A simplex is the convex hull of d+1 points in general position (IGP), i.e. they do not lie on the same hyperplane. More...

#include <mpblocks/clarkson93/Simplex2.h>

Public Types
typedef std::bitset < simplex::NUM_BITS >	BitSet

typedef Traits::Deref	Deref

typedef Traits::Point	Point

typedef Traits::PointRef	PointRef

typedef Traits::Scalar	Scalar

typedef Traits::SimplexRef	SimplexRef

Public Member Functions
	Simplex2 (PointRef pNull, SimplexRef sNull)

Public Attributes
uint32_t	iPeak
	index of the peak vertex More...

SimplexRef	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...

BitSet	sets
	sets this simplex is a member of 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::Simplex2< Traits >

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.

In this second version of the Simplex structure we do not maintain the zeroth vertex/Neighbor pair as the designated peak vertex, base facet. Instead we store the vertex references in sorted order so that we can efficiently perform queries regarding various dimensional facets of 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 58 of file Simplex2.h.