org.bonej.ops.ellipsoid.EllipsoidPoints.java Source code

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Here is the source code for org.bonej.ops.ellipsoid.EllipsoidPoints.java

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/*
BSD 2-Clause License
Copyright (c) 2018, Michael Doube, Richard Domander, Alessandro Felder
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this
  list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice,
  this list of conditions and the following disclaimer in the documentation
  and/or other materials provided with the distribution.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/

package org.bonej.ops.ellipsoid;

import static java.util.stream.Collectors.toList;
import static java.util.stream.Stream.generate;

import java.util.Arrays;
import java.util.List;
import java.util.Random;
import java.util.function.Function;
import java.util.function.Predicate;
import java.util.function.Supplier;
import java.util.stream.DoubleStream;

import net.imagej.ops.Contingent;
import net.imagej.ops.Op;
import net.imagej.ops.special.function.AbstractBinaryFunctionOp;

import org.apache.commons.math3.random.MersenneTwister;
import org.apache.commons.math3.random.UnitSphereRandomVectorGenerator;
import org.joml.Vector3d;
import org.scijava.plugin.Plugin;

/**
 * Generates isotropically located random points on an ellipsoid surface.
 *
 * @author Richard Domander
 */
@Plugin(type = Op.class)
public class EllipsoidPoints extends AbstractBinaryFunctionOp<double[], Long, List<Vector3d>>
        implements Contingent {

    private static final Random rng = new Random();
    private static UnitSphereRandomVectorGenerator sphereRng = new UnitSphereRandomVectorGenerator(3);
    /** Smallest radius of the ellipsoid (x) */
    private double a;
    /** Second radius of the ellipsoid (y) */
    private double b;
    /** Largest radius of the ellipsoid (z) */
    private double c;

    /**
     * Creates random points on an ellipsoid surface.
     *
     * @param radii the radii of the ellipsoid. They'll be sorted in ascending
     *          order.
     * @param n number of points to be created.
     * @return ellipsoid points.
     */
    @Override
    public List<Vector3d> calculate(final double[] radii, final Long n) {
        Arrays.sort(radii);
        a = radii[0];
        b = radii[1];
        c = radii[2];
        return sampleEllipsoidPoints(n);
    }

    @Override
    public boolean conforms() {
        final double[] radii = in1();
        final Long n = in2();
        return n >= 0 && radii.length == 3 && Arrays.stream(radii).allMatch(r -> r > 0 && Double.isFinite(r));
    }

    /**
     * Calculates the &mu;-factor of a point.
     *
     * @param v a point on a unit sphere surface.
     * @return inverse ratio of ellipsoid surface area around given point.
     */
    private double mu(final Vector3d v) {
        final DoubleStream terms = DoubleStream.of(a * c * v.y, a * b * v.z, b * c * v.x);
        final double sqSum = terms.map(x -> x * x).sum();
        return Math.sqrt(sqSum);
    }

    private List<Vector3d> sampleEllipsoidPoints(final long n) {
        final Supplier<Vector3d> spherePoint = () -> {
            final double[] v = sphereRng.nextVector();
            return new Vector3d(v[0], v[1], v[2]);
        };
        // Probability function to keep a sphere point
        final double muMax = b * c;
        final Predicate<Vector3d> p = v -> rng.nextDouble() <= mu(v) / muMax;
        // Mapping function from sphere to ellipsoid
        final Function<Vector3d, Vector3d> toEllipsoid = v -> new Vector3d(a * v.x, b * v.y, c * v.z);
        return generate(spherePoint).filter(p).limit(n).map(toEllipsoid).collect(toList());
    }

    /**
     * Sets the seed of the random generators used in point creation.
     * <p>
     * Setting a constant seed makes testing easier.
     * </p>
     *
     * @param seed the seed number.
     * @see Random#setSeed(long)
     * @see MersenneTwister#MersenneTwister(long)
     */
    static void setSeed(final long seed) {
        rng.setSeed(seed);
        sphereRng = new UnitSphereRandomVectorGenerator(3, new MersenneTwister(seed));
    }
}