LSMG: MBA Class Reference

List of all members.


Public Member Functions
	MBA (boost::shared_ptr< dVec > U, boost::shared_ptr< dVec > V, boost::shared_ptr< dVec > Z)
void	init (boost::shared_ptr< dVec > U, boost::shared_ptr< dVec > V, boost::shared_ptr< dVec > Z)
void	init (UCBspl::SplineSurface &surf)
void	setDomain (double umin, double vmin, double umax, double vmax)
void	setBaseType (MBAbaseType baseType)
void	setBaseValue (double base)
	Level of the base surface if MBA_CONSTVAL is used as base type.
void	MBAalg (int m0, int n0, int h=0, int smoothing_steps=0)
const MBAdata &	getData () const
	Get the data object (See class MBAdata).
void	readScatteredData (char filename[])
	Read scattered data from file in the format u v z on each line.
void	smoothZeros (int no_iter)
	Smooth the spline surface without affecting the approximation accuracy.
UCBspl::SplineSurface	getSplineSurface () const
void	getIndexDomain (int &m, int &n) const
void	cleanup (int type=0)
boost::shared_ptr< GenMatrixType >	PHI () const
void	checkSparsity () const
void	checkError () const
Static Public Member Functions
static void	smoothMatrix (GenMatrixType &matrix, int no_iter)

Detailed Description

MBA - Multilevel B-spline approximation (and interpolation). This is the main interface to multilevel B-spline approximation of scattered data for functional surfaces. The method is based on B-spline refinement and produces one single B-spline surface, as opposed to MBAadaptive that produces a hierarchy of spline surfaces. The domain of the surface will be the rectangular domain of the given scattered data in the (x,y)-axes directions as default. (We use u and v for x and y in function headers) The function MBA::MBAalg produces the spline surface from the scattered data. The spline surface can be retrieved as a SplineSurface object with MBA::getSplineSurface. Note that this is a (mathematical) lower level interface; thus there is no check for the validity of given scattered data or of arguments passed to member functions.

   MBA mba(x_arr, y_arr, z_arr);      // initialize with scattered data
   mba.MBAalg(1,1,7);                 // create spline surface

   UCBspl::SplineSurface surf = mba.getSplineSurface();
   double z = surf.f(x,y);            // evaluate (height of) surface in (x,y)
   surf.normalVector(x,y, nx,ny,nz);  // evaluate normal vector in (x,y)

Constructor & Destructor Documentation

MBA::MBA	(	boost::shared_ptr< dVec >	U,
		boost::shared_ptr< dVec >	V,
		boost::shared_ptr< dVec >	Z
	)			`[inline]`

Constructor with (standard) shared pointers to scattered data

Member Function Documentation

void MBA::init	(	boost::shared_ptr< dVec >	U,
		boost::shared_ptr< dVec >	V,
		boost::shared_ptr< dVec >	Z
	)			`[inline]`

Initialization that takes reference to arrays of scattered data. Note: see documenation of corresponding constructor above.

void MBA::init ( UCBspl::SplineSurface & surf )

Initialization of surface using data retrieved by getSplineSurface()

void MBA::setDomain	(	double	umin,
		double	vmin,
		double	umax,
		double	vmax
	)			`[inline]`

Set the domain over which the surface is defined. The default is the xy-range of the scattered data.

Note:: This function can only be used to expand the domain boyond the xy-range of the scattered data. It is the users responsibility to check that no scattered data falls outside the domain. (use std::min_element and std::max_element to find range of data for std::vector)

void MBA::setBaseType ( MBAbaseType baseType ) [inline]

Set surface base. Since the multilevel spline method is not affine-invariant, it is recommended to set a base surface over which the approximation is created.

Parameters:

	MBA_ZERO,:	A planar surface at level zero.
	MBA_CONSTLS,:	A konstant (least square) surface at the level of the mean z-value (default and recommended).
	MBA_CONSTVAL,:	A konstant surface at the level as given by setBaseValue.

void MBA::MBAalg	(	int	m0,
		int	n0,
		int	h = `0`,
		int	smoothing_steps = `0`
	)

Create a B-spline approximation to the scattered data.

Parameters:

	m0,n0	(>=1): The initial size of the spline space in the hierarchical construction. If the rectangular domain is a square, m0=n0=1 is recommended. If the rectangular domain in the y-direction is twice of that the x-direction, m0=1, n0=2 is recommended. In general, if the rectangular domain in the y-direction is k times the length in the x-direction, m0=1, n0=k is recommended.
	h,:	Number of levels in the hierarchical construction. If, e.g., m0=n0=1 and h=8, The resulting spline surface has a coefficient grid of size 2^h + 3 = 259 in each direction if a cubic C^2 spline surface is created. (Currently a compile option `UNIFORM_CUBIC_C1_SPLINES` can be set in `MBAunifBsplines.h` to create a cubic C^1 surface. In this case the coefficient grid will be approx. twice the size of that in the C^2 case when using the same h value.)

UCBspl::SplineSurface MBA::getSplineSurface ( ) const [inline]

Retrieve the spline surface.

void MBA::getIndexDomain	(	int &	m,
		int &	n
	)			const `[inline]`

Index domain of spline coefficient matrix. The surface can also be evaluated by f(i,j) and other functions with 0 <= i <= m and 0 <= j <= n. Note that the size of the tensor product grid (in the C2 case) is (m+3) x (n+3)

void MBA::cleanup ( int type = 0 )

Clean-up array structures and reduce memory usage. Depending on the given type described below, temporary array structures will be deleted. All options preserve information necessary to evaluate the surface.

Parameters:

	0,:	Temporary (mathematical) stuff not used further after MBA::MBAalg.
	1,:	The scattered data arrays and data derived from them.
	2,:	Everything, including that above, that is not needed by evaluators.

MBA Class Reference

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation