#include <LeastSquaresConformalSurfaceMapper.h>

Inheritance diagram for mirtk::LeastSquaresConformalSurfaceMapper:

Collaboration diagram for mirtk::LeastSquaresConformalSurfaceMapper:

Public Member Functions
void	AddFixedPoint (int i, double u, double v)

int	FixedPointId (int i) const

int	FixedPointIndex (int i) const

int	FreePointId (int i) const

int	FreePointIndex (int i) const

double	GetFixedValue (int i, int j=0) const

double	GetFreeValue (int i, int j=0) const

double	GetValue (int i, int j=0) const

bool	IsFixedPoint (int i) const
	Whether the map value of the specified surface point is fixed.

bool	IsFreePoint (int i) const
	Whether the map value of the specified surface point is free.

	LeastSquaresConformalSurfaceMapper ()
	Default constructor.

	LeastSquaresConformalSurfaceMapper (const LeastSquaresConformalSurfaceMapper &)
	Copy constructor.

int	NumberOfFixedPoints () const
	Number of surface points with fixed map value.

int	NumberOfFreePoints () const
	Number of surface points with free map value.

LeastSquaresConformalSurfaceMapper &	operator= (const LeastSquaresConformalSurfaceMapper &)
	Assignment operator.

virtual	~LeastSquaresConformalSurfaceMapper ()
	Destructor.

Public Member Functions inherited from mirtk::FreeBoundarySurfaceMapper
int	NumberOfComponents () const
	Dimension of map codomain.

virtual	~FreeBoundarySurfaceMapper ()
	Destructor.

Public Member Functions inherited from mirtk::SurfaceMapper
void	Run ()
	Compute surface map.

virtual	~SurfaceMapper ()
	Destructor.

Public Member Functions inherited from mirtk::Object
virtual const char *	NameOfClass () const =0
	Get name of class, which this object is an instance of.

virtual ParameterList	Parameter () const
	Get parameter name/value pairs.

bool	Parameter (const ParameterList &)
	Set parameters from name/value pairs.

virtual bool	Set (const char name, const char value)

virtual	~Object ()
	Destructor.

Protected Member Functions
virtual void	ComputeMap ()
	Compute surface map.

virtual void	Finalize ()
	Finalize filter execution.

virtual void	Initialize ()
	Initialize filter after input and parameters are set.

void	SetFreeValue (int i, double v)

void	SetFreeValue (int i, int j, double v)

void	SetValue (int i, double v)

void	SetValue (int i, int j, double v)

virtual double	Weight (int i, int j) const

Protected Member Functions inherited from mirtk::FreeBoundarySurfaceMapper
	FreeBoundarySurfaceMapper ()
	Default constructor.

	FreeBoundarySurfaceMapper (const FreeBoundarySurfaceMapper &)
	Copy constructor.

FreeBoundarySurfaceMapper &	operator= (const FreeBoundarySurfaceMapper &)
	Assignment operator.

Protected Member Functions inherited from mirtk::SurfaceMapper
int	GetEdgeNeighborPoints (int i, int j, int &k, int &l) const

void	GetPoint (int ptId, double p[3]) const

int	NumberOfInteriorPoints () const
	Number of surface points minus the number of boundary points.

int	NumberOfPoints () const
	Number of surface points.

SurfaceMapper &	operator= (const SurfaceMapper &)
	Assignment operator.

class Point	Point (int ptId) const

	SurfaceMapper ()
	Default constructor.

	SurfaceMapper (const SurfaceMapper &)
	Copy constructor.

Protected Member Functions inherited from mirtk::Object
template<typename... Args>
void	Throw (ErrorType err, const char *func, Args... args) const

Additional Inherited Members
Static Public Member Functions inherited from mirtk::Object
static const char *	NameOfType ()
	Get name of this class type.

Static Protected Member Functions inherited from mirtk::Object
template<typename... Args>
static void	ThrowStatic (ErrorType err, const char cls, const char func, Args... args)

Detailed Description

Least squares conformal parameterization

This filter implements the least squares conformal map (LSCM) proposed by Levy (2002) and the identical discrete natural conformal parameterization (DNCP) proposed by Meyer et al. (2002). It follows the formulation of in Mullen et al. (2002), where the LSCM is defined as the minimizer of the conformal energy \(E_C(\vec{u}) = E_LSCM\vec{u} = E_D(\vec{u}) - A(\vec{u})\), where \(E_D(\vec{u})\) is the discrete Dirichlet energy and \(A(\vec{u})\) is the total area of the parameteric domain. The geometric cotangent weights are used to discretize the Laplace operator needed for the computation of the derivative of the Dirichlet energy.

The LSCM requires at least two fixed points. When no point constraints are given, a boundary point is selected automatically. A second fixed boundary point is chosen to be as farthest away from the first fixed point as possible based on geodesic distances on the input surface mesh.

Levy et al. (2002). Least squares conformal maps for automatic texture atlas generation. ACM Trans. Graphics, 21(3), 362–371.
Desbrun, Meyer, and Alliez (2002). Intrinsic parameterizations of surface meshes. Computer Graphics Forum, 21(3), 209–218.
Mullen et al. (2008). Spectral conformal parameterization. Eurographics Symposium on Geometry Processing, 27(5), 1487–1494.

Todo:: Implement area weighting extension as described in Mullen et al. (2008) to account for irregular surface sampling.

Definition at line 62 of file LeastSquaresConformalSurfaceMapper.h.

