org.apache.commons.math3.analysis.interpolation

Class InterpolatingMicrosphere

java.lang.Object

org.apache.commons.math3.analysis.interpolation.InterpolatingMicrosphere

Direct Known Subclasses:

InterpolatingMicrosphere2D

public class InterpolatingMicrosphere
extends java.lang.Object

Utility class for the MicrosphereProjectionInterpolator algorithm.

Since:

3.6

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
private static class	InterpolatingMicrosphere.Facet Microsphere "facet" (surface element).
private static class	InterpolatingMicrosphere.FacetData Data associated with each InterpolatingMicrosphere.Facet.

Field Summary

Fields

Modifier and Type	Field and Description
private double	background Background value.
private double	darkThreshold Lowest non-zero illumination.
private int	dimension Space dimension.
private double	maxDarkFraction Maximum fraction of the facets that can be dark.
private java.util.List<InterpolatingMicrosphere.Facet>	microsphere Microsphere.
private java.util.List<InterpolatingMicrosphere.FacetData>	microsphereData Microsphere data.
private int	size Number of surface elements.

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	InterpolatingMicrosphere(InterpolatingMicrosphere other) Copy constructor.
protected	InterpolatingMicrosphere(int dimension, int size, double maxDarkFraction, double darkThreshold, double background) Create an unitialiazed sphere.
	InterpolatingMicrosphere(int dimension, int size, double maxDarkFraction, double darkThreshold, double background, UnitSphereRandomVectorGenerator rand) Create a sphere from randomly sampled vectors.

Method Summary

Methods

Modifier and Type	Method and Description
protected void	add(double[] normal, boolean copy) Replace i-th facet of the microsphere.
private void	clear() Reset the all the facets data to zero.
InterpolatingMicrosphere	copy() Perform a copy.
int	getDimension() Get the space dimensionality.
int	getSize() Get the size of the sphere.
private void	illuminate(double[] sampleDirection, double sampleValue, double weight) Illumination.
private double	interpolate() Interpolation.
double	value(double[] point, double[][] samplePoints, double[] sampleValues, double exponent, double noInterpolationTolerance) Estimate the value at the requested location.

Methods inherited from class java.lang.Object

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

Field Detail

microsphere

private final java.util.List<InterpolatingMicrosphere.Facet> microsphere

Microsphere.

microsphereData

private final java.util.List<InterpolatingMicrosphere.FacetData> microsphereData

Microsphere data.

dimension

private final int dimension

Space dimension.

size

private final int size

Number of surface elements.

maxDarkFraction

private final double maxDarkFraction

Maximum fraction of the facets that can be dark.

darkThreshold

private final double darkThreshold

Lowest non-zero illumination.

background

private final double background

Background value.

Constructor Detail

InterpolatingMicrosphere

protected InterpolatingMicrosphere(int dimension,
                        int size,
                        double maxDarkFraction,
                        double darkThreshold,
                        double background)

Create an unitialiazed sphere. Sub-classes are responsible for calling the add(double[]) add method in order to initialize all the sphere's facets.

Parameters:

dimension - Dimension of the data space.

size - Number of surface elements of the sphere.

maxDarkFraction - Maximum fraction of the facets that can be dark. If the fraction of "non-illuminated" facets is larger, no estimation of the value will be performed, and the background value will be returned instead.

darkThreshold - Value of the illumination below which a facet is considered dark.

background - Value returned when the maxDarkFraction threshold is exceeded.

Throws:

NotStrictlyPositiveException - if dimension <= 0 or size <= 0.

NotPositiveException - if darkThreshold < 0.

OutOfRangeException - if maxDarkFraction does not belong to the interval [0, 1].

InterpolatingMicrosphere

public InterpolatingMicrosphere(int dimension,
                        int size,
                        double maxDarkFraction,
                        double darkThreshold,
                        double background,
                        UnitSphereRandomVectorGenerator rand)

Create a sphere from randomly sampled vectors.

Parameters:

dimension - Dimension of the data space.

size - Number of surface elements of the sphere.

rand - Unit vector generator for creating the microsphere.

maxDarkFraction - Maximum fraction of the facets that can be dark. If the fraction of "non-illuminated" facets is larger, no estimation of the value will be performed, and the background value will be returned instead.

darkThreshold - Value of the illumination below which a facet is considered dark.

background - Value returned when the maxDarkFraction threshold is exceeded.

Throws:

DimensionMismatchException - if the size of the generated vectors does not match the dimension set in the constructor.

NotStrictlyPositiveException - if dimension <= 0 or size <= 0.

NotPositiveException - if darkThreshold < 0.

OutOfRangeException - if maxDarkFraction does not belong to the interval [0, 1].

InterpolatingMicrosphere

protected InterpolatingMicrosphere(InterpolatingMicrosphere other)

Copy constructor.

Parameters:

other - Instance to copy.

Method Detail

copy

public InterpolatingMicrosphere copy()

Perform a copy.

Returns:

a copy of this instance.

getDimension

public int getDimension()

Get the space dimensionality.

Returns:

the number of space dimensions.

getSize

public int getSize()

Get the size of the sphere.

Returns:

the number of surface elements of the microspshere.

value

public double value(double[] point,
           double[][] samplePoints,
           double[] sampleValues,
           double exponent,
           double noInterpolationTolerance)

Estimate the value at the requested location. This microsphere is placed at the given point, contribution of the given samplePoints to each sphere facet is computed (illumination) and the interpolation is performed (integration of the illumination).

Parameters:

point - Interpolation point.

samplePoints - Sampling data points.

sampleValues - Sampling data values at the corresponding samplePoints.

exponent - Exponent used in the power law that computes the weights (distance dimming factor) of the sample data.

noInterpolationTolerance - When the distance between the point and one of the samplePoints is less than this value, no interpolation will be performed, and the value of the sample will just be returned.

Returns:

the estimated value at the given point.

Throws:

NotPositiveException - if exponent < 0.

add

protected void add(double[] normal,
       boolean copy)

Replace i-th facet of the microsphere. Method for initializing the microsphere facets.

Parameters:

normal - Facet's normal vector.

copy - Whether to copy the given array.

Throws:

DimensionMismatchException - if the length of n does not match the space dimension.

MaxCountExceededException - if the method has been called more times than the size of the sphere.

interpolate

private double interpolate()

Interpolation.

Returns:

the value estimated from the current illumination of the microsphere.

illuminate

private void illuminate(double[] sampleDirection,
              double sampleValue,
              double weight)

Illumination.

Parameters:

sampleDirection - Vector whose origin is at the interpolation point and tail is at the sample location.

sampleValue - Data value of the sample.

weight - Weight.

clear

private void clear()

Reset the all the facets data to zero.