/**********************************************************************
*
* 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 <geos/export.h>
#include <geos/geom/Coordinate.h>
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
* <tt>false</tt>. A triangle which is not acute is either right or obtuse.
* <p>
* 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