src/core/SkGeometry.h - skia - Git at Google


 /*
  * Copyright 2006 The Android Open Source Project
  *
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */


 #ifndef SkGeometry_DEFINED
 #define SkGeometry_DEFINED

 #include "SkMatrix.h"

 /** An XRay is a half-line that runs from the specific point/origin to
     +infinity in the X direction. e.g. XRay(3,5) is the half-line
     (3,5)....(infinity, 5)
  */
 typedef SkPoint SkXRay;

 /** Given a line segment from pts[0] to pts[1], and an xray, return true if
     they intersect. Optional outgoing "ambiguous" argument indicates
     whether the answer is ambiguous because the query occurred exactly at
     one of the endpoints' y coordinates, indicating that another query y
     coordinate is preferred for robustness.
 */
 bool SkXRayCrossesLine(const SkXRay& pt, const SkPoint pts[2],
                        bool* ambiguous = NULL);

 /** Given a quadratic equation Ax^2 + Bx + C = 0, return 0, 1, 2 roots for the
     equation.
 */
 int SkFindUnitQuadRoots(SkScalar A, SkScalar B, SkScalar C, SkScalar roots[2]);

 ///////////////////////////////////////////////////////////////////////////////

 /** Set pt to the point on the src quadratic specified by t. t must be
     0 <= t <= 1.0
 */
 void SkEvalQuadAt(const SkPoint src[3], SkScalar t, SkPoint* pt,
                   SkVector* tangent = NULL);
 void SkEvalQuadAtHalf(const SkPoint src[3], SkPoint* pt,
                       SkVector* tangent = NULL);

 /** Given a src quadratic bezier, chop it at the specified t value,
     where 0 < t < 1, and return the two new quadratics in dst:
     dst[0..2] and dst[2..4]
 */
 void SkChopQuadAt(const SkPoint src[3], SkPoint dst[5], SkScalar t);

 /** Given a src quadratic bezier, chop it at the specified t == 1/2,
     The new quads are returned in dst[0..2] and dst[2..4]
 */
 void SkChopQuadAtHalf(const SkPoint src[3], SkPoint dst[5]);

 /** Given the 3 coefficients for a quadratic bezier (either X or Y values), look
     for extrema, and return the number of t-values that are found that represent
     these extrema. If the quadratic has no extrema betwee (0..1) exclusive, the
     function returns 0.
     Returned count      tValues[]
     0                   ignored
     1                   0 < tValues[0] < 1
 */
 int SkFindQuadExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar tValues[1]);

 /** Given 3 points on a quadratic bezier, chop it into 1, 2 beziers such that
     the resulting beziers are monotonic in Y. This is called by the scan converter.
     Depending on what is returned, dst[] is treated as follows
     0   dst[0..2] is the original quad
     1   dst[0..2] and dst[2..4] are the two new quads
 */
 int SkChopQuadAtYExtrema(const SkPoint src[3], SkPoint dst[5]);
 int SkChopQuadAtXExtrema(const SkPoint src[3], SkPoint dst[5]);

 /** Given 3 points on a quadratic bezier, if the point of maximum
     curvature exists on the segment, returns the t value for this
     point along the curve. Otherwise it will return a value of 0.
 */
 float SkFindQuadMaxCurvature(const SkPoint src[3]);

 /** Given 3 points on a quadratic bezier, divide it into 2 quadratics
     if the point of maximum curvature exists on the quad segment.
     Depending on what is returned, dst[] is treated as follows
     1   dst[0..2] is the original quad
     2   dst[0..2] and dst[2..4] are the two new quads
     If dst == null, it is ignored and only the count is returned.
 */
 int SkChopQuadAtMaxCurvature(const SkPoint src[3], SkPoint dst[5]);

 /** Given 3 points on a quadratic bezier, use degree elevation to
     convert it into the cubic fitting the same curve. The new cubic
     curve is returned in dst[0..3].
 */
 SK_API void SkConvertQuadToCubic(const SkPoint src[3], SkPoint dst[4]);

 ///////////////////////////////////////////////////////////////////////////////

 /** Convert from parametric from (pts) to polynomial coefficients
     coeff[0]*T^3 + coeff[1]*T^2 + coeff[2]*T + coeff[3]
 */
 void SkGetCubicCoeff(const SkPoint pts[4], SkScalar cx[4], SkScalar cy[4]);

