michael@0: 
michael@0: /*
michael@0:  * Copyright 2006 The Android Open Source Project
michael@0:  *
michael@0:  * Use of this source code is governed by a BSD-style license that can be
michael@0:  * found in the LICENSE file.
michael@0:  */
michael@0: 
michael@0: 
michael@0: #ifndef SkGeometry_DEFINED
michael@0: #define SkGeometry_DEFINED
michael@0: 
michael@0: #include "SkMatrix.h"
michael@0: 
michael@0: /** An XRay is a half-line that runs from the specific point/origin to
michael@0:     +infinity in the X direction. e.g. XRay(3,5) is the half-line
michael@0:     (3,5)....(infinity, 5)
michael@0:  */
michael@0: typedef SkPoint SkXRay;
michael@0: 
michael@0: /** Given a line segment from pts[0] to pts[1], and an xray, return true if
michael@0:     they intersect. Optional outgoing "ambiguous" argument indicates
michael@0:     whether the answer is ambiguous because the query occurred exactly at
michael@0:     one of the endpoints' y coordinates, indicating that another query y
michael@0:     coordinate is preferred for robustness.
michael@0: */
michael@0: bool SkXRayCrossesLine(const SkXRay& pt, const SkPoint pts[2],
michael@0:                        bool* ambiguous = NULL);
michael@0: 
michael@0: /** Given a quadratic equation Ax^2 + Bx + C = 0, return 0, 1, 2 roots for the
michael@0:     equation.
michael@0: */
michael@0: int SkFindUnitQuadRoots(SkScalar A, SkScalar B, SkScalar C, SkScalar roots[2]);
michael@0: 
michael@0: ///////////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: /** Set pt to the point on the src quadratic specified by t. t must be
michael@0:     0 <= t <= 1.0
michael@0: */
michael@0: void SkEvalQuadAt(const SkPoint src[3], SkScalar t, SkPoint* pt,
michael@0:                   SkVector* tangent = NULL);
michael@0: void SkEvalQuadAtHalf(const SkPoint src[3], SkPoint* pt,
michael@0:                       SkVector* tangent = NULL);
michael@0: 
michael@0: /** Given a src quadratic bezier, chop it at the specified t value,
michael@0:     where 0 < t < 1, and return the two new quadratics in dst:
michael@0:     dst[0..2] and dst[2..4]
michael@0: */
michael@0: void SkChopQuadAt(const SkPoint src[3], SkPoint dst[5], SkScalar t);
michael@0: 
michael@0: /** Given a src quadratic bezier, chop it at the specified t == 1/2,
michael@0:     The new quads are returned in dst[0..2] and dst[2..4]
michael@0: */
michael@0: void SkChopQuadAtHalf(const SkPoint src[3], SkPoint dst[5]);
michael@0: 
michael@0: /** Given the 3 coefficients for a quadratic bezier (either X or Y values), look
michael@0:     for extrema, and return the number of t-values that are found that represent
michael@0:     these extrema. If the quadratic has no extrema betwee (0..1) exclusive, the
michael@0:     function returns 0.
michael@0:     Returned count      tValues[]
michael@0:     0                   ignored
michael@0:     1                   0 < tValues[0] < 1
michael@0: */
michael@0: int SkFindQuadExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar tValues[1]);
michael@0: 
michael@0: /** Given 3 points on a quadratic bezier, chop it into 1, 2 beziers such that
michael@0:     the resulting beziers are monotonic in Y. This is called by the scan converter.
michael@0:     Depending on what is returned, dst[] is treated as follows
michael@0:     0   dst[0..2] is the original quad
michael@0:     1   dst[0..2] and dst[2..4] are the two new quads
michael@0: */
michael@0: int SkChopQuadAtYExtrema(const SkPoint src[3], SkPoint dst[5]);
michael@0: int SkChopQuadAtXExtrema(const SkPoint src[3], SkPoint dst[5]);
michael@0: 
michael@0: /** Given 3 points on a quadratic bezier, if the point of maximum
michael@0:     curvature exists on the segment, returns the t value for this
michael@0:     point along the curve. Otherwise it will return a value of 0.
