DYT/Tool/OpenSceneGraph-3.6.5/include/geos/geom/Triangle.h

/**********************************************************************
 *
 * 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