MFChart
[MFAtlas]

Collaboration diagram for MFChart:

Modules
	MFPolytope
Classes
class	MFChart
	A chart, which represents a neighborhood on a manifold. More...
Functions
double	MFVolumeOfChart (MFChart chart, MFNRegion Omega, MFErrorHandler e)
	Finds the volume of the polyhedra of a chart.
MFChart	MFCreateChart (MFImplicitMF M, MFNVector u, MFNKMatrix Phi, double R, MFErrorHandler e)
	Creates a chart.
void	MFSubtractHalfSpaceFromChart (MFChart chart, int i, MFKVector n, double o, MFErrorHandler e)
	Subtracts a half space from a chart, i.e. the polyhedron associated with the chart is intersected with the set x.n>o.
void	MFRefChart (MFChart chart, MFErrorHandler e)
	Adds a reference to the chart.
void	MFFreeChart (MFChart chart, MFErrorHandler e)
	Frees a reference to the chart, and deletes the chart if there are no references left.
MFPolytope	MFChartPolytope (MFChart chart, MFErrorHandler e)
	Returns the polyhedron (polytope) for the chart.
MFNVector	MFChartCenter (MFChart chart, MFErrorHandler e)
	Returns the center of the chart.
double	MFChartRadius (MFChart chart, MFErrorHandler e)
	Returns the radius of the domain of the chart.
MFNKMatrix	MFChartTangentSpace (MFChart chart, MFErrorHandler e)
	Returns the nxk matrix whose columns are a basis for the tangent space of the chart.
int	MFChartEvaluate (MFChart chart, MFKVector s, MFNVector u, MFErrorHandler e)
	Projects a point s in the domain of the chart, onto the manifold.
int	MFChartInterior (MFChart chart, MFKVector s, MFErrorHandler e)
	Tests to see if a point s is in the domain of the chart (the spherical ball, not the polyhedron).
int	MFChartHasBoundary (MFChart chart, MFErrorHandler e)
	Determines if the chart contributes to the boundary of the atlas of charts.
int	MFChartK (MFChart chart, MFErrorHandler e)
	Returns the dimension of the manifold, which is also the dimension of the domain of the chart mapping.
int	MFChartN (MFChart chart, MFErrorHandler e)
	Returns the dimension of the embedding space of the manifold, which is the dimension of the range of the chart mapping.
void	MFChartProjectIntoTangentSpace (MFChart chart, MFNVector u, MFKVector s, MFErrorHandler e)
	Projects a point in the embedding space onto the tangent space of the chart.
void	MFChartProjectVectorIntoTangentSpace (MFChart chart, MFNVector u, MFKVector s, MFErrorHandler e)
	Projects a point in the embedding space onto the tangent space of the chart.
void	MFChartPointInTangentSpace (MFChart chart, MFKVector s, MFNVector u, MFErrorHandler e)
	Finds the point in the embedding space which lies on the linear approximation of the chart mapping.
void	MFWriteChart (FILE *fid, MFChart chart, MFErrorHandler e)
	Writes a chart to a file.
MFChart	MFReadChart (FILE *fid, MFAtlas A, MFErrorHandler e)
	Reads a chart from a file.
MFImplicitMF	MFChartGetManifold (MFChart chart, MFErrorHandler e)
	Returns the implicitly defined manifold which the chart represents.
int	MFChartIsSingular (MFChart chart, MFErrorHandler e)
	Returns TRUE if the chart has been marked as singular (i.e. the chart mapping may not be one to one.
int	MFChartPaged (MFChart chart, MFErrorHandler e)
	Returns TRUE if the chart has been paged to file.
int	MFChartNearBoundary (MFChart chart, MFErrorHandler e)
	Returns TRUE if the chart has been marked as near the boundary of the atlas.
int	MFChartNumberOfFaces (MFChart chart, MFErrorHandler e)
	Returns the number of faces of the chart polyhedron (i.e. the number of neighbors of the chart.
double	MFChartSuggestedRadius (MFChart chart, MFErrorHandler e)
	Returns the hint at the radius of the chart domain.
int	MFChartReferenceNumber (MFChart chart, MFErrorHandler e)
	Returns the reference number identifying the chart.

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Function Documentation

MFNVector MFChartCenter (  MFChart  chart, MFErrorHandler  e )

Returns the center of the chart. Parameters: chart  The chart being accessed. e  A place to return errors. Returns: The center of the chart.

int MFChartEvaluate (  MFChart  chart, MFKVector  s, MFNVector  u, MFErrorHandler  e )

Projects a point s in the domain of the chart, onto the manifold. Parameters: chart  The chart defining the projection. s  The k-vector defining a point in the tangent space. u  (output) The point in the embedding space corresponding to s. e  A place to return errors. Returns: TRUE if the projection was succesful.

