Tcpolytope Struct Reference

Detailed Description

The area of influence of a chart is bounded by a polytope. This is used to determine which charts are exterior (belong to the expanding frontier of the exploration) and which are interior (completely sorrounded by other local charts). (See the atlas structure to see how charts are ensambled together.) The polytope is represented as a set of vertices that is updated every time a new chart is added to the atlas. In this case, the polytope stored in the chart is cut (removing vertices and adding new ones) with a plane derived from the intersection with the new neighbouring charts. Charts with all vertices inside the (hyper)sphere are interior.

Being able to differentiate between interior and exterior charts allows to control the ratio of expansion/refinement of the atlas.

See Also

chart.h,chart.c.

Definition at line 52 of file cpolytope.h.

Data Fields
unsigned int	k
double	r
double	v
boolean	emptyPolytope
unsigned int	nFaces
unsigned int	maxFaces
double **	face
unsigned int *	ID
unsigned int	maxVertices
unsigned int	nVertices
double **	vertex
boolean *	expandible
unsigned int	nExpandible
unsigned int	freeVertex
unsigned int *	nIndices
unsigned int *	maxIndices
unsigned int **	indices
Tbox	bb
boolean	open

Field Documentation

unsigned int Tcpolytope::k

Dimension of the manifold

Definition at line 53 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytope(), CutPolytopeWithFace(), DefinePolytope(), GetPolytopeDim(), GetPolytopeInteriorPoint(), GetPolytopeNeighboursFromVertices(), GetPolytopeVertices(), HaveEdge(), InitEmptyPolytope(), InsidePolytope(), LoadPolytope(), Polytope2SPolytope(), PolytopeBoundaryPointFromExternalCornerInt(), PolytopeBoundaryPointsFromExternalCorners(), PolytopeCenter(), PolytopeMaxVolume(), PolytopeMemSize(), PolytopeRandomPointOnBoundary(), PolytopeVolume(), RandomPointInPolytope(), and SavePolytope().

double Tcpolytope::r

Radius around p (in tangent space) where the linearization holds. About half the size of the box containing the ball (it is not exactly half due to the POLYTOPE_R_ENLARGEMENT).

Definition at line 54 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytope(), CutPolytopeWithFace(), DefinePolytope(), GetPolytopeRadius(), InitEmptyPolytope(), InsidePolytope(), LoadPolytope(), Polytope2SPolytope(), PolytopeBoundaryPointFromExternalCornerInt(), PolytopeMaxVolume(), RandomPointInPolytope(), and SavePolytope().

double Tcpolytope::v

Volume of the polytope.

Definition at line 57 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytopeWithFace(), InitEmptyPolytope(), LoadPolytope(), PolytopeVolume(), and SavePolytope().

boolean Tcpolytope::emptyPolytope

TRUE if the polytope information is initialized. We defer the polytope initialization as much as possible. In this way temporary charts never have polytope with the savings in memory allocation/free.

Definition at line 59 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytope(), CutPolytopeWithFace(), DefinePolytope(), DeletePolytope(), ExpandiblePolytope(), GetPolytopeBB(), GetPolytopeEdges(), GetPolytopeNeighboursFromVertices(), GetPolytopeVertices(), HaveEdge(), InitEmptyPolytope(), InsidePolytope(), LoadPolytope(), PolytopeBoundaryPointFromExternalCorner(), PolytopeBoundaryPointsFromExternalCorners(), PolytopeCenter(), PolytopeMaxVolume(), PolytopeNeighbourID(), PolytopeNumNeighbours(), PrintPolytopeInfo(), RandomPointInPolytope(), SavePolytope(), SetPolytopeBB(), and WrongPolytopeCorner().

unsigned int Tcpolytope::nFaces

Num faces defining the polytope so far.

Definition at line 65 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytopeWithFace(), DefinePolytope(), DeletePolytope(), GetPolytopeEdges(), GetPolytopeNeighboursFromVertices(), LoadPolytope(), Polytope2SPolytope(), PolytopeMemSize(), PolytopeNumNeighbours(), PrintPolytopeInfo(), and SavePolytope().

unsigned int Tcpolytope::maxFaces

Space for faces

Definition at line 66 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytopeWithFace(), DefinePolytope(), DeletePolytope(), LoadPolytope(), PolytopeMemSize(), PrintPolytopeInfo(), and SavePolytope().

double** Tcpolytope::face

Parameters of the faces defining the polytope

Definition at line 67 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytopeWithFace(), DefinePolytope(), DeletePolytope(), InsidePolytope(), LoadPolytope(), Polytope2SPolytope(), PrintPolytopeInfo(), and SavePolytope().

unsigned int* Tcpolytope::ID

Identifiers of the neighbouring charts (one per face).

