - fPts[3];
        return v03.dot(v01) > 0 && v03.dot(v02) > 0 && v03.dot(v13) > 0 && v03.dot(v23) > 0;
    }

    static bool IsCubic() { return true; }

    const SkDPoint& operator[](int n) const { SkASSERT(n >= 0 && n < kPointCount); return fPts[n]; }
    SkDPoint& operator[](int n) { SkASSERT(n >= 0 && n < kPointCount); return fPts[n]; }

    void align(int endIndex, int ctrlIndex, SkDPoint* dstPt) const;
    double binarySearch(double min, double max, double axisIntercept, SearchAxis xAxis) const;
    double calcPrecision() const;
    SkDCubicPair chopAt(double t) const;
    static void Coefficients(const double* cubic, double* A, double* B, double* C, double* D);
    static bool ComplexBreak(const SkPoint pts[4], SkScalar* t, CubicType* cubicType);
    int convexHull(char order[kPointCount]) const;

    void debugInit() {
        sk_bzero(fPts, sizeof(fPts));
    }

    void dump() const;  // callable from the debugger when the implementation code is linked in
    void dumpID(int id) const;
    void dumpInner() const;
    SkDVector dxdyAtT(double t) const;
    bool endsAreExtremaInXOrY() const;
    static int FindExtrema(const double src[], double tValue[2]);
    int findInflections(double tValues[2]) const;

    static int FindInflections(const SkPoint a[kPointCount], double tValues[2]) {
        SkDCubic cubic;
        return cubic.set(a).findInflections(tValues);
    }

    int findMaxCurvature(double tValues[]) const;
    bool hullIntersects(const SkDCubic& c2, bool* isLinear) const;
    bool hullIntersects(const SkDConic& c, bool* isLinear) const;
    bool hullIntersects(const SkDQuad& c2, bool* isLinear) const;
    bool hullIntersects(const SkDPoint* pts, int ptCount, bool* isLinear) const;
    bool isLinear(int startIndex, int endIndex) const;
    bool monotonicInX() const;
    bool monotonicInY() const;
    void otherPts(int index, const SkDPoint* o1Pts[kPointCount - 1]) const;
    SkDPoint ptAtT(double t) const;
    static int RootsReal(double A, double B, double C, double D, double t[3]);
    static int RootsValidT(const double A, const double B, const double C, double D, double s[3]);

    int searchRoots(double extremes[6], int extrema, double axisIntercept,
                    SearchAxis xAxis, double* validRoots) const;

    /**
     *  Return the number of valid roots (0 < root < 1) for this cubic intersecting the
     *  specified horizontal line.
     */
    int horizontalIntersect(double yIntercept, double roots[3]) const;
    /**
     *  Return the number of valid roots (0 < root < 1) for this cubic intersecting the
     *  specified vertical line.
     */
    int verticalIntersect(double xIntercept, double roots[3]) const;

    const SkDCubic& set(const SkPoint pts[kPointCount]) {
        fPts[0] = pts[0];
        fPts[1] = pts[1];
        fPts[2] = pts[2];
        fPts[3] = pts[3];
        return *this;
    }

    SkDCubic subDivide(double t1, double t2) const;

    static SkDCubic SubDivide(const SkPoint a[kPointCount], double t1, double t2) {
        SkDCubic cubic;
        return cubic.set(a).subDivide(t1, t2);
    }

    void subDivide(const SkDPoint& a, const SkDPoint& d, double t1, double t2, SkDPoint p[2]) const;

    static void SubDivide(const SkPoint pts[kPointCount], const SkDPoint& a, const SkDPoint& d, double t1,
                          double t2, SkDPoint p[2]) {
        SkDCubic cubic;
        cubic.set(pts).subDivide(a, d, t1, t2, p);
    }

    double top(const SkDCubic& dCurve, double startT, double endT, SkDPoint*topPt) const;
    SkDQuad toQuad() const;

    static const int gPrecisionUnit;

    SkDPoint fPts[kPointCount];
};

/* Given the set [0, 1, 2, 3], and two of the four members, compute an XOR mask
   that computes the other two. Note that:

   one ^ two == 3 for (0, 3), (1, 2)
   one ^ two <  3 for (0, 1), (0, 2), (1, 3), (2, 3)
   3 - (one ^ two) is either 0, 1, or 2
   1 >> (3 - (one ^ two)) is either 0 or 1
thus:
   returned == 2 for (0, 3), (1, 2)
   returned == 3 for (0, 1), (0, 2), (1, 3), (2, 3)
given that:
   (0, 3) ^ 2 -> (2, 1)  (1, 2) ^ 2 -> (3, 0)
   (0, 1) ^ 3 -> (3, 2)  (0, 2) ^ 3 -> (3, 1)  (1, 3) ^ 3 -> (2, 0)  (2, 3) ^ 3 -> (1, 0)
*/
inline int other_two(int one, int two) {
    return 1 >> (3 - (one ^ two)) ^ 3;
}

#endif