/* * 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. */ SkScalar 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 SkCubicType { kSerpentine_SkCubicType, kCusp_SkCubicType, kLoop_SkCubicType, kQuadratic_SkCubicType, kLine_SkCubicType, kPoint_SkCubicType }; /** Returns the cubic classification. Pass scratch storage for computing inflection data, which can be used with additional work to find the loop intersections and so on. */ SkCubicType SkClassifyCubic(const SkPoint p[4], SkScalar inflection[3]); /////////////////////////////////////////////////////////////////////////////// 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 fStorage; int fQuadCount; // #quads for current usage }; #endif