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/********************************************************************** * * 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. * **********************************************************************/ #pragma once #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: CoordinateXY p0, p1, p2; Triangle(const CoordinateXY& nP0, const CoordinateXY& nP1, const CoordinateXY& 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(CoordinateXY& 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(CoordinateXY& resultPoint); /** Calculates the circumcentre using double precision math * @param resultPoint the point into which to write the inCentre of the triangle */ void circumcentreDD(CoordinateXY& resultPoint); /** Computes the circumcentre of a triangle. The circumcentre is the centre * of the circumcircle, the smallest circle which passes through all the triangle vertices. * It is also the common intersection point of the perpendicular bisectors of the * @param p0 corner of the triangle * @param p1 corner of the triangle * @param p2 corner of the triangle * @return the center of the the smallest circle that encloses the triangle */ static const CoordinateXY circumcentre(const CoordinateXY& p0, const CoordinateXY& p1, const CoordinateXY& p2); /** * Computes the radius of the circumcircle of a triangle. * Formula is as per https://math.stackexchange.com/a/3610959 * * @param a a vertex of the triangle * @param b a vertex of the triangle * @param c a vertex of the triangle * @return the circumradius of the triangle */ static double circumradius(const CoordinateXY& a, const CoordinateXY& b, const CoordinateXY& c); /** * Computes the radius of the circumcircle of a triangle. * * @return the triangle circumradius */ double circumradius() const { return circumradius(p0, p1, 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 CoordinateXY& a, const CoordinateXY& b, const CoordinateXY& 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 CoordinateXY& a, const CoordinateXY& b, const CoordinateXY& 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 CoordinateXY& a, const CoordinateXY& b, const CoordinateXY& c, const CoordinateXY& 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 CoordinateXY& 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); }; /** * Computes the length of the longest side of a triangle * * @param a a vertex of the triangle * @param b a vertex of the triangle * @param c a vertex of the triangle * @return the length of the longest side of the triangle */ static double longestSideLength( const CoordinateXY& a, const CoordinateXY& b, const CoordinateXY& c); /** * Compute the length of the perimeter of a triangle * * @param a a vertex of the triangle * @param b a vertex of the triangle * @param c a vertex of the triangle * @return the length of the triangle perimeter */ static double length(const CoordinateXY& a, const CoordinateXY& b, const CoordinateXY& c); /** * Computes the length of the perimeter of this triangle. * * @return the length of the perimeter */ double length() const; /** * Computes the 2D area of a triangle. The area value is always non-negative. * * @param a vertex of the triangle * @param b vertex of the triangle * @param c vertex of the triangle * @return the area of the triangle * */ static double area(const CoordinateXY& a, const CoordinateXY& b, const CoordinateXY& c); double area() const; 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