gsParametrization< T > Class Template Reference

Detailed Description

template<class T>
class gismo::gsParametrization< T >

Class that maintains parametrization This class Parametrization stores the mesh information and the two-dimensional parameter points. The parameter points are stored in a vector, where the i-th vector element is the parameter point for the vertex with index i. This means that the first n elements in the vector are the inner parameter points, the rest of them are the boundary parameter points.

The parametrization gets constructed from a gsHalfEdgeMesh object, the boundary method and the parametrization method. For boundary methods one can choose between chords corners smallest opposite restrict distributed and for parametrization method one can choose between uniform shape distance

There are functions for returning the number of vertices and the number of inner vertices. Also every parameter point can be returned. The parametrization can be printed by printing all parameter points.

Inherited by gsPeriodicParametrization< T >.

Collaboration diagram for gsParametrization< T >:

Classes
class	LocalNeighbourhood
	Class that maintains the local neighbourhood properties. More...
class	LocalParametrization
	Class maintains local parametrization This class represents a local parametrization for a point in the triangle mesh, which is identified by the vertex index. The parametrization is given by the weights lambda(i,j) which is the weight of vertex x(i) regarding x(j) according to Floater's algorithm. More...
class	Neighbourhood
	Class that maintains neighbourhood information of triangle mesh. Represents the neighbourhood properties of a vertex in the triangle mesh. More...

Public Member Functions
virtual void	compute ()
	Main function which performs the computation.
virtual gsMesh< T >	createFlatMesh () const
gsMatrix< T >	createUVmatrix ()
gsMatrix< T >	createXYZmatrix ()
	gsParametrization (const gsMesh< T > &mesh, const gsOptionList &list=defaultOptions())
	Constructor using the input mesh and (possibly) options.
virtual void	restrictMatrices (gsMatrix< T > &, const gsMatrix< T > &, real_t=0, real_t=1) const
	It might make sense in the derived classes to restrict the parameters to [0, 1]^2.
void	writeTexturedMesh (std::string filename) const

Static Public Member Functions
static gsOptionList	defaultOptions ()
	Returns the list of default options for gsParametrization.

Protected Member Functions
void	constructAndSolveEquationSystem (const Neighbourhood &neighbourhood, const size_t n, const size_t N)
	Constructs linear equation system and solves it. More...
const Point2D &	getParameterPoint (size_t vertexIndex) const
	Get parameter point Returns the parameter point with given vertex index. More...

Protected Attributes
const gsHalfEdgeMesh< T >	m_mesh
	mesh information
VectorType	m_parameterPoints
	parameter points

Member Function Documentation

void constructAndSolveEquationSystem ( const Neighbourhood &  neighbourhood, const size_t  n, const size_t  N  )

protected

Constructs linear equation system and solves it.

The last step in Floater's algorithm is solving the linear equation system to obtain the parameter values for the inner vertices of the triangle mesh. This method constructs the above-mentioned system using information from neighbourhood. The matrix is given by a(i,i) = 1 a(i,j) = -lambda(i,j) for j!=i and the right hand side is calculated using the boundary parameters found beforehand. The parameter values are multiplied with corresponding lambda values and summed up. In the last step the system is solved and the parameter points are stored in m_parameterPoints.

Parameters

[in]	neighbourhood	const Neighbourhood& - neighbourhood information of the mesh
[in]	n	const int - number of inner vertices and therefore size of the square matrix
[in]	N	const int - number of the vertices and therefore N-n is the size of the right-hand-side vector

gsMesh< T > createFlatMesh ( ) const

virtual

Creates a flat mesh

Returns

Reimplemented in gsPeriodicOverlap< T >, and gsPeriodicStitch< T >.

gsMatrix< T > createUVmatrix

(

)

Parametric Coordinates u,v from 0..1

Returns

gsMatrix< T > createXYZmatrix

(

)

Corresponding mapped values in R3 to parametric coordinates.

Returns

const gsParametrization< T >::Point2D & getParameterPoint ( size_t  vertexIndex ) const

protected

Get parameter point Returns the parameter point with given vertex index.

Parameters

[in]

vertexIndex

int - vertex index

Returns

two-dimensional parameter point

void writeTexturedMesh

(

std::string

filename

)

const

Writes m_mesh into filename.vtk with the vertices coloured according to the parameters.

Parameters

filename

The name of the output file (without extension).