 /** Set pt to the point on the src cubic specified by t. t must be
     0 <= t <= 1.0
 */
 void SkEvalCubicAt(const SkPoint src[4], SkScalar t, SkPoint* locOrNull,
                    SkVector* tangentOrNull, SkVector* curvatureOrNull);

 /** Given a src cubic bezier, chop it at the specified t value,
     where 0 < t < 1, and return the two new cubics in dst:
     dst[0..3] and dst[3..6]
 */
 void SkChopCubicAt(const SkPoint src[4], SkPoint dst[7], SkScalar t);
 /** Given a src cubic bezier, chop it at the specified t values,
     where 0 < t < 1, and return the new cubics in dst:
     dst[0..3],dst[3..6],...,dst[3*t_count..3*(t_count+1)]
 */
 void SkChopCubicAt(const SkPoint src[4], SkPoint dst[], const SkScalar t[],
                    int t_count);

 /** Given a src cubic bezier, chop it at the specified t == 1/2,
     The new cubics are returned in dst[0..3] and dst[3..6]
 */
 void SkChopCubicAtHalf(const SkPoint src[4], SkPoint dst[7]);

 /** Given the 4 coefficients for a cubic bezier (either X or Y values), look
     for extrema, and return the number of t-values that are found that represent
     these extrema. If the cubic has no extrema betwee (0..1) exclusive, the
     function returns 0.
     Returned count      tValues[]
     0                   ignored
     1                   0 < tValues[0] < 1
     2                   0 < tValues[0] < tValues[1] < 1
 */
 int SkFindCubicExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar d,
                        SkScalar tValues[2]);

 /** Given 4 points on a cubic bezier, chop it into 1, 2, 3 beziers such that
     the resulting beziers are monotonic in Y. This is called by the scan converter.
     Depending on what is returned, dst[] is treated as follows
     0   dst[0..3] is the original cubic
     1   dst[0..3] and dst[3..6] are the two new cubics
     2   dst[0..3], dst[3..6], dst[6..9] are the three new cubics
     If dst == null, it is ignored and only the count is returned.
 */
 int SkChopCubicAtYExtrema(const SkPoint src[4], SkPoint dst[10]);
 int SkChopCubicAtXExtrema(const SkPoint src[4], SkPoint dst[10]);

 /** Given a cubic bezier, return 0, 1, or 2 t-values that represent the
     inflection points.
 */
 int SkFindCubicInflections(const SkPoint src[4], SkScalar tValues[2]);

 /** Return 1 for no chop, 2 for having chopped the cubic at a single
     inflection point, 3 for having chopped at 2 inflection points.
     dst will hold the resulting 1, 2, or 3 cubics.
 */
 int SkChopCubicAtInflections(const SkPoint src[4], SkPoint dst[10]);

 int SkFindCubicMaxCurvature(const SkPoint src[4], SkScalar tValues[3]);
 int SkChopCubicAtMaxCurvature(const SkPoint src[4], SkPoint dst[13],
                               SkScalar tValues[3] = NULL);

 /** Given a monotonic cubic bezier, determine whether an xray intersects the
     cubic.
     By definition the cubic is open at the starting point; in other
     words, if pt.fY is equivalent to cubic[0].fY, and pt.fX is to the
     left of the curve, the line is not considered to cross the curve,
     but if it is equal to cubic[3].fY then it is considered to
     cross.
     Optional outgoing "ambiguous" argument indicates whether the answer is
     ambiguous because the query occurred exactly at one of the endpoints' y
     coordinates, indicating that another query y coordinate is preferred
     for robustness.
  */
 bool SkXRayCrossesMonotonicCubic(const SkXRay& pt, const SkPoint cubic[4],
                                  bool* ambiguous = NULL);

 /** Given an arbitrary cubic bezier, return the number of times an xray crosses
     the cubic. Valid return values are [0..3]
     By definition the cubic is open at the starting point; in other
     words, if pt.fY is equivalent to cubic[0].fY, and pt.fX is to the
     left of the curve, the line is not considered to cross the curve,
     but if it is equal to cubic[3].fY then it is considered to
     cross.
     Optional outgoing "ambiguous" argument indicates whether the answer is
     ambiguous because the query occurred exactly at one of the endpoints' y
     coordinates or at a tangent point, indicating that another query y
     coordinate is preferred for robustness.
  */
 int SkNumXRayCrossingsForCubic(const SkXRay& pt, const SkPoint cubic[4],
                                bool* ambiguous = NULL);

