/**********************************************************************
*
* 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
*
**********************************************************************/
#ifndef GEOS_TRIANGULATE_QUADEDGE_VERTEX_H
#define GEOS_TRIANGULATE_QUADEDGE_VERTEX_H
#include <math.h>
#include <memory>
#include <cstring>
#include <geos/geom/Coordinate.h>
#include <geos/algorithm/HCoordinate.h>
#include <geos/triangulate/quadedge/TrianglePredicate.h>
//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<Vertex>
times(double c) const
{
return std::unique_ptr<Vertex>(new Vertex(c * p.x, c * p.y));
}
/* Vector addition */
inline std::unique_ptr<Vertex>
sum(Vertex v) const
{
return std::unique_ptr<Vertex>(new Vertex(p.x + v.getX(), p.y + v.getY()));
}
/* and subtraction */
inline std::unique_ptr<Vertex>
sub(const Vertex& v) const
{
return std::unique_ptr<Vertex>(new Vertex(p.x - v.getX(), p.y - v.getY()));
}
/* magnitude of vector */
inline double
magn() const
{
return (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<Vertex>
cross() const
{
return std::unique_ptr<Vertex>(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);
}
/**
* 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<algorithm::HCoordinate> bisector(const Vertex& a, const Vertex& b);
inline double
distance(const Vertex& v1, const Vertex& v2)
{
return 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<Vertex> 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<Vertex> 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
#endif //GEOS_TRIANGULATE_QUADEDGE_VERTEX_H