vtkCurvatures Class Reference

#include <vtkCurvatures.h>

Inheritance diagram for vtkCurvatures:

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Collaboration diagram for vtkCurvatures:

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List of all members.

Detailed Description

compute curvatures (Gauss and mean) of a Polydata object

vtkCurvatures takes a polydata input and computes the curvature of the mesh at each point. Four possible methods of computation are available :

Gauss Curvature discrete Gauss curvature (K) computation, $K(vertex v) = 2*PI-\sum_{facet neighbs f of v} (angle_f at v)$ The contribution of every facet is for the moment weighted by $Area(facet)/3$ The units of Gaussian Curvature are $[1/m^2]$

Mean Curvature $H(vertex v) = average over edges neighbs e of H(e)$ $H(edge e) = length(e)*dihedral_angle(e)$ NB: dihedral_angle is the ORIENTED angle between -PI and PI, this means that the surface is assumed to be orientable the computation creates the orientation The units of Mean Curvature are [1/m]

Maximum ( $k_max$ ) and Minimum ( $k_min$ ) Principal Curvatures $k_max = H + sqrt(H^2 - K)$ $k_min = H - sqrt(H^2 - K)$ Excepting spherical and planar surfaces which have equal principal curvatures, the curvature at a point on a surface varies with the direction one "sets off" from the point. For all directions, the curvature will pass through two extrema: a minimum ( $k_min$ ) and a maximum ( $k_max$ ) which occur at mutually orthogonal directions to each other.

NB. The sign of the Gauss curvature is a geometric ivariant, it should be +ve when the surface looks like a sphere, -ve when it looks like a saddle, however, the sign of the Mean curvature is not, it depends on the convention for normals - This code assumes that normals point outwards (ie from the surface of a sphere outwards). If a given mesh produces curvatures of opposite senses then the flag InvertMeanCurvature can be set and the Curvature reported by the Mean calculation will be inverted.

Thanks:: Philip Batchelor philipp.batchelor@kcl.ac.uk for creating and contributing the class and Andrew Maclean a.maclean@acfr.usyd.edu.au for cleanups and fixes. Thanks also to Goodwin Lawlor for contributing patch to calculate principal curvatures

Tests:: vtkCurvatures (Tests)

Definition at line 75 of file vtkCurvatures.h.


Public Types
typedef vtkPolyDataAlgorithm	Superclass
Public Member Functions
virtual const char *	GetClassName ()
virtual int	IsA (const char *type)
void	PrintSelf (ostream &os, vtkIndent indent)

virtual void	SetCurvatureType (int)
virtual int	GetCurvatureType ()
void	SetCurvatureTypeToGaussian ()
void	SetCurvatureTypeToMean ()
void	SetCurvatureTypeToMaximum ()
void	SetCurvatureTypeToMinimum ()

virtual void	SetInvertMeanCurvature (int)
virtual int	GetInvertMeanCurvature ()
virtual void	InvertMeanCurvatureOn ()
virtual void	InvertMeanCurvatureOff ()
Static Public Member Functions
static int	IsTypeOf (const char *type)
static vtkCurvatures *	SafeDownCast (vtkObject *o)
static vtkCurvatures *	New ()
Protected Member Functions
	vtkCurvatures ()
int	RequestData (vtkInformation , vtkInformationVector , vtkInformationVector )
void	GetGaussCurvature (vtkPolyData *output)
void	GetMeanCurvature (vtkPolyData *output)
void	GetMaximumCurvature (vtkPolyData input, vtkPolyData output)
void	GetMinimumCurvature (vtkPolyData input, vtkPolyData output)
Protected Attributes
int	CurvatureType
int	InvertMeanCurvature

Member Typedef Documentation

typedef vtkPolyDataAlgorithm vtkCurvatures::Superclass

Reimplemented from vtkPolyDataAlgorithm.

Definition at line 78 of file vtkCurvatures.h.

Constructor & Destructor Documentation

vtkCurvatures::vtkCurvatures ( ) [protected]

Member Function Documentation

virtual const char* vtkCurvatures::GetClassName ( ) [virtual]

Reimplemented from vtkPolyDataAlgorithm.

static int vtkCurvatures::IsTypeOf ( const char * name ) [static]

Return 1 if this class type is the same type of (or a subclass of) the named class. Returns 0 otherwise. This method works in combination with vtkTypeRevisionMacro found in vtkSetGet.h.

Reimplemented from vtkPolyDataAlgorithm.

virtual int vtkCurvatures::IsA ( const char * name ) [virtual]

Return 1 if this class is the same type of (or a subclass of) the named class. Returns 0 otherwise. This method works in combination with vtkTypeRevisionMacro found in vtkSetGet.h.

Reimplemented from vtkPolyDataAlgorithm.

static vtkCurvatures* vtkCurvatures::SafeDownCast ( vtkObject * o ) [static]

Reimplemented from vtkPolyDataAlgorithm.

void vtkCurvatures::PrintSelf	(	ostream &	os,
		vtkIndent	indent
	)			`[virtual]`

Methods invoked by print to print information about the object including superclasses. Typically not called by the user (use Print() instead) but used in the hierarchical print process to combine the output of several classes.

Reimplemented from vtkPolyDataAlgorithm.

static vtkCurvatures* vtkCurvatures::New ( ) [static]

Construct with curvature type set to Gauss

Reimplemented from vtkPolyDataAlgorithm.

virtual void vtkCurvatures::SetCurvatureType ( int ) [virtual]