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/********************************************************************** * * GEOS - Geometry Engine Open Source * http://geos.osgeo.org * * Copyright (C) 2014 Mateusz Loskot * * This is free software; you can redistribute and/or modify it under * the terms of the GNU Lesser General Public Licence as published * by the Free Software Foundation. * See the COPYING file for more information. * ********************************************************************** * * Last port: algorithm/CGAlgorithmsDD.java r789 (JTS-1.14) * **********************************************************************/ #pragma once #include #include // Forward declarations namespace geos { namespace geom { class CoordinateXY; class CoordinateSequence; } } using namespace geos::math; namespace geos { namespace algorithm { // geos::algorithm /// Implements basic computational geometry algorithms using extended precision float-point arithmetic. class GEOS_DLL CGAlgorithmsDD { public: enum { CLOCKWISE = -1, COLLINEAR = 0, COUNTERCLOCKWISE = 1 }; enum { RIGHT = -1, LEFT = 1, STRAIGHT = 0, FAILURE = 2 }; /** \brief * Returns the index of the direction of the point `q` relative to * a vector specified by `p1-p2`. * * @param p1 the origin point of the vector * @param p2 the final point of the vector * @param q the point to compute the direction to * * @return 1 if q is counter-clockwise (left) from p1-p2 * @return -1 if q is clockwise (right) from p1-p2 * @return 0 if q is collinear with p1-p2 */ static int orientationIndex(const geom::CoordinateXY& p1, const geom::CoordinateXY& p2, const geom::CoordinateXY& q); static int orientationIndex(double p1x, double p1y, double p2x, double p2y, double qx, double qy); /** * A filter for computing the orientation index of three coordinates. * * If the orientation can be computed safely using standard DP arithmetic, * this routine returns the orientation index. Otherwise, a value `i > 1` is * returned. In this case the orientation index must be computed using some * other more robust method. * * The filter is fast to compute, so can be used to avoid the use of slower * robust methods except when they are really needed, thus providing better * average performance. * * Uses an approach due to Jonathan Shewchuk, which is in the public domain. */ static inline int orientationIndexFilter( double pax, double pay, double pbx, double pby, double pcx, double pcy) { /** * A value which is safely greater than the relative round-off * error in double-precision numbers */ double constexpr DP_SAFE_EPSILON = 1e-15; double detsum; double const detleft = (pax - pcx) * (pby - pcy); double const detright = (pay - pcy) * (pbx - pcx); double const det = detleft - detright; if(detleft > 0.0) { if(detright <= 0.0) { return orientation(det); } else { detsum = detleft + detright; } } else if(detleft < 0.0) { if(detright >= 0.0) { return orientation(det); } else { detsum = -detleft - detright; } } else { return orientation(det); } double const errbound = DP_SAFE_EPSILON * detsum; if((det >= errbound) || (-det >= errbound)) { return orientation(det); } return CGAlgorithmsDD::FAILURE; }; static int orientation(double x) { if(x < 0) { return CGAlgorithmsDD::RIGHT; } if(x > 0) { return CGAlgorithmsDD::LEFT; } return CGAlgorithmsDD::STRAIGHT; }; /** * If the lines are parallel (either identical * or separate) a null value is returned. * @param p1 an endpoint of line segment 1 * @param p2 an endpoint of line segment 1 * @param q1 an endpoint of line segment 2 * @param q2 an endpoint of line segment 2 * @return an intersection point if one exists, or null if the lines are parallel */ static geom::CoordinateXY intersection(const geom::CoordinateXY& p1, const geom::CoordinateXY& p2, const geom::CoordinateXY& q1, const geom::CoordinateXY& q2); static int signOfDet2x2(double dx1, double dy1, double dx2, double dy2); static DD detDD(double x1, double y1, double x2, double y2); static DD detDD(const DD& x1, const DD& y1, const DD& x2, const DD& y2); /** \brief * Computes the circumcentre of a triangle. * * The circumcentre is the centre of the circumcircle, the smallest circle * which encloses the triangle. It is also the common intersection point of * the perpendicular bisectors of the sides of the triangle, and is the only * point which has equal distance to all three vertices of the triangle. * * The circumcentre does not necessarily lie within the triangle. For example, * the circumcentre of an obtuse isosceles triangle lies outside the triangle. * * This method uses @ref geos::math::DD extended-precision arithmetic to provide more accurate * results than geos::geom::Triangle::circumcentre. * * @param a a vertex of the triangle * @param b a vertex of the triangle * @param c a vertex of the triangle * @return the circumcentre of the triangle */ static geom::CoordinateXY circumcentreDD(const geom::CoordinateXY& a, const geom::CoordinateXY& b, const geom::CoordinateXY& c); protected: static int signOfDet2x2(const DD& x1, const DD& y1, const DD& x2, const DD& y2); }; } // namespace geos::algorithm } // namespace geos