MFPolytope
[MFChart]

Collaboration diagram for MFPolytope:

Classes
class	MFPolytope
	A polytope, which represents a neighborhood on a manifold. More...
Functions
MFPolytope	MFCreateHyperCubeAtOrigin (int d, double halfedge, MFErrorHandler e)
	Creates a d-dimensional hypercube whose faces are orthogonal to one coorindate axis, whose edges are length 2*halfedge, and whose center is at the origin.
MFPolytope	MFCreateSimplexAtOrigin (int d, double side, MFErrorHandler e)
	Creates a d-dimensional simplex. The last d-k coordinates of the kth vertex are zero.
void	MFSubtractHalfSpaceFromPolytope (MFPolytope P, int side, MFKVector n, double o, MFErrorHandler e)
	Removes a half space from a polytope. The positive (side>0) side is the set of points x that satisfy x.n-o>0.
void	MFClipPolytope (MFPolytope P, int index, double *din, int mark, MFErrorHandler e)
	Clips a polytope. index is the label to use for the new face, din[nv] is an array indicating which side of the plane each vertex lies. mark is simply an integer carried along with the face. multifario uses it to determine the polytop which lies opposite the face.
int	MFPolytopeDimension (MFPolytope P, MFErrorHandler e)
	returns the embedding dimension of the polytope.
void	MFPolytopeVertex (MFPolytope P, int i, MFKVector v, MFErrorHandler e)
	returns the embedding dimension of the polytope.
int	MFPolytopeVertexIndex (MFPolytope P, int v, int i, MFErrorHandler e)
	Returns an index (face number) of a vertex.
int	MFPolytopeNumberOfVertexIndices (MFPolytope P, int v, MFErrorHandler e)
	Returns the number of indices of a vertex (how many faces it lies on).
double	MFPolytopeRadiusOfVertex (MFPolytope P, int v, MFErrorHandler e)
	Returns the distance between a vertex and the origin.
double	MFPolytopeLargestRadiusOfVertex (MFPolytope P, MFErrorHandler e)
	Returns the largest distance between a vertex and the origin over all the vertices.
int	MFPolytopeNumberOfFaces (MFPolytope P, MFErrorHandler e)
	Returns the number of faces of the polytope.
int	MFPolytopeFaceIndex (MFPolytope P, int f, MFErrorHandler e)
	Returns the index of a face.
MFKVector	MFPolytopeFaceNormal (MFPolytope P, int f, MFErrorHandler e)
	Returns the nroaml to a face.
double	MFPolytopeFaceOrigin (MFPolytope P, int f, MFErrorHandler e)
	Returns the origin of a face (the signed distance from the origin along the normal to the face).
int	MFPolytopeNumberOfVerticesOnFace (MFPolytope P, int f, MFErrorHandler e)
	Returns the number of vertices that lie on a face.
int	MFPolytopeInterior (MFPolytope P, MFKVector x, MFErrorHandler e)
	Returns TRUE if x is inside the polytope.
MFPolytope	MFPolytopeRemoveSmallEdges (MFPolytope P, double epsilon, MFErrorHandler e)
	Returns a new polytope which has no edges shorter than epsilon. This is done by merging the endpoints of such edges.
int	MFPolytopeClosestFace (MFPolytope P, MFKVector x, double *d, MFErrorHandler e)
	Finds the closest face to a point.
void	MFPolytopeSetVertexMark (MFPolytope P, int v, int mark, MFErrorHandler e)
	Sets the mark associated with a vertex.
void	MFRefPolytope (MFPolytope polytope, MFErrorHandler e)
	Adds a reference to a polytope.
void	MFFreePolytope (MFPolytope polytope, MFErrorHandler e)
	Frees a reference to a polytope, and deletes the polytope if there are no references left.
void	MFWritePolytope (FILE *fid, MFPolytope polytope, MFErrorHandler e)
	Writes a polytope to a file.
MFPolytope	MFReadPolytope (FILE *fid, MFAtlas A, MFErrorHandler e)
	Reads a polytope from a file.

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Function Documentation

void MFClipPolytope (  MFPolytope  P, int  index, double *  din, int  mark, MFErrorHandler  e )

Clips a polytope. index is the label to use for the new face, din[nv] is an array indicating which side of the plane each vertex lies. mark is simply an integer carried along with the face. multifario uses it to determine the polytop which lies opposite the face. Parameters: P  The original polytope (will be modified). index  The index used for this new face. din  An array of length at least the number of vertices. Vertices with positive din are kept, negative are removed. mark  A number carried along on the face. e  A place to report errors.

MFPolytope MFCreateHyperCubeAtOrigin (  int  d, double  halfedge, MFErrorHandler  e )

Creates a d-dimensional hypercube whose faces are orthogonal to one coorindate axis, whose edges are length 2*halfedge, and whose center is at the origin. Parameters: d  The dimension. halfedge  Half the length of an edge. e  A place to report errors. Returns: A new polytope.