 ///////////////////////////////////////////////////////////////////////////////

 enum SkRotationDirection {
     kCW_SkRotationDirection,
     kCCW_SkRotationDirection
 };

 /** Maximum number of points needed in the quadPoints[] parameter for
     SkBuildQuadArc()
 */
 #define kSkBuildQuadArcStorage  17

 /** Given 2 unit vectors and a rotation direction, fill out the specified
     array of points with quadratic segments. Return is the number of points
     written to, which will be { 0, 3, 5, 7, ... kSkBuildQuadArcStorage }

     matrix, if not null, is appled to the points before they are returned.
 */
 int SkBuildQuadArc(const SkVector& unitStart, const SkVector& unitStop,
                    SkRotationDirection, const SkMatrix*, SkPoint quadPoints[]);

 // experimental
 struct SkConic {
     SkPoint  fPts[3];
     SkScalar fW;

     void set(const SkPoint pts[3], SkScalar w) {
         memcpy(fPts, pts, 3 * sizeof(SkPoint));
         fW = w;
     }

     /**
      *  Given a t-value [0...1] return its position and/or tangent.
      *  If pos is not null, return its position at the t-value.
      *  If tangent is not null, return its tangent at the t-value. NOTE the
      *  tangent value's length is arbitrary, and only its direction should
      *  be used.
      */
     void evalAt(SkScalar t, SkPoint* pos, SkVector* tangent = NULL) const;
     void chopAt(SkScalar t, SkConic dst[2]) const;
     void chop(SkConic dst[2]) const;

     void computeAsQuadError(SkVector* err) const;
     bool asQuadTol(SkScalar tol) const;

     /**
      *  return the power-of-2 number of quads needed to approximate this conic
      *  with a sequence of quads. Will be >= 0.
      */
     int computeQuadPOW2(SkScalar tol) const;

     /**
      *  Chop this conic into N quads, stored continguously in pts[], where
      *  N = 1 << pow2. The amount of storage needed is (1 + 2 * N)
      */
     int chopIntoQuadsPOW2(SkPoint pts[], int pow2) const;

     bool findXExtrema(SkScalar* t) const;
     bool findYExtrema(SkScalar* t) const;
     bool chopAtXExtrema(SkConic dst[2]) const;
     bool chopAtYExtrema(SkConic dst[2]) const;

     void computeTightBounds(SkRect* bounds) const;
     void computeFastBounds(SkRect* bounds) const;

     /** Find the parameter value where the conic takes on its maximum curvature.
      *
      *  @param t   output scalar for max curvature.  Will be unchanged if
      *             max curvature outside 0..1 range.
      *
      *  @return  true if max curvature found inside 0..1 range, false otherwise
      */
     bool findMaxCurvature(SkScalar* t) const;
 };

 #include "SkTemplates.h"

 /**
  *  Help class to allocate storage for approximating a conic with N quads.
  */
 class SkAutoConicToQuads {
 public:
     SkAutoConicToQuads() : fQuadCount(0) {}

     /**
      *  Given a conic and a tolerance, return the array of points for the
      *  approximating quad(s). Call countQuads() to know the number of quads
      *  represented in these points.
      *
      *  The quads are allocated to share end-points. e.g. if there are 4 quads,
      *  there will be 9 points allocated as follows
      *      quad[0] == pts[0..2]
      *      quad[1] == pts[2..4]
      *      quad[2] == pts[4..6]
      *      quad[3] == pts[6..8]
      */
     const SkPoint* computeQuads(const SkConic& conic, SkScalar tol) {
         int pow2 = conic.computeQuadPOW2(tol);
         fQuadCount = 1 << pow2;
         SkPoint* pts = fStorage.reset(1 + 2 * fQuadCount);
         conic.chopIntoQuadsPOW2(pts, pow2);
         return pts;
     }

     const SkPoint* computeQuads(const SkPoint pts[3], SkScalar weight,
                                 SkScalar tol) {
         SkConic conic;
         conic.set(pts, weight);
         return computeQuads(conic, tol);
     }

     int countQuads() const { return fQuadCount; }

 private:
     enum {
         kQuadCount = 8, // should handle most conics
         kPointCount = 1 + 2 * kQuadCount,
     };
     SkAutoSTMalloc<kPointCount, SkPoint> fStorage;
     int fQuadCount; // #quads for current usage
 };