Definition at line 69 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytopeWithFace(), DefinePolytope(), DeletePolytope(), GetPolytopeNeighboursFromVertices(), LoadPolytope(), Polytope2SPolytope(), PolytopeNeighbourID(), PolytopeNumNeighbours(), and SavePolytope().

unsigned int Tcpolytope::maxVertices

Space for vertices.

Definition at line 71 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytopeWithFace(), DefinePolytope(), DeletePolytope(), GetPolytopeEdges(), GetPolytopeNeighboursFromVertices(), GetPolytopeVertices(), LoadPolytope(), PolytopeMemSize(), PrintPolytopeInfo(), and SavePolytope().

unsigned int Tcpolytope::nVertices

Number of vertices (if 0 the chart is un-used)

Definition at line 72 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytopeWithFace(), DefinePolytope(), DeletePolytope(), GetPolytopeEdges(), GetPolytopeInteriorPoint(), InsidePolytope(), LoadPolytope(), PolytopeCenter(), PolytopeMemSize(), PrintPolytopeInfo(), and SavePolytope().

double** Tcpolytope::vertex

Polytope vertices.

Definition at line 73 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytopeWithFace(), DefinePolytope(), DeletePolytope(), GetPolytopeInteriorPoint(), GetPolytopeVertices(), LoadPolytope(), PolytopeBoundaryPointFromExternalCornerInt(), PolytopeCenter(), and SavePolytope().

boolean* Tcpolytope::expandible

TRUE for that can not be used to expand the chart (vertices out of the chart ball, vertices with some error)

Definition at line 74 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytopeWithFace(), DefinePolytope(), DeletePolytope(), LoadPolytope(), PolytopeBoundaryPointFromExternalCornerInt(), SavePolytope(), and WrongPolytopeCorner().

unsigned int Tcpolytope::nExpandible

Number of expandible vertices for the chart.

Definition at line 76 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytopeWithFace(), DefinePolytope(), DeletePolytope(), ExpandiblePolytope(), LoadPolytope(), PolytopeBoundaryPointFromExternalCorner(), PolytopeBoundaryPointsFromExternalCorners(), SavePolytope(), and WrongPolytopeCorner().

unsigned int Tcpolytope::freeVertex

First free vertex.

Definition at line 78 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytopeWithFace(), DefinePolytope(), DeletePolytope(), LoadPolytope(), and SavePolytope().

unsigned int* Tcpolytope::nIndices

Number of face index per vertex.

Definition at line 80 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytopeWithFace(), DefinePolytope(), DeletePolytope(), LoadPolytope(), PrintPolytopeInfo(), and SavePolytope().

unsigned int* Tcpolytope::maxIndices

Space for face indices. Also used to link free vertices.

Definition at line 81 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytopeWithFace(), DefinePolytope(), DeletePolytope(), GetPolytopeEdges(), GetPolytopeInteriorPoint(), GetPolytopeNeighboursFromVertices(), GetPolytopeVertices(), LoadPolytope(), PolytopeBoundaryPointFromExternalCornerInt(), PolytopeCenter(), PolytopeMemSize(), PrintPolytopeInfo(), and SavePolytope().

unsigned int** Tcpolytope::indices

Indices of the faces defining a vertex. Vertices with k-1 common faces define an edge. Edges that cross new faces added to the polytope define the new vertices (and the vertices to be removed).

Definition at line 82 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytopeWithFace(), DefinePolytope(), DeletePolytope(), HaveEdge(), LoadPolytope(), PrintPolytopeInfo(), and SavePolytope().

Tbox Tcpolytope::bb

Axis aligned bounding box of the polytope.

Definition at line 86 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytopeWithFace(), DefinePolytope(), DeletePolytope(), GetPolytopeBB(), LoadPolytope(), PolytopeMaxVolume(), RandomPointInPolytope(), SavePolytope(), and SetPolytopeBB().

boolean Tcpolytope::open

TRUE if the polytope has "open" borders, i.e., faces not given by another chart but with an undefined neighbour. These are undefined or given by the global domain borders.

Definition at line 88 of file cpolytope.h.

Referenced by CopyPolytope(), CutPolytopeWithFace(), DefinePolytope(), InitEmptyPolytope(), LoadPolytope(), and SavePolytope().