Member Function Documentation

§ AddFixedPoint()

void mirtk::LeastSquaresConformalSurfaceMapper::AddFixedPoint	(	int	i,
		double	u,
		double	v
	)

Add hard point constraint

Parameters

[in]	i	Surface point index.
[in]	u	First constraint value component.
[in]	v	Second constraint value component.

§ FixedPointId()

int mirtk::LeastSquaresConformalSurfaceMapper::FixedPointId ( int i ) const

inline

Get surface point ID of i-th point with fixed map value

Parameters

[in] i Index of point in set of points with fixed map value.

Returns: Surface point index.

Definition at line 292 of file LeastSquaresConformalSurfaceMapper.h.

§ FixedPointIndex()

int mirtk::LeastSquaresConformalSurfaceMapper::FixedPointIndex ( int i ) const

inline

Get index of i-th point with fixed map value or -1 if map value of point is free

Parameters

[in] i Surface point index.

Returns: Index of point in set of points with fixed map value.

Definition at line 285 of file LeastSquaresConformalSurfaceMapper.h.

§ FreePointId()

int mirtk::LeastSquaresConformalSurfaceMapper::FreePointId ( int i ) const

inline

Get surface point ID of i-th point with free map value

Parameters

[in] i Index of point in set of points with free map value.

Returns: Surface point index.

Definition at line 273 of file LeastSquaresConformalSurfaceMapper.h.

§ FreePointIndex()

int mirtk::LeastSquaresConformalSurfaceMapper::FreePointIndex ( int i ) const

inline

Get index of i-th point with free map value or -1 if map value of point is fixed

Parameters

[in] i Surface point index.

Returns: Index of point in set of points with free map value.

Definition at line 266 of file LeastSquaresConformalSurfaceMapper.h.

§ GetFixedValue()

double mirtk::LeastSquaresConformalSurfaceMapper::GetFixedValue	(	int	i,
		int	j = `0`
	)		const

inline

Get component of map value at i-th fixed point

Parameters

[in]	i	Index of point in set of points with fixed map value.
[in]	j	Map value component index.

Returns: The j-th component of the map value evaluated at the i-th fixed point.

Definition at line 316 of file LeastSquaresConformalSurfaceMapper.h.

§ GetFreeValue()

double mirtk::LeastSquaresConformalSurfaceMapper::GetFreeValue	(	int	i,
		int	j = `0`
	)		const

inline

Get component of map value at i-th free point

Parameters

[in]	i	Index of point in set of points with free map value.
[in]	j	Map value component index.

Returns: The j-th component of the map value evaluated at the i-th free point.

Definition at line 310 of file LeastSquaresConformalSurfaceMapper.h.

§ GetValue()

double mirtk::LeastSquaresConformalSurfaceMapper::GetValue	(	int	i,
		int	j = `0`
	)		const

inline

Get component of map value at surface vertex

Parameters

[in]	i	Surface point index.
[in]	j	Map value component index.

Returns: The j-th component of the map value evaluated at the i-th surface point.

Definition at line 304 of file LeastSquaresConformalSurfaceMapper.h.

§ SetFreeValue() [1/2]

void mirtk::LeastSquaresConformalSurfaceMapper::SetFreeValue	(	int	i,
		double	v
	)

inlineprotected

Set scalar map value at i-th free point

Parameters

[in]	i	Index of point in set of points with free map value.
[in]	v	Map value.

Definition at line 334 of file LeastSquaresConformalSurfaceMapper.h.

§ SetFreeValue() [2/2]

void mirtk::LeastSquaresConformalSurfaceMapper::SetFreeValue	(	int	i,
		int	j,
		double	v
	)

inlineprotected

Set component of map value at i-th free point

Parameters

[in]	i	Index of point in set of points with free map value.
[in]	j	Map component index.
[in]	v	Map component value.

Definition at line 340 of file LeastSquaresConformalSurfaceMapper.h.

§ SetValue() [1/2]

void mirtk::LeastSquaresConformalSurfaceMapper::SetValue	(	int	i,
		double	v
	)

inlineprotected

Set scalar map value at surface vertex

Parameters

[in]	i	Surface point index.
[in]	v	Map value.

Definition at line 322 of file LeastSquaresConformalSurfaceMapper.h.

§ SetValue() [2/2]

void mirtk::LeastSquaresConformalSurfaceMapper::SetValue	(	int	i,
		int	j,
		double	v
	)

inlineprotected

Set component of map value at surface vertex

Parameters

[in]	i	Surface point index.
[in]	j	Map component index.
[in]	v	Map component value.

Definition at line 328 of file LeastSquaresConformalSurfaceMapper.h.

§ Weight()

virtual double mirtk::LeastSquaresConformalSurfaceMapper::Weight	(	int	i,
		int	j
	)		const

protectedvirtual

Weight of undirected edge (i, j)

Parameters

[in]	i	First end point.
[in]	j	Second end point.

Returns: Weight of undirected edge (i, j).

The documentation for this class was generated from the following file:

LeastSquaresConformalSurfaceMapper.h

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

§ AddFixedPoint()

§ FixedPointId()

§ FixedPointIndex()

§ FreePointId()

§ FreePointIndex()

§ GetFixedValue()

§ GetFreeValue()

§ GetValue()

§ SetFreeValue() [1/2]

§ SetFreeValue() [2/2]

§ SetValue() [1/2]

§ SetValue() [2/2]

§ Weight()