 #endif

	/*
	* Copyright 2006 The Android Open Source Project
	*
	* Use of this source code is governed by a BSD-style license that can be
	* found in the LICENSE file.
	*/


	#ifndef SkGeometry_DEFINED
	#define SkGeometry_DEFINED

	#include "SkMatrix.h"

	/** An XRay is a half-line that runs from the specific point/origin to
	+infinity in the X direction. e.g. XRay(3,5) is the half-line
	(3,5)....(infinity, 5)
	*/
	typedef SkPoint SkXRay;

	/** Given a line segment from pts[0] to pts[1], and an xray, return true if
	they intersect. Optional outgoing "ambiguous" argument indicates
	whether the answer is ambiguous because the query occurred exactly at
	one of the endpoints' y coordinates, indicating that another query y
	coordinate is preferred for robustness.
	*/
	bool SkXRayCrossesLine(const SkXRay& pt, const SkPoint pts[2],
	bool* ambiguous = NULL);

	/** Given a quadratic equation Ax^2 + Bx + C = 0, return 0, 1, 2 roots for the
	equation.
	*/
	int SkFindUnitQuadRoots(SkScalar A, SkScalar B, SkScalar C, SkScalar roots[2]);

	///////////////////////////////////////////////////////////////////////////////

	/** Set pt to the point on the src quadratic specified by t. t must be
	0 <= t <= 1.0
	*/
	void SkEvalQuadAt(const SkPoint src[3], SkScalar t, SkPoint* pt,
	SkVector* tangent = NULL);
	void SkEvalQuadAtHalf(const SkPoint src[3], SkPoint* pt,
	SkVector* tangent = NULL);

	/** Given a src quadratic bezier, chop it at the specified t value,
	where 0 < t < 1, and return the two new quadratics in dst:
	dst[0..2] and dst[2..4]
	*/
	void SkChopQuadAt(const SkPoint src[3], SkPoint dst[5], SkScalar t);

	/** Given a src quadratic bezier, chop it at the specified t == 1/2,
	The new quads are returned in dst[0..2] and dst[2..4]
	*/
	void SkChopQuadAtHalf(const SkPoint src[3], SkPoint dst[5]);

	/** Given the 3 coefficients for a quadratic bezier (either X or Y values), look
	for extrema, and return the number of t-values that are found that represent
	these extrema. If the quadratic has no extrema betwee (0..1) exclusive, the
	function returns 0.
	Returned count tValues[]
	0 ignored
	1 0 < tValues[0] < 1
	*/
	int SkFindQuadExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar tValues[1]);

	/** Given 3 points on a quadratic bezier, chop it into 1, 2 beziers such that
	the resulting beziers are monotonic in Y. This is called by the scan converter.
	Depending on what is returned, dst[] is treated as follows
	0 dst[0..2] is the original quad
	1 dst[0..2] and dst[2..4] are the two new quads
	*/
	int SkChopQuadAtYExtrema(const SkPoint src[3], SkPoint dst[5]);
	int SkChopQuadAtXExtrema(const SkPoint src[3], SkPoint dst[5]);

	/** Given 3 points on a quadratic bezier, if the point of maximum
	curvature exists on the segment, returns the t value for this
	point along the curve. Otherwise it will return a value of 0.
	*/
	float SkFindQuadMaxCurvature(const SkPoint src[3]);

	/** Given 3 points on a quadratic bezier, divide it into 2 quadratics
	if the point of maximum curvature exists on the quad segment.
	Depending on what is returned, dst[] is treated as follows
	1 dst[0..2] is the original quad
	2 dst[0..2] and dst[2..4] are the two new quads
	If dst == null, it is ignored and only the count is returned.
	*/
	int SkChopQuadAtMaxCurvature(const SkPoint src[3], SkPoint dst[5]);

	/** Given 3 points on a quadratic bezier, use degree elevation to
	convert it into the cubic fitting the same curve. The new cubic
	curve is returned in dst[0..3].
	*/
	SK_API void SkConvertQuadToCubic(const SkPoint src[3], SkPoint dst[4]);

	///////////////////////////////////////////////////////////////////////////////

	/** Convert from parametric from (pts) to polynomial coefficients
	coeff[0]T^3 + coeff[1]T^2 + coeff[2]*T + coeff[3]
	*/
	void SkGetCubicCoeff(const SkPoint pts[4], SkScalar cx[4], SkScalar cy[4]);