MFPolytope MFCreateSimplexAtOrigin (  int  d, double  side, MFErrorHandler  e )

Creates a d-dimensional simplex. The last d-k coordinates of the kth vertex are zero. Parameters: d  The dimension. side  The length of an edge. e  A place to report errors. Returns: A new polytope.

void MFFreePolytope (  MFPolytope  polytope, MFErrorHandler  e )

Frees a reference to a polytope, and deletes the polytope if there are no references left. Parameters: polytope  The polytope being unreferenced. e  A place to report errors. See also: ReferenceCounting MFRefPolytope

int MFPolytopeClosestFace (  MFPolytope  P, MFKVector  x, double *  d, MFErrorHandler  e )

Finds the closest face to a point. Parameters: P  The polytope. x  The point. d  A pointer to double to set to the distance. e  A place to report errors. Returns: The face.

int MFPolytopeDimension (  MFPolytope  P, MFErrorHandler  e )

returns the embedding dimension of the polytope. Parameters: P  The polytope. e  A place to report errors. Returns: The dimension.

int MFPolytopeFaceIndex (  MFPolytope  P, int  f, MFErrorHandler  e )

Returns the index of a face. Parameters: P  The polytope. f  Which face. e  A place to report errors. Returns: The index of the face.

MFKVector MFPolytopeFaceNormal (  MFPolytope  P, int  f, MFErrorHandler  e )

Returns the nroaml to a face. Parameters: P  The polytope. f  Which face. e  A place to report errors. Returns: The normal to a face.

double MFPolytopeFaceOrigin (  MFPolytope  P, int  f, MFErrorHandler  e )

Returns the origin of a face (the signed distance from the origin along the normal to the face). Parameters: P  The polytope. f  Which face. e  A place to report errors. Returns: The origin of the face.

int MFPolytopeInterior (  MFPolytope  P, MFKVector  x, MFErrorHandler  e )

Returns TRUE if x is inside the polytope. Parameters: P  The polytope. x  The point. e  A place to report errors. Returns: TRUE if the point is interior, FALSE otherwise.

double MFPolytopeLargestRadiusOfVertex (  MFPolytope  P, MFErrorHandler  e )

Returns the largest distance between a vertex and the origin over all the vertices. Parameters: P  The polytope. e  A place to report errors. Returns: The greatest distance from the origin to a vertex.

int MFPolytopeNumberOfFaces (  MFPolytope  P, MFErrorHandler  e )

Returns the number of faces of the polytope. Parameters: P  The polytope. e  A place to report errors. Returns: The number of faces.

int MFPolytopeNumberOfVertexIndices (  MFPolytope  P, int  v, MFErrorHandler  e )

Returns the number of indices of a vertex (how many faces it lies on). Parameters: P  The polytope. v  Which vertex. e  A place to report errors. Returns: The number of vertices.

int MFPolytopeNumberOfVerticesOnFace (  MFPolytope  P, int  f, MFErrorHandler  e )

Returns the number of vertices that lie on a face. Parameters: P  The polytope. f  Which face. e  A place to report errors. Returns: The number of vertices on the face.

double MFPolytopeRadiusOfVertex (  MFPolytope  P, int  v, MFErrorHandler  e )

Returns the distance between a vertex and the origin. Parameters: P  The polytope. v  Which vertex. e  A place to report errors. Returns: The distance from the origin to the vertex.

MFPolytope MFPolytopeRemoveSmallEdges (  MFPolytope  P, double  epsilon, MFErrorHandler  e )

Returns a new polytope which has no edges shorter than epsilon. This is done by merging the endpoints of such edges. Parameters: P  The polytope. epsilon  The smallest edge allowed.. e  A place to report errors. Returns: A new polytope with no short edges.

void MFPolytopeSetVertexMark (  MFPolytope  P, int  v, int  mark, MFErrorHandler  e )

Sets the mark associated with a vertex. Parameters: P  The polytope. v  The vertex. mark  The new vertex mark. e  A place to report errors. Returns: The current vertex mark.

void MFPolytopeVertex (  MFPolytope  P, int  i, MFKVector  v, MFErrorHandler  e )

returns the embedding dimension of the polytope. Parameters: P  The polytope. i  Which vertex. v  A place to put the coordinates of the vertex. e  A place to report errors.

int MFPolytopeVertexIndex (  MFPolytope  P, int  v, int  i, MFErrorHandler  e )

Returns an index (face number) of a vertex. Parameters: P  The polytope. v  Which vertex. i  Which index. e  A place to report errors. Returns: The index.

MFPolytope MFReadPolytope (  FILE *  fid, MFAtlas  A, MFErrorHandler  e )

Reads a polytope from a file. Parameters: fid  The file to write to. A  The Atlas for the polytope. e  A place to report errors. Returns: polytope The polytope.

void MFRefPolytope (  MFPolytope  polytope, MFErrorHandler  e )

Adds a reference to a polytope. Parameters: polytope  The polytope being referenced. e  A place to report errors. See also: ReferenceCounting MFFreePolytope

void MFSubtractHalfSpaceFromPolytope (  MFPolytope  P, int  side, MFKVector  n, double  o, MFErrorHandler  e )

Removes a half space from a polytope. The positive (side>0) side is the set of points x that satisfy x.n-o>0. Parameters: P  The original polytope (will be modified). side  Which side, positive or negative of the hyperplane. n  The normal of the hyperplane. o  The distance from the origin along the normal to the hyperplane. e  A place to report errors.

void MFWritePolytope (  FILE *  fid, MFPolytope  polytope, MFErrorHandler  e )

Writes a polytope to a file. Parameters: fid  The file to write to. polytope  The polytope being queried. e  A place to report errors.

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