michael@0: */
michael@0: float SkFindQuadMaxCurvature(const SkPoint src[3]);
michael@0: 
michael@0: /** Given 3 points on a quadratic bezier, divide it into 2 quadratics
michael@0:     if the point of maximum curvature exists on the quad segment.
michael@0:     Depending on what is returned, dst[] is treated as follows
michael@0:     1   dst[0..2] is the original quad
michael@0:     2   dst[0..2] and dst[2..4] are the two new quads
michael@0:     If dst == null, it is ignored and only the count is returned.
michael@0: */
michael@0: int SkChopQuadAtMaxCurvature(const SkPoint src[3], SkPoint dst[5]);
michael@0: 
michael@0: /** Given 3 points on a quadratic bezier, use degree elevation to
michael@0:     convert it into the cubic fitting the same curve. The new cubic
michael@0:     curve is returned in dst[0..3].
michael@0: */
michael@0: SK_API void SkConvertQuadToCubic(const SkPoint src[3], SkPoint dst[4]);
michael@0: 
michael@0: ///////////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: /** Convert from parametric from (pts) to polynomial coefficients
michael@0:     coeff[0]*T^3 + coeff[1]*T^2 + coeff[2]*T + coeff[3]
michael@0: */
michael@0: void SkGetCubicCoeff(const SkPoint pts[4], SkScalar cx[4], SkScalar cy[4]);
michael@0: 
michael@0: /** Set pt to the point on the src cubic specified by t. t must be
michael@0:     0 <= t <= 1.0
michael@0: */
michael@0: void SkEvalCubicAt(const SkPoint src[4], SkScalar t, SkPoint* locOrNull,
michael@0:                    SkVector* tangentOrNull, SkVector* curvatureOrNull);
michael@0: 
michael@0: /** Given a src cubic bezier, chop it at the specified t value,
michael@0:     where 0 < t < 1, and return the two new cubics in dst:
michael@0:     dst[0..3] and dst[3..6]
michael@0: */
michael@0: void SkChopCubicAt(const SkPoint src[4], SkPoint dst[7], SkScalar t);
michael@0: /** Given a src cubic bezier, chop it at the specified t values,
michael@0:     where 0 < t < 1, and return the new cubics in dst:
michael@0:     dst[0..3],dst[3..6],...,dst[3*t_count..3*(t_count+1)]
michael@0: */
michael@0: void SkChopCubicAt(const SkPoint src[4], SkPoint dst[], const SkScalar t[],
michael@0:                    int t_count);
michael@0: 
michael@0: /** Given a src cubic bezier, chop it at the specified t == 1/2,
michael@0:     The new cubics are returned in dst[0..3] and dst[3..6]
michael@0: */
michael@0: void SkChopCubicAtHalf(const SkPoint src[4], SkPoint dst[7]);
michael@0: 
michael@0: /** Given the 4 coefficients for a cubic bezier (either X or Y values), look
michael@0:     for extrema, and return the number of t-values that are found that represent
michael@0:     these extrema. If the cubic has no extrema betwee (0..1) exclusive, the
michael@0:     function returns 0.
michael@0:     Returned count      tValues[]
michael@0:     0                   ignored
michael@0:     1                   0 < tValues[0] < 1
michael@0:     2                   0 < tValues[0] < tValues[1] < 1
michael@0: */
michael@0: int SkFindCubicExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar d,
michael@0:                        SkScalar tValues[2]);
michael@0: 
michael@0: /** Given 4 points on a cubic bezier, chop it into 1, 2, 3 beziers such that
michael@0:     the resulting beziers are monotonic in Y. This is called by the scan converter.
michael@0:     Depending on what is returned, dst[] is treated as follows
michael@0:     0   dst[0..3] is the original cubic
michael@0:     1   dst[0..3] and dst[3..6] are the two new cubics
michael@0:     2   dst[0..3], dst[3..6], dst[6..9] are the three new cubics
michael@0:     If dst == null, it is ignored and only the count is returned.
michael@0: */
michael@0: int SkChopCubicAtYExtrema(const SkPoint src[4], SkPoint dst[10]);
michael@0: int SkChopCubicAtXExtrema(const SkPoint src[4], SkPoint dst[10]);
michael@0: 
michael@0: /** Given a cubic bezier, return 0, 1, or 2 t-values that represent the
michael@0:     inflection points.
