/********************************************************************** * * GEOS - Geometry Engine Open Source * http://geos.osgeo.org * * Copyright (C) 2006 Refractions Research Inc. * * 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. * **********************************************************************/ #ifndef GEOS_GEOM_TRIANGLE_H #define GEOS_GEOM_TRIANGLE_H #include #include #include namespace geos { namespace geom { // geos::geom /** * \brief * Represents a planar triangle, and provides methods for calculating various * properties of triangles. */ class GEOS_DLL Triangle { public: Coordinate p0, p1, p2; Triangle(const Coordinate& nP0, const Coordinate& nP1, const Coordinate& nP2) : p0(nP0) , p1(nP1) , p2(nP2) {} /** \brief * The inCentre of a triangle is the point which is equidistant * from the sides of the triangle. * * This is also the point at which the bisectors of the angles meet. * * @param resultPoint the point into which to write the inCentre of the triangle */ void inCentre(Coordinate& resultPoint); /** \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 isoceles triangle lies outside the triangle. * * This method uses an algorithm due to J.R.Shewchuk which uses normalization * to the origin to improve the accuracy of computation. (See *Lecture Notes * on Geometric Robustness*, Jonathan Richard Shewchuk, 1999). * * @param resultPoint the point into which to write the inCentre of the triangle */ void circumcentre(Coordinate& resultPoint); void circumcentreDD(Coordinate& resultPoint); /** Computes the circumcentre of a triangle. */ static const Coordinate circumcentre( const Coordinate& p0, const Coordinate& p1, const Coordinate& p2); bool isIsoceles(); /** * Tests whether a triangle is acute. A triangle is acute if all interior * angles are acute. This is a strict test - right triangles will return * false. A triangle which is not acute is either right or obtuse. *

* Note: this implementation is not robust for angles very close to 90 * degrees. * * @param a a vertex of the triangle * @param b a vertex of the triangle * @param c a vertex of the triangle * @return true if the triangle is acute */ static bool isAcute(const Coordinate& a, const Coordinate& b, const Coordinate& c); /** * Tests whether a triangle is oriented counter-clockwise. * * @param a a vertex of the triangle * @param b a vertex of the triangle * @param c a vertex of the triangle * @return true if the triangle orientation is counter-clockwise */ static bool isCCW(const Coordinate& a, const Coordinate& b, const Coordinate& c); /** * Tests whether a triangle intersects a point. * * @param a a vertex of the triangle * @param b a vertex of the triangle * @param c a vertex of the triangle * @param p the point to test * @return true if the triangle intersects the point */ static bool intersects(const Coordinate& a, const Coordinate& b, const Coordinate& c, const Coordinate& p); /** * Tests whether a triangle intersects a point. * @param p the point to test * @return true if the triangle intersects the point */ bool intersects(const Coordinate& p) { return intersects(p0, p1, p2, p); }; /** * Tests whether this triangle is oriented counter-clockwise. * @return true if the triangle orientation is counter-clockwise */ bool isCCW() { return isCCW(p0, p1, p2); }; /** * Tests whether this triangle is acute. * @return true if this triangle is acute */ bool isAcute() { return isAcute(p0, p1, p2); }; private: /** * Computes the determinant of a 2x2 matrix. Uses standard double-precision * arithmetic, so is susceptible to round-off error. * * @param m00 * the [0,0] entry of the matrix * @param m01 * the [0,1] entry of the matrix * @param m10 * the [1,0] entry of the matrix * @param m11 * the [1,1] entry of the matrix * @return the determinant */ double det(double m00, double m01, double m10, double m11) const; }; } // namespace geos::geom } // namespace geos //#ifdef GEOS_INLINE //# include "geos/geom/Triangle.inl" //#endif #endif // ndef GEOS_GEOM_TRIANGLE_H