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/********************************************************************** * * GEOS - Geometry Engine Open Source * http://geos.osgeo.org * * Copyright (C) 2012 Excensus LLC. * * This is free software; you can redistribute and/or modify it under * the terms of the GNU Lesser General Licence as published * by the Free Software Foundation. * See the COPYING file for more information. * ********************************************************************** * * Last port: triangulate/quadedge/Vertex.java r705 * **********************************************************************/ #pragma once #include #include #include #include #include #include //fwd declarations namespace geos { namespace triangulate { namespace quadedge { class QuadEdge; } } } namespace geos { namespace triangulate { //geos.triangulate namespace quadedge { //geos.triangulate.quadedge /** \brief * Models a site (node) in a QuadEdgeSubdivision. * * The sites can be points on a line string representing a linear site. * * The vertex can be considered as a vector with a norm, length, inner product, cross * product, etc. Additionally, point relations (e.g., is a point to the left of a line, the circle * defined by this point and two others, etc.) are also defined in this class. * * It is common to want to attach user-defined data to the vertices of a subdivision. * One way to do this is to subclass `Vertex` to carry any desired information. * * @author JTS: David Skea * @author JTS: Martin Davis * @author Benjamin Campbell * */ class GEOS_DLL Vertex { public: static const int LEFT = 0; static const int RIGHT = 1; static const int BEYOND = 2; static const int BEHIND = 3; static const int BETWEEN = 4; static const int ORIGIN = 5; static const int DESTINATION = 6; private: geom::Coordinate p; public: Vertex(double _x, double _y); Vertex(double _x, double _y, double _z); Vertex(const geom::Coordinate& _p); Vertex(); ~Vertex() {}; inline double getX() const { return p.x; } inline double getY() const { return p.y; } inline double getZ() const { return p.z; } inline void setZ(double _z) { p.z = _z; } inline const geom::Coordinate& getCoordinate() const { return p; } inline bool equals(const Vertex& _x) const { return p.equals2D(_x.p); } inline bool equals(const Vertex& _x, double tolerance) const { if(p.distance(_x.getCoordinate()) < tolerance) { return true; } return false; } int classify(const Vertex& p0, const Vertex& p1); /** * Computes the cross product k = u X v. * * @param v a vertex * @return returns the magnitude of u X v */ inline double crossProduct(const Vertex& v) const { return (p.x * v.getY() - p.y * v.getX()); } /** * Computes the inner or dot product * * @param v a vertex * @return returns the dot product u.v */ inline double dot(Vertex v) const { return (p.x * v.getX() + p.y * v.getY()); } /** * Computes the scalar product c(v) * * @param c scaling factor * @return returns the scaled vector */ inline std::unique_ptr times(double c) const { return std::unique_ptr(new Vertex(c * p.x, c * p.y)); } /* Vector addition */ inline std::unique_ptr sum(Vertex v) const { return std::unique_ptr(new Vertex(p.x + v.getX(), p.y + v.getY())); } /* and subtraction */ inline std::unique_ptr sub(const Vertex& v) const { return std::unique_ptr(new Vertex(p.x - v.getX(), p.y - v.getY())); } /* magnitude of vector */ inline double magn() const { return (std::sqrt(p.x * p.x + p.y * p.y)); } /* returns k X v (cross product). this is a vector perpendicular to v */ inline std::unique_ptr cross() const { return std::unique_ptr(new Vertex(p.y, -p.x)); } /** ************************************************************* */ /*********************************************************************************************** * Geometric primitives / **********************************************************************************************/ /** * Tests if the vertex is inside the circle defined by * the triangle with vertices a, b, c (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 this vertex is in the circumcircle of (a,b,c) */ bool isInCircle(const Vertex& a, const Vertex& b, const Vertex& c) const { return triangulate::quadedge::TrianglePredicate::isInCircleRobust(a.p, b.p, c.p, this->p) == geom::Location::INTERIOR; } /** * Tests whether the triangle formed by this vertex and two * other vertices is in CCW orientation. * * @param b a vertex * @param c a vertex * @returns true if the triangle is oriented CCW */ inline bool isCCW(const Vertex& b, const Vertex& c) const { // check if signed area is positive return (b.p.x - p.x) * (c.p.y - p.y) > (b.p.y - p.y) * (c.p.x - p.x); } bool rightOf(const QuadEdge& e) const; bool leftOf(const QuadEdge& e) const; private: static std::unique_ptr bisector(const Vertex& a, const Vertex& b); inline double distance(const Vertex& v1, const Vertex& v2) { return std::sqrt(pow(v2.getX() - v1.getX(), 2.0) + pow(v2.getY() - v1.getY(), 2.0)); } /** * Computes the value of the ratio of the circumradius to shortest edge. If smaller than some * given tolerance B, the associated triangle is considered skinny. For an equal lateral * triangle this value is 0.57735. The ratio is related to the minimum triangle angle theta by: * circumRadius/shortestEdge = 1/(2sin(theta)). * * @param b second vertex of the triangle * @param c third vertex of the triangle * @return ratio of circumradius to shortest edge. */ double circumRadiusRatio(const Vertex& b, const Vertex& c); /** * returns a new vertex that is mid-way between this vertex and another end point. * * @param a the other end point. * @return the point mid-way between this and that. */ std::unique_ptr midPoint(const Vertex& a); /** * Computes the centre of the circumcircle of this vertex and two others. * * @param b * @param c * @return the Coordinate which is the circumcircle of the 3 points. */ std::unique_ptr circleCenter(const Vertex& b, const Vertex& c) const; /** * For this vertex enclosed in a triangle defined by three vertices v0, v1 and v2, interpolate * a z value from the surrounding vertices. */ double interpolateZValue(const Vertex& v0, const Vertex& v1, const Vertex& v2) const; /** * Interpolates the Z-value (height) of a point enclosed in a triangle * whose vertices all have Z values. * The containing triangle must not be degenerate * (in other words, the three vertices must enclose a * non-zero area). * * @param p the point to interpolate the Z value of * @param v0 a vertex of a triangle containing the p * @param v1 a vertex of a triangle containing the p * @param v2 a vertex of a triangle containing the p * @return the interpolated Z-value (height) of the point */ static double interpolateZ(const geom::Coordinate& p, const geom::Coordinate& v0, const geom::Coordinate& v1, const geom::Coordinate& v2); /** * Computes the interpolated Z-value for a point p lying on the segment p0-p1 * * @param p * @param p0 * @param p1 * @return the interpolated Z value */ static double interpolateZ(const geom::Coordinate& p, const geom::Coordinate& p0, const geom::Coordinate& p1); }; inline bool operator<(const Vertex& v1, const Vertex& v2) { return v1.getCoordinate() < v2.getCoordinate(); } } //namespace geos.triangulate.quadedge } //namespace geos.triangulate } //namespace geos