jvx.numeric

Class PnPCA

java.lang.Object

jvx.numeric.PnPCA

public class PnPCA
extends java.lang.Object

Principal component analysis of an element set and tetra set.

Author:

Ulrich Bauer

Version:

25.03.19, 3.00 revised (ms) Corrected bug in transformToNormalPosition method.
09.03.15, 2.00 revised (kp) Moved to jvx.numeric from dev.numeric.
03.09.09, 1.20 revised (mn) Cleaned code and comment methods.
xx.xx.09, 1.10 revised (mn) Add method transformToNormalPosition().
14.06.07, 1.00 created (ep)

Constructor Summary

Constructors

Constructor and Description
PnPCA()

Method Summary

Modifier and Type	Method and Description
static PdVector	getBarycenter(PgElementSet geom) Compute the barycenter of an element set.
static PdVector	getBarycenter(PgElementSet geom, int[] indices) Compute the barycenter of a subset of an element set.
static PdVector	getBarycenter(PgTetraSet geom) Compute the barycenter of an element set.
static PdVector	getBarycenter(PgTetraSet geom, int[] indices) Compute the barycenter of a tetra set.
static PdMatrix	getCovarianceMatrix(PgElementSet geom) Compute the covariance matrix of an element set.
static PdMatrix	getCovarianceMatrix(PgElementSet geom, PdVector center) Compute the covariance matrix of an element set.
static PdMatrix	getCovarianceMatrix(PgElementSet geom, PdVector center, int[] indices) Compute the covariance matrix of a subset of an element set.
static PdMatrix	getCovarianceMatrix(PgTetraSet geom) Compute the covariance matrix of a tetra set.
static PdMatrix	getCovarianceMatrix(PgTetraSet geom, PdVector center) Compute the covariance matrix of a tetra set.
static PdMatrix	getCovarianceMatrix(PgTetraSet geom, PdVector center, int[] indices) Compute the covariance matrix of a tetra set.
static PdVector	getNormal(PgElementSet geom, PdVector center) Compute the normal of the best-fitting plane to an element set.
static PdVector	getNormal(PgElementSet geom, PdVector center, int[] indices) Compute the normal of the best-fitting plane to a subset of an element set.
static PdVector	getNormal(PgTetraSet geom, PdVector center) Compute the normal of the best-fitting plane to a tetra set.
static PdVector	getNormal(PgTetraSet geom, PdVector center, int[] indices) Compute the normal of the best-fitting plane to a subset of a tetra set.
static PdVector	getWeightedBarycenter(PgTetraSet geom, PdMatrix[] tensorField, int[] indices) Compute the barycenter of a tetra set.
static PdVector	getWeightedBarycenter(PgTetraSet geom, PgVectorField vf, int[] indices) Compute the barycenter of a tetra set.
static PdMatrix	getWeightedCovarianceMatrix(PgTetraSet geom, PdMatrix[] tensorField, PdVector center, int[] indices) Compute the covariance matrix of a tetra set.
static PdMatrix	getWeightedCovarianceMatrix(PgTetraSet geom, PgVectorField vf, PdVector center, int[] indices) Compute the covariance matrix of a tetra set.
static PdVector	getWeightedNormal(PgTetraSet geom, PgVectorField vf, PdVector center, int[] indices) Compute the normal of the best-fitting plane to a subset of a tetra set.
static void	transformCoordinateSystem(PgGeometry geom, PdVector origin, PdVector[] basis, int nov, int noe) This method expresses a PgPointSet (given in standard basis) in a new coordinate system, given by a new origin and basis.
static void	transformToNormalPosition(PgElementSet geom) Translates and rotates a surface, such that its barycenter lies in the origin and the three eigenvectors of the covariance matrix are aligned to the axes.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

PnPCA

public PnPCA()

Method Detail

getCovarianceMatrix

public static PdMatrix getCovarianceMatrix(PgElementSet geom)

Compute the covariance matrix of an element set.

Parameters:

geom - The element set to analyze

Returns:

The covariance matrix of the element set

getCovarianceMatrix

public static PdMatrix getCovarianceMatrix(PgElementSet geom,
                                           PdVector center)

Compute the covariance matrix of an element set.

Parameters:

geom - The element set to analyze

center - The center of covariance analysis (expectation)

Returns:

The covariance matrix of the element set

getCovarianceMatrix

public static PdMatrix getCovarianceMatrix(PgElementSet geom,
                                           PdVector center,
                                           int[] indices)

Compute the covariance matrix of a subset of an element set.

Parameters:

geom - The element set to analyze

center - The center of covariance analysis (expectation)

indices - The indices of the subset

Returns:

The covariance matrix of the subset of the element set

getCovarianceMatrix

public static PdMatrix getCovarianceMatrix(PgTetraSet geom)

Compute the covariance matrix of a tetra set.

Parameters:

geom - The tetra set to analyze

Returns:

The covariance matrix of the tetra set

getCovarianceMatrix

public static PdMatrix getCovarianceMatrix(PgTetraSet geom,
                                           PdVector center)

Compute the covariance matrix of a tetra set.

Parameters:

geom - The tetra set to analyze

center - The center of covariance analysis (expectation)

Returns:

The covariance matrix of the tetra set

getCovarianceMatrix

public static PdMatrix getCovarianceMatrix(PgTetraSet geom,
                                           PdVector center,
                                           int[] indices)

Compute the covariance matrix of a tetra set.