	/** Set pt to the point on the src cubic specified by t. t must be
	0 <= t <= 1.0
	*/
	void SkEvalCubicAt(const SkPoint src[4], SkScalar t, SkPoint* locOrNull,
	SkVector* tangentOrNull, SkVector* curvatureOrNull);

	/** Given a src cubic bezier, chop it at the specified t value,
	where 0 < t < 1, and return the two new cubics in dst:
	dst[0..3] and dst[3..6]
	*/
	void SkChopCubicAt(const SkPoint src[4], SkPoint dst[7], SkScalar t);
	/** Given a src cubic bezier, chop it at the specified t values,
	where 0 < t < 1, and return the new cubics in dst:
	dst[0..3],dst[3..6],...,dst[3t_count..3(t_count+1)]
	*/
	void SkChopCubicAt(const SkPoint src[4], SkPoint dst[], const SkScalar t[],
	int t_count);

	/** Given a src cubic bezier, chop it at the specified t == 1/2,
	The new cubics are returned in dst[0..3] and dst[3..6]
	*/
	void SkChopCubicAtHalf(const SkPoint src[4], SkPoint dst[7]);

	/** Given the 4 coefficients for a cubic bezier (either X or Y values), look
	for extrema, and return the number of t-values that are found that represent
	these extrema. If the cubic has no extrema betwee (0..1) exclusive, the
	function returns 0.
	Returned count tValues[]
	0 ignored
	1 0 < tValues[0] < 1
	2 0 < tValues[0] < tValues[1] < 1
	*/
	int SkFindCubicExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar d,
	SkScalar tValues[2]);

	/** Given 4 points on a cubic bezier, chop it into 1, 2, 3 beziers such that
	the resulting beziers are monotonic in Y. This is called by the scan converter.
	Depending on what is returned, dst[] is treated as follows
	0 dst[0..3] is the original cubic
	1 dst[0..3] and dst[3..6] are the two new cubics
	2 dst[0..3], dst[3..6], dst[6..9] are the three new cubics
	If dst == null, it is ignored and only the count is returned.
	*/
	int SkChopCubicAtYExtrema(const SkPoint src[4], SkPoint dst[10]);
	int SkChopCubicAtXExtrema(const SkPoint src[4], SkPoint dst[10]);

	/** Given a cubic bezier, return 0, 1, or 2 t-values that represent the
	inflection points.
	*/
	int SkFindCubicInflections(const SkPoint src[4], SkScalar tValues[2]);

	/** Return 1 for no chop, 2 for having chopped the cubic at a single
	inflection point, 3 for having chopped at 2 inflection points.
	dst will hold the resulting 1, 2, or 3 cubics.
	*/
	int SkChopCubicAtInflections(const SkPoint src[4], SkPoint dst[10]);

	int SkFindCubicMaxCurvature(const SkPoint src[4], SkScalar tValues[3]);
	int SkChopCubicAtMaxCurvature(const SkPoint src[4], SkPoint dst[13],
	SkScalar tValues[3] = NULL);

	/** Given a monotonic cubic bezier, determine whether an xray intersects the
	cubic.
	By definition the cubic is open at the starting point; in other
	words, if pt.fY is equivalent to cubic[0].fY, and pt.fX is to the
	left of the curve, the line is not considered to cross the curve,
	but if it is equal to cubic[3].fY then it is considered to
	cross.
	Optional outgoing "ambiguous" argument indicates whether the answer is
	ambiguous because the query occurred exactly at one of the endpoints' y
	coordinates, indicating that another query y coordinate is preferred
	for robustness.
	*/
	bool SkXRayCrossesMonotonicCubic(const SkXRay& pt, const SkPoint cubic[4],
	bool* ambiguous = NULL);

	/** Given an arbitrary cubic bezier, return the number of times an xray crosses
	the cubic. Valid return values are [0..3]
	By definition the cubic is open at the starting point; in other
	words, if pt.fY is equivalent to cubic[0].fY, and pt.fX is to the
	left of the curve, the line is not considered to cross the curve,
	but if it is equal to cubic[3].fY then it is considered to
	cross.
	Optional outgoing "ambiguous" argument indicates whether the answer is
	ambiguous because the query occurred exactly at one of the endpoints' y
	coordinates or at a tangent point, indicating that another query y
	coordinate is preferred for robustness.
	*/
	int SkNumXRayCrossingsForCubic(const SkXRay& pt, const SkPoint cubic[4],
	bool* ambiguous = NULL);

	///////////////////////////////////////////////////////////////////////////////

	enum SkRotationDirection {
	kCW_SkRotationDirection,
	kCCW_SkRotationDirection
	};

	/** Maximum number of points needed in the quadPoints[] parameter for
	SkBuildQuadArc()
	*/
	#define kSkBuildQuadArcStorage 17

	/** Given 2 unit vectors and a rotation direction, fill out the specified
	array of points with quadratic segments. Return is the number of points
	written to, which will be { 0, 3, 5, 7, ... kSkBuildQuadArcStorage }

	matrix, if not null, is appled to the points before they are returned.
	*/
	int SkBuildQuadArc(const SkVector& unitStart, const SkVector& unitStop,
	SkRotationDirection, const SkMatrix*, SkPoint quadPoints[]);

	// experimental
	struct SkConic {
	SkPoint fPts[3];
	SkScalar fW;

	void set(const SkPoint pts[3], SkScalar w) {
	memcpy(fPts, pts, 3 * sizeof(SkPoint));
	fW = w;
	}

	/**
	* Given a t-value [0...1] return its position and/or tangent.
	* If pos is not null, return its position at the t-value.
	* If tangent is not null, return its tangent at the t-value. NOTE the
	* tangent value's length is arbitrary, and only its direction should
	* be used.
	*/
	void evalAt(SkScalar t, SkPoint* pos, SkVector* tangent = NULL) const;
	void chopAt(SkScalar t, SkConic dst[2]) const;
	void chop(SkConic dst[2]) const;

	void computeAsQuadError(SkVector* err) const;
	bool asQuadTol(SkScalar tol) const;

	/**
	* return the power-of-2 number of quads needed to approximate this conic
	* with a sequence of quads. Will be >= 0.
	*/
	int computeQuadPOW2(SkScalar tol) const;

	/**
	* Chop this conic into N quads, stored continguously in pts[], where
	* N = 1 << pow2. The amount of storage needed is (1 + 2 * N)
	*/
	int chopIntoQuadsPOW2(SkPoint pts[], int pow2) const;

	bool findXExtrema(SkScalar* t) const;
	bool findYExtrema(SkScalar* t) const;
	bool chopAtXExtrema(SkConic dst[2]) const;
	bool chopAtYExtrema(SkConic dst[2]) const;

	void computeTightBounds(SkRect* bounds) const;
	void computeFastBounds(SkRect* bounds) const;

	/** Find the parameter value where the conic takes on its maximum curvature.
	*
	* @param t output scalar for max curvature. Will be unchanged if
	* max curvature outside 0..1 range.
	*
	* @return true if max curvature found inside 0..1 range, false otherwise
	*/
	bool findMaxCurvature(SkScalar* t) const;
	};

	#include "SkTemplates.h"

	/**
	* Help class to allocate storage for approximating a conic with N quads.
	*/
	class SkAutoConicToQuads {
	public:
	SkAutoConicToQuads() : fQuadCount(0) {}

	/**
	* Given a conic and a tolerance, return the array of points for the
	* approximating quad(s). Call countQuads() to know the number of quads
	* represented in these points.
	*
	* The quads are allocated to share end-points. e.g. if there are 4 quads,
	* there will be 9 points allocated as follows
	* quad[0] == pts[0..2]
	* quad[1] == pts[2..4]
	* quad[2] == pts[4..6]
	* quad[3] == pts[6..8]
	*/
	const SkPoint* computeQuads(const SkConic& conic, SkScalar tol) {
	int pow2 = conic.computeQuadPOW2(tol);
	fQuadCount = 1 << pow2;
	SkPoint* pts = fStorage.reset(1 + 2 * fQuadCount);
	conic.chopIntoQuadsPOW2(pts, pow2);
	return pts;
	}

	const SkPoint* computeQuads(const SkPoint pts[3], SkScalar weight,
	SkScalar tol) {
	SkConic conic;
	conic.set(pts, weight);
	return computeQuads(conic, tol);
	}

	int countQuads() const { return fQuadCount; }

	private:
	enum {
	kQuadCount = 8, // should handle most conics
	kPointCount = 1 + 2 * kQuadCount,
	};
	SkAutoSTMalloc<kPointCount, SkPoint> fStorage;
	int fQuadCount; // #quads for current usage
	};

	#endif