encapsulates a vertex, simplex pair where the simplex is the neighbor across from the specified vertex More...

#include <mpblocks/clarkson93/Simplex.h>

Inheritance diagram for mpblocks::clarkson93::SimplexBase< Traits >:

Public Types
typedef HorizonRidge< Traits >	HorizonRidge_t

typedef Traits::idx_t	idx_t

enum	Orientation { INSIDE, OUTSIDE }

typedef Traits::Point	Point

typedef Traits::PointDeref	PointDeref

typedef Traits::PointRef	PointRef

typedef Traits::Scalar	Scalar

typedef Traits::Simplex	Simplex

typedef SimplexBase< Traits >	SimplexBase_t

typedef SimplexBase< Traits >	This_t

Public Member Functions
void	calculateConstraint (PointDeref &deref)
	calculate the normal and offset of the constraint given the d vertices on it's base facet (does not compute orientation / sign) More...

bool	isInfinite (PointRef antiOrigin)
	returns true if vertex[0] is the anti origin More...

bool	isVisible (const Point &x)
	returns true if x is on the inside of the base facet (i.e. x is in the same half space as the simplex) More...

Scalar	normalProjection (const Point &x)
	returns the distance of x to the base facet, used in walking the triangulation to x More...

void	orientConstraint (const Point &x, Orientation orient=INSIDE)
	orient the constraint by ensuring that the point x satisfies it (i.e. $n \cdot x \le c$ ) More...

Public Member Functions inherited from mpblocks::clarkson93::BitMember< SimplexBits, simplex::NUM_BITS >
void	addTo (SimplexBitssetBit)

bool	isMemberOf (SimplexBitssetBit)

void	removeFrom (SimplexBitssetBit)

Public Attributes
Simplex *	N [NDim+1]
	simplices which share a facet More...

Point	n
	normal vector of base facet More...

Scalar	o
	offset of base facet inequality hyperplane More...

PointRef	V [NDim+1]
	vertices of the simplex More...

Static Public Attributes
static const unsigned int	NDim = Traits::NDim

Detailed Description

template<class Traits>
struct mpblocks::clarkson93::SimplexBase< Traits >

encapsulates a vertex, simplex pair where the simplex is the neighbor across from the specified vertex

A simplex is the convex hull of d+1 points in general position (IGP), i.e. they do not lie on the same hyperplane In order to implicitly maintain the convensions of Clarkson.compgeo93, we will order the vertices and facets of the simplex such that the i'th facet is opposite the i'th vertex (using the definition of clarkson), and thus is defined by the d vertices excluding the i'th. In addition, the i'th neighbor is the neighbor sharing the i'th facet and opposite the i'th vertex.

By the uniformity conventions of Clarkson.compgeo93, we'll reserve the 0 index for the 'peak' vertex, and the 'base' facet

Because the 0'th vertex is the 'peak' vertex and the 'peak' vertex of a boundary simplex in the extended triangulation is the anti origin, the address stored in vertices[0] will be equal to the address of Triangulation::origin for the triangulation which owns this simplex.

The simplex also stores a normal vector n and an offset c defining a linear inequality whose hyperplane is coincident to the 'base' facet and oriented such that n' x < c is the half-space containing the 'peak' vertex

Definition at line 88 of file Simplex.h.