Parameters:

geom - The tetra set to analyze

center - The center of covariance analysis (expectation)

indices - Set of elements, which are treated by this method

Returns:

The covariance matrix of the tetra set

getWeightedCovarianceMatrix

public static PdMatrix getWeightedCovarianceMatrix(PgTetraSet geom,
                                                   PgVectorField vf,
                                                   PdVector center,
                                                   int[] indices)

Compute the covariance matrix of a tetra set.

Parameters:

geom - The tetra set to analyze

center - The center of covariance analysis (expectation)

Returns:

The covariance matrix of the tetra set

getWeightedCovarianceMatrix

public static PdMatrix getWeightedCovarianceMatrix(PgTetraSet geom,
                                                   PdMatrix[] tensorField,
                                                   PdVector center,
                                                   int[] indices)

Compute the covariance matrix of a tetra set.

Parameters:

geom - The tetra set to analyze

tensorField -

center - The center of covariance analysis (expectation)

indices -

Returns:

The covariance matrix of the tetra set

getBarycenter

public static PdVector getBarycenter(PgElementSet geom)

Compute the barycenter of an element set.

Parameters:

geom - The element set

Returns:

The barycenter of the element set

getBarycenter

public static PdVector getBarycenter(PgTetraSet geom)

Compute the barycenter of an element set.

Parameters:

geom - The element set

Returns:

The barycenter of the element set

getBarycenter

public static PdVector getBarycenter(PgElementSet geom,
                                     int[] indices)

Compute the barycenter of a subset of an element set.

Parameters:

geom - The element set

indices - The indices of the subset

Returns:

The barycenter of the element set

getBarycenter

public static PdVector getBarycenter(PgTetraSet geom,
                                     int[] indices)

Compute the barycenter of a tetra set.

Parameters:

geom - The tetra set

indices - The indices of the subset

Returns:

The barycenter of the tetra set

getWeightedBarycenter

public static PdVector getWeightedBarycenter(PgTetraSet geom,
                                             PgVectorField vf,
                                             int[] indices)

Compute the barycenter of a tetra set.

Parameters:

geom - The tetra set

indices - The indices of the subset

Returns:

The barycenter of the tetra set

getNormal

public static PdVector getNormal(PgElementSet geom,
                                 PdVector center)

Compute the normal of the best-fitting plane to an element set. Together with the barycenter, this defines the best fitting plane.

Parameters:

geom - the element set

center - the barycenter of the element set

Returns:

the normal of the best-fitting plane

getNormal

public static PdVector getNormal(PgTetraSet geom,
                                 PdVector center)

Compute the normal of the best-fitting plane to a tetra set. Together with the barycenter, this defines the best fitting plane.

Parameters:

geom - the tetra set

center - the barycenter of the tetra set

Returns:

the normal of the best-fitting plane

getNormal

public static PdVector getNormal(PgElementSet geom,
                                 PdVector center,
                                 int[] indices)

Compute the normal of the best-fitting plane to a subset of an element set. Together with the barycenter, this defines the best fitting plane.

Parameters:

geom - the element set

center - the barycenter of the element set

indices - the indices of the subset

Returns:

The normal of the best-fitting plane

getNormal

public static PdVector getNormal(PgTetraSet geom,
                                 PdVector center,
                                 int[] indices)

Compute the normal of the best-fitting plane to a subset of a tetra set. Together with the barycenter, this defines the best fitting plane.

Parameters:

geom - the tetra set

center - the barycenter of the element set

indices - the indices of the subset

Returns:

The normal of the best-fitting plane

getWeightedNormal

public static PdVector getWeightedNormal(PgTetraSet geom,
                                         PgVectorField vf,
                                         PdVector center,
                                         int[] indices)

Compute the normal of the best-fitting plane to a subset of a tetra set. Together with the barycenter, this defines the best fitting plane.

Parameters:

geom - the tetra set

center - the barycenter of the tetra set

indices - the indices of the subset

Returns:

The normal of the best-fitting plane

getWeightedBarycenter

public static PdVector getWeightedBarycenter(PgTetraSet geom,
                                             PdMatrix[] tensorField,
                                             int[] indices)

Compute the barycenter of a tetra set.

Parameters:

geom - the tetra set

tensorField - specifies the weights

indices - the indices of the subset

Returns:

the barycenter of the tetra set

transformToNormalPosition

public static void transformToNormalPosition(PgElementSet geom)

Translates and rotates a surface, such that its barycenter lies in the origin and the three eigenvectors of the covariance matrix are aligned to the axes. The x-axis corresponds to the biggest eigenvalue, the z-axis to the smallest one.

Author:

Matthias Nieser, Martin Skrodzki

Version:

25.03.19, 2.00 revised (ms) Removed a bug that caused the method to not provide a unique result. 18.05.09, 1.00 created (mn)

transformCoordinateSystem

public static void transformCoordinateSystem(PgGeometry geom,
                                             PdVector origin,
                                             PdVector[] basis,
                                             int nov,
                                             int noe)

This method expresses a PgPointSet (given in standard basis) in a new coordinate system, given by a new origin and basis.

Parameters:

geom - The point cloud, which we want to express in new coordinates.

origin - The new location to which the coordinate system gets moved.

basis - The new basis for our new coordinate system.

nov - The number of vertices of the underlying geometry

noe - The number of elements of the underlying geometry

Version:

15.11.2017, 1.10 revised (ez) matrix m needs basis as columns 13.11.2017, 1.00 created (ez)