edu.stanford.math.plex4.examples

Class PointCloudExamples

java.lang.Object

edu.stanford.math.plex4.examples.PointCloudExamples

public class PointCloudExamples
extends java.lang.Object

This static class contains various functions which produce examples of point cloud data sets.

Author:

Andrew Tausz

Constructor Summary

Constructors

Constructor and Description
PointCloudExamples()

Method Summary

Methods

Modifier and Type	Method and Description
static double[][]	getAnnulusVertices(int width, int length)
static double[][]	getDisjointPatches(int n)
static double[][]	getEquispacedCirclePoints(int n) This function returns a point set containing n equally spaced points on a circle.
static double[][]	getGaussianPoints(int n, int d) This function returns n points distributed to a standard Gaussian distribution in d-dimensional Euclidean space.
static double[][]	getHouseExample() This produces the house example in the tutorial by Henry Adams.
static double[][]	getIcosahedronVertices()
static double[][]	getOctahedronVertices() This function returns the vertices of an octahedron.
static double[][]	getRandomCirclePoints(int n) This function returns a point set containing n randomly selected points, ordered clockwise on a circle.
static double[][]	getRandomFigure8Points(int n) This function returns randomly generated points on a figure-8 in the plane.
static double[][]	getRandomSpherePoints(int n, int d) This function returns n uniformly random point on the d-dimensional sphere as a subset of R^{d+1}.
static double[][]	getRandomSphereProductPoints(int numPoints, int sphereDimension, int numFactors) This function returns uniformly distributed points on the space S^k x ...
static double[][]	getRandomTorusPoints(int n, double r, double R) This function returns non-uniformly generated points on the torus in R^3.
static double[][]	getRandomTrefoilKnotPoints(int n)
static double[][]	getSquare() This function produces a square in the plane.
static double[][]	getTetrahedronVertices() This function returns the vertices of an tetrahedron.

Methods inherited from class java.lang.Object

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

Constructor Detail

PointCloudExamples

public PointCloudExamples()

Method Detail

getHouseExample

public static double[][] getHouseExample()

This produces the house example in the tutorial by Henry Adams.

Returns:

the requested point cloud

getSquare

public static double[][] getSquare()

This function produces a square in the plane.

Returns:

the requested point cloud

getEquispacedCirclePoints

public static double[][] getEquispacedCirclePoints(int n)

This function returns a point set containing n equally spaced points on a circle.

Parameters:

n -

Returns:

the requested point cloud

getRandomCirclePoints

public static double[][] getRandomCirclePoints(int n)

This function returns a point set containing n randomly selected points, ordered clockwise on a circle.

Parameters:

n -

Returns:

the requested point cloud

getOctahedronVertices

public static double[][] getOctahedronVertices()

This function returns the vertices of an octahedron.

Returns:

the requested point cloud

getTetrahedronVertices

public static double[][] getTetrahedronVertices()

This function returns the vertices of an tetrahedron.

Returns:

the requested point cloud

getAnnulusVertices

public static double[][] getAnnulusVertices(int width,
                            int length)

getIcosahedronVertices

public static double[][] getIcosahedronVertices()

getRandomSpherePoints

public static double[][] getRandomSpherePoints(int n,
                               int d)

This function returns n uniformly random point on the d-dimensional sphere as a subset of R^{d+1}.

Parameters:

n - the number of points to generate

d - the dimension of the sphere to generate on

Returns:

n points in (d+1)-dimensional Euclidean space uniformly distributed on the d-sphere

getGaussianPoints

public static double[][] getGaussianPoints(int n,
                           int d)

This function returns n points distributed to a standard Gaussian distribution in d-dimensional Euclidean space.

Parameters:

n - the number of points to generate

d - the dimension of the space to generate in

Returns:

n Gaussian points in R^d

getRandomTorusPoints

public static double[][] getRandomTorusPoints(int n,
                              double r,
                              double R)

This function returns non-uniformly generated points on the torus in R^3.

Parameters:

n - the number of points to generate

r - the inner radius

R - the outer radius

Returns:

randomly generated points on the torus in R^3

getRandomTrefoilKnotPoints

public static double[][] getRandomTrefoilKnotPoints(int n)

getRandomSphereProductPoints

public static double[][] getRandomSphereProductPoints(int numPoints,
                                      int sphereDimension,
                                      int numFactors)

This function returns uniformly distributed points on the space S^k x ... x S^k. Special cases of this include the 2-torus S^1 x S^1 in R^4, as well as the sphere S^k.

Parameters:

numPoints - the number of points to generate

sphereDimension - the sphere dimension (ie. the k in S^k x ... x S^k)

numFactors - the number of factors in the product S^k x ... x S^k

Returns:

uniformly generated points on the set S^k x ... x S^k

getRandomFigure8Points

public static double[][] getRandomFigure8Points(int n)

This function returns randomly generated points on a figure-8 in the plane. This consists of two circles - one translated up by 1 unit, and the other translated down by 1 unit.

Parameters:

n - the number of points to generate

Returns:

randomly generated points on a figure-8.

getDisjointPatches

public static double[][] getDisjointPatches(int n)