michael@0: */
michael@0: int SkFindCubicInflections(const SkPoint src[4], SkScalar tValues[2]);
michael@0: 
michael@0: /** Return 1 for no chop, 2 for having chopped the cubic at a single
michael@0:     inflection point, 3 for having chopped at 2 inflection points.
michael@0:     dst will hold the resulting 1, 2, or 3 cubics.
michael@0: */
michael@0: int SkChopCubicAtInflections(const SkPoint src[4], SkPoint dst[10]);
michael@0: 
michael@0: int SkFindCubicMaxCurvature(const SkPoint src[4], SkScalar tValues[3]);
michael@0: int SkChopCubicAtMaxCurvature(const SkPoint src[4], SkPoint dst[13],
michael@0:                               SkScalar tValues[3] = NULL);
michael@0: 
michael@0: /** Given a monotonic cubic bezier, determine whether an xray intersects the
michael@0:     cubic.
michael@0:     By definition the cubic is open at the starting point; in other
michael@0:     words, if pt.fY is equivalent to cubic[0].fY, and pt.fX is to the
michael@0:     left of the curve, the line is not considered to cross the curve,
michael@0:     but if it is equal to cubic[3].fY then it is considered to
michael@0:     cross.
michael@0:     Optional outgoing "ambiguous" argument indicates whether the answer is
michael@0:     ambiguous because the query occurred exactly at one of the endpoints' y
michael@0:     coordinates, indicating that another query y coordinate is preferred
michael@0:     for robustness.
michael@0:  */
michael@0: bool SkXRayCrossesMonotonicCubic(const SkXRay& pt, const SkPoint cubic[4],
michael@0:                                  bool* ambiguous = NULL);
michael@0: 
michael@0: /** Given an arbitrary cubic bezier, return the number of times an xray crosses
michael@0:     the cubic. Valid return values are [0..3]
michael@0:     By definition the cubic is open at the starting point; in other
michael@0:     words, if pt.fY is equivalent to cubic[0].fY, and pt.fX is to the
michael@0:     left of the curve, the line is not considered to cross the curve,
michael@0:     but if it is equal to cubic[3].fY then it is considered to
michael@0:     cross.
michael@0:     Optional outgoing "ambiguous" argument indicates whether the answer is
michael@0:     ambiguous because the query occurred exactly at one of the endpoints' y
michael@0:     coordinates or at a tangent point, indicating that another query y
michael@0:     coordinate is preferred for robustness.
michael@0:  */
michael@0: int SkNumXRayCrossingsForCubic(const SkXRay& pt, const SkPoint cubic[4],
michael@0:                                bool* ambiguous = NULL);
michael@0: 
michael@0: ///////////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: enum SkRotationDirection {
michael@0:     kCW_SkRotationDirection,
michael@0:     kCCW_SkRotationDirection
michael@0: };
michael@0: 
michael@0: /** Maximum number of points needed in the quadPoints[] parameter for
michael@0:     SkBuildQuadArc()
michael@0: */
michael@0: #define kSkBuildQuadArcStorage  17
michael@0: 
michael@0: /** Given 2 unit vectors and a rotation direction, fill out the specified
michael@0:     array of points with quadratic segments. Return is the number of points
michael@0:     written to, which will be { 0, 3, 5, 7, ... kSkBuildQuadArcStorage }
michael@0: 
michael@0:     matrix, if not null, is appled to the points before they are returned.
michael@0: */
michael@0: int SkBuildQuadArc(const SkVector& unitStart, const SkVector& unitStop,
michael@0:                    SkRotationDirection, const SkMatrix*, SkPoint quadPoints[]);
michael@0: 
michael@0: // experimental
michael@0: struct SkConic {
michael@0:     SkPoint  fPts[3];
michael@0:     SkScalar fW;
michael@0: 
michael@0:     void set(const SkPoint pts[3], SkScalar w) {
michael@0:         memcpy(fPts, pts, 3 * sizeof(SkPoint));
michael@0:         fW = w;
michael@0:     }
michael@0: 
michael@0:     /**
michael@0:      *  Given a t-value [0...1] return its position and/or tangent.
michael@0:      *  If pos is not null, return its position at the t-value.
michael@0:      *  If tangent is not null, return its tangent at the t-value. NOTE the
michael@0:      *  tangent value's length is arbitrary, and only its direction should
michael@0:      *  be used.
