Implements the Moving Least Squares interpolation method. More...

#include <gmMlsInterpolatorObject.h>

Inheritance diagram for GmMlsInterpolatorObject:

Collaboration diagram for GmMlsInterpolatorObject:

Public Member Functions
virtual GmInterpolatorType	type () const
	Returns the interpolator object type.

virtual bool	supportsInterpolatorKind (GmInterpolatorKind kind) const
	Returns whether this interpolator object supports the given interpolator kind or not.

virtual bool	distanceBasedWeights (GmInterpolatorCoordinateSetBinding *pointSet, const GmVector &coord, const GmVector &squaredDistances, const QVariant &typeParam, GmVector &weights) const
	Implements the GmInterpolatorObject::distanceBasedWeights() virtual function to calculate interpolation weights by the MLS method.

Public Member Functions inherited from GmInterpolatorObject
virtual bool	typeParamIsValid (const QVariant &v) const
	Is the given interpolator type parameter valid? The default implementation accepts only empty variants.

virtual QString	typeParamToStr (const QVariant &v) const
	Converts an interpolator type parameter to a string.

virtual bool	requiresElement () const
	Does this interpolator object requires that the coordinate set provided to interpolationWeights() contains points from a single element, whose identity can be queried by a call to GmCoordinateSet::cell()? Default = false.

virtual bool	requiresMesh () const
	Does this interpolator object requires that the coordinate set provided to interpolationWeights() contains information about the underlying mesh, whose identity can be queried by a call to GmCoordinateSet::mesh()? Default = false.

virtual bool	requiresNaturalCoordinates () const
	Does this interpolator object requires that the coordinate passed as parameter to interpolationWeights() be expressed in natural coordinates? By default, this is false and the provided coordinate should be cartesian coordinates.

virtual bool	interpolationWeights (GmInterpolatorCoordinateSetBinding *pointSet, const GmVector &coord, const QVariant &typeParam, GmVector &weights) const
	Basic function for calculating the interpolation weights that should be associated with each point (coordinate) in the given point set.

virtual const GmMatrix &	gaussToNodesExtrapolationMatrix (GmInterpolatorGaussCoordinateSetBinding *pointSet, const QVariant &typeParam, GmMatrix &weights) const
	Basic function for returning the extrapolation matrix used by the GM_GAUSS_TO_NODE_INTERPOLATOR interpolator kind.

Private Member Functions
bool	checkColinearity (GmInterpolatorCoordinateSetBinding *pointSet) const
	Check collinearity: returns true if there is at least 3 non-collinear nodes in the point set.

bool	checkCoplanarity (GmInterpolatorCoordinateSetBinding *pointSet) const
	Check coplanarity: returns true if there is at least 4 non-coplanar nodes in the point set.

Additional Inherited Members
Protected Member Functions inherited from GmInterpolatorObject
	GmInterpolatorObject ()
	Protected default constructor to make sure that Interpolator objects are created only by the GmInterpolator friend class.

Detailed Description

Implements the Moving Least Squares interpolation method.

Moving least squares formulation:

w.t = p.t * inv( P.t * Phi * P) * P.t * Phi (1 x n) (1 x d+1) (d+1 x n) (n x n) (n x d+1) (d+1 x n) (n x n)

Where, considering n = number of known points and d = coordinate dimension:

w is the weight column vector (n x 1)
p is the (d+1 x 1) interpolation point coordinate vector with an added 1 in the beginning [1, x, y, z]
P is the (n x d+1) matrix with known point coordinates with an added 1 column at the beginning [[1, x1, y1, z1], [1, x2, y2, z2], ... [1, xn, yn, zn]]
Phi is the (n x n) diagonal matrix with the radial basis functions evaluated at the distance between the known point and the interpolation point [[rbf(|x - x1|), 0, 0 ...], [0, rbf(|x - x2|), 0, ...], ...]

Member Function Documentation

◆ distanceBasedWeights()

bool GmMlsInterpolatorObject::distanceBasedWeights	(	GmInterpolatorCoordinateSetBinding *	pointSet,
		const GmVector &	coord,
		const GmVector &	squaredDistances,
		const QVariant &	typeParam,
		GmVector &	weights ) const

virtual

Implements the GmInterpolatorObject::distanceBasedWeights() virtual function to calculate interpolation weights by the MLS method.

The typeParam parameter should be an integer specifying the RBF function to be used (see class description). If absent, the default XXXX will be used. See the documentation for GmInterpolatorObject::distanceBasedWeights() and GmInterpolatorObject::interpolationWeights() for additional information on the function parameters.

Reimplemented from GmInterpolatorObject.