MFImplicitMF MFChartGetManifold (  MFChart  chart, MFErrorHandler  e )

Returns the implicitly defined manifold which the chart represents. Parameters: chart  The chart being queried. e  A place to return errors. Returns: Returns the implicitly defined manifold which the chart represents.

int MFChartHasBoundary (  MFChart  chart, MFErrorHandler  e )

Determines if the chart contributes to the boundary of the atlas of charts. Parameters: chart  The chart. e  A place to return errors. Returns: Returns TRUE if the chart contributes to the boundary of the atlas of charts.

int MFChartInterior (  MFChart  chart, MFKVector  s, MFErrorHandler  e )

Tests to see if a point s is in the domain of the chart (the spherical ball, not the polyhedron). Parameters: chart  The chart being queried. s  The k-vector defining a point in the tangent space. e  A place to return errors. Returns: TRUE if s is in the domain of the chart.

int MFChartIsSingular (  MFChart  chart, MFErrorHandler  e )

Returns TRUE if the chart has been marked as singular (i.e. the chart mapping may not be one to one. Parameters: chart  The chart being queried. e  A place to return errors. Returns: Returns TRUE if the chart has been marked as singular (i.e. the chart mapping may not be one to one.

int MFChartK (  MFChart  chart, MFErrorHandler  e )

Returns the dimension of the manifold, which is also the dimension of the domain of the chart mapping. Parameters: chart  The chart being queried. e  A place to return errors.

int MFChartN (  MFChart  chart, MFErrorHandler  e )

Returns the dimension of the embedding space of the manifold, which is the dimension of the range of the chart mapping. Parameters: chart  The chart being queried. e  A place to return errors.

int MFChartNearBoundary (  MFChart  chart, MFErrorHandler  e )

Returns TRUE if the chart has been marked as near the boundary of the atlas. Parameters: chart  The chart being queried. e  A place to return errors. Returns: TRUE if the chart has been marked as near the boundary of the atlas.

int MFChartNumberOfFaces (  MFChart  chart, MFErrorHandler  e )

Returns the number of faces of the chart polyhedron (i.e. the number of neighbors of the chart. Parameters: chart  The chart being queried. e  A place to return errors. Returns: The number of faces.

int MFChartPaged (  MFChart  chart, MFErrorHandler  e )

Returns TRUE if the chart has been paged to file. Parameters: chart  The chart being queried. e  A place to return errors. Returns: Returns TRUE if the chart has been paged to file.

void MFChartPointInTangentSpace (  MFChart  chart, MFKVector  s, MFNVector  u, MFErrorHandler  e )

Finds the point in the embedding space which lies on the linear approximation of the chart mapping. Parameters: chart  The chart. s  The k-vector of the point in the tangent space. u  (output) The n-vector defining a point in the embedding space which lies on the linear approximation of the manifold at the center of the chart. e  A place to return errors.

MFPolytope MFChartPolytope (  MFChart  chart, MFErrorHandler  e )

Returns the polyhedron (polytope) for the chart. Parameters: chart  The chart being accessed. e  A place to return errors. Returns: The polyhedron of the chart.

void MFChartProjectIntoTangentSpace (  MFChart  chart, MFNVector  u, MFKVector  s, MFErrorHandler  e )

Projects a point in the embedding space onto the tangent space of the chart. Parameters: chart  The chart. u  The n-vector defining a point in the embedding space. s  (output) The k-vector of the point in the tangent space. e  A place to return errors.

void MFChartProjectVectorIntoTangentSpace (  MFChart  chart, MFNVector  u, MFKVector  s, MFErrorHandler  e )

Projects a point in the embedding space onto the tangent space of the chart. Parameters: chart  The chart. u  The n-vector defining a point in the embedding space, relative to the center of the chart. s  (output) The k-vector of the point in the tangent space. e  A place to return errors.

double MFChartRadius (  MFChart  chart, MFErrorHandler  e )

Returns the radius of the domain of the chart. Parameters: chart  The chart being accessed. e  A place to return errors. Returns: The radius of the domain of the chart.

int MFChartReferenceNumber (  MFChart  chart, MFErrorHandler  e )

Returns the reference number identifying the chart. Parameters: chart  The chart being queried. e  A place to return errors. Returns: The reference number identifying the chart.

double MFChartSuggestedRadius (  MFChart  chart, MFErrorHandler  e )

Returns the hint at the radius of the chart domain. Parameters: chart  The chart being queried. e  A place to return errors. Returns: The suggest chart radius.

MFNKMatrix MFChartTangentSpace (  MFChart  chart, MFErrorHandler  e )

Returns the nxk matrix whose columns are a basis for the tangent space of the chart. Parameters: chart  The chart being accessed. e  A place to return errors. Returns: The basis of the tangent space of the chart.

MFChart MFCreateChart (  MFImplicitMF  M, MFNVector  u, MFNKMatrix  Phi, double  R, MFErrorHandler  e )

Creates a chart. Parameters: M  the implicitly defined manifold this chart describes. u  the center of the new chart (an MFNVector). Phi  a basis for the tangent space of the chart (an MFNKMatrix). R  the radius of the chart. e  A place to return errors. Returns: A new chart.

void MFFreeChart (  MFChart  chart, MFErrorHandler  e )

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

MFChart MFReadChart (  FILE *  fid, MFAtlas  A, MFErrorHandler  e )

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

void MFRefChart (  MFChart  chart, MFErrorHandler  e )

Adds a reference to the chart. Parameters: chart  The chart being referenced. e  A place to return errors. See also: ReferenceCounting MFFreeChart

void MFSubtractHalfSpaceFromChart (  MFChart  chart, int  i, MFKVector  n, double  o, MFErrorHandler  e )

Subtracts a half space from a chart, i.e. the polyhedron associated with the chart is intersected with the set x.n>o. Parameters: chart  the chart being modified. i  a label to be associated with the boundary of the half space. n  the normal to the bounding plane of the halfspace (an MFKVector s). o  the origin of the bounding plane of the half space. e  A place to return errors.

double MFVolumeOfChart (  MFChart  chart, MFNRegion  Omega, MFErrorHandler  e )

Finds the volume of the polyhedra of a chart. Parameters: chart  The chart. Omega  A region to limit the calculation. e  A place to return errors. Returns: The volume.

void MFWriteChart (  FILE *  fid, MFChart  chart, MFErrorHandler  e )

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

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