michael@0:      */
michael@0:     void evalAt(SkScalar t, SkPoint* pos, SkVector* tangent = NULL) const;
michael@0:     void chopAt(SkScalar t, SkConic dst[2]) const;
michael@0:     void chop(SkConic dst[2]) const;
michael@0: 
michael@0:     void computeAsQuadError(SkVector* err) const;
michael@0:     bool asQuadTol(SkScalar tol) const;
michael@0: 
michael@0:     /**
michael@0:      *  return the power-of-2 number of quads needed to approximate this conic
michael@0:      *  with a sequence of quads. Will be >= 0.
michael@0:      */
michael@0:     int computeQuadPOW2(SkScalar tol) const;
michael@0: 
michael@0:     /**
michael@0:      *  Chop this conic into N quads, stored continguously in pts[], where
michael@0:      *  N = 1 << pow2. The amount of storage needed is (1 + 2 * N)
michael@0:      */
michael@0:     int chopIntoQuadsPOW2(SkPoint pts[], int pow2) const;
michael@0: 
michael@0:     bool findXExtrema(SkScalar* t) const;
michael@0:     bool findYExtrema(SkScalar* t) const;
michael@0:     bool chopAtXExtrema(SkConic dst[2]) const;
michael@0:     bool chopAtYExtrema(SkConic dst[2]) const;
michael@0: 
michael@0:     void computeTightBounds(SkRect* bounds) const;
michael@0:     void computeFastBounds(SkRect* bounds) const;
michael@0: 
michael@0:     /** Find the parameter value where the conic takes on its maximum curvature.
michael@0:      *
michael@0:      *  @param t   output scalar for max curvature.  Will be unchanged if
michael@0:      *             max curvature outside 0..1 range.
michael@0:      *
michael@0:      *  @return  true if max curvature found inside 0..1 range, false otherwise
michael@0:      */
michael@0:     bool findMaxCurvature(SkScalar* t) const;
michael@0: };
michael@0: 
michael@0: #include "SkTemplates.h"
michael@0: 
michael@0: /**
michael@0:  *  Help class to allocate storage for approximating a conic with N quads.
michael@0:  */
michael@0: class SkAutoConicToQuads {
michael@0: public:
michael@0:     SkAutoConicToQuads() : fQuadCount(0) {}
michael@0: 
michael@0:     /**
michael@0:      *  Given a conic and a tolerance, return the array of points for the
michael@0:      *  approximating quad(s). Call countQuads() to know the number of quads
michael@0:      *  represented in these points.
michael@0:      *
michael@0:      *  The quads are allocated to share end-points. e.g. if there are 4 quads,
michael@0:      *  there will be 9 points allocated as follows
michael@0:      *      quad[0] == pts[0..2]
michael@0:      *      quad[1] == pts[2..4]
michael@0:      *      quad[2] == pts[4..6]
michael@0:      *      quad[3] == pts[6..8]
michael@0:      */
michael@0:     const SkPoint* computeQuads(const SkConic& conic, SkScalar tol) {
michael@0:         int pow2 = conic.computeQuadPOW2(tol);
michael@0:         fQuadCount = 1 << pow2;
michael@0:         SkPoint* pts = fStorage.reset(1 + 2 * fQuadCount);
michael@0:         conic.chopIntoQuadsPOW2(pts, pow2);
michael@0:         return pts;
michael@0:     }
michael@0: 
michael@0:     const SkPoint* computeQuads(const SkPoint pts[3], SkScalar weight,
michael@0:                                 SkScalar tol) {
michael@0:         SkConic conic;
michael@0:         conic.set(pts, weight);
michael@0:         return computeQuads(conic, tol);
michael@0:     }
michael@0: 
michael@0:     int countQuads() const { return fQuadCount; }
michael@0: 
michael@0: private:
michael@0:     enum {
michael@0:         kQuadCount = 8, // should handle most conics
michael@0:         kPointCount = 1 + 2 * kQuadCount,
michael@0:     };
michael@0:     SkAutoSTMalloc<kPointCount, SkPoint> fStorage;
michael@0:     int fQuadCount; // #quads for current usage
michael@0: };
michael@0: 
michael@0: #endif