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Java example source code file (Quaternion.java)

This example Java source code file (Quaternion.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

dimensionmismatchexception, identity, override, quaternion, serializable, string, stringbuilder, zero

The Quaternion.java Java example source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package org.apache.commons.math3.complex;

import java.io.Serializable;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathUtils;
import org.apache.commons.math3.util.Precision;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.ZeroException;
import org.apache.commons.math3.exception.util.LocalizedFormats;

/**
 * This class implements <a href="http://mathworld.wolfram.com/Quaternion.html">
 * quaternions</a> (Hamilton's hypercomplex numbers).
 * <br/>
 * Instance of this class are guaranteed to be immutable.
 *
 * @since 3.1
 */
public final class Quaternion implements Serializable {
    /** Identity quaternion. */
    public static final Quaternion IDENTITY = new Quaternion(1, 0, 0, 0);
    /** Zero quaternion. */
    public static final Quaternion ZERO = new Quaternion(0, 0, 0, 0);
    /** i */
    public static final Quaternion I = new Quaternion(0, 1, 0, 0);
    /** j */
    public static final Quaternion J = new Quaternion(0, 0, 1, 0);
    /** k */
    public static final Quaternion K = new Quaternion(0, 0, 0, 1);

    /** Serializable version identifier. */
    private static final long serialVersionUID = 20092012L;

    /** First component (scalar part). */
    private final double q0;
    /** Second component (first vector part). */
    private final double q1;
    /** Third component (second vector part). */
    private final double q2;
    /** Fourth component (third vector part). */
    private final double q3;

    /**
     * Builds a quaternion from its components.
     *
     * @param a Scalar component.
     * @param b First vector component.
     * @param c Second vector component.
     * @param d Third vector component.
     */
    public Quaternion(final double a,
                      final double b,
                      final double c,
                      final double d) {
        this.q0 = a;
        this.q1 = b;
        this.q2 = c;
        this.q3 = d;
    }

    /**
     * Builds a quaternion from scalar and vector parts.
     *
     * @param scalar Scalar part of the quaternion.
     * @param v Components of the vector part of the quaternion.
     *
     * @throws DimensionMismatchException if the array length is not 3.
     */
    public Quaternion(final double scalar,
                      final double[] v)
        throws DimensionMismatchException {
        if (v.length != 3) {
            throw new DimensionMismatchException(v.length, 3);
        }
        this.q0 = scalar;
        this.q1 = v[0];
        this.q2 = v[1];
        this.q3 = v[2];
    }

    /**
     * Builds a pure quaternion from a vector (assuming that the scalar
     * part is zero).
     *
     * @param v Components of the vector part of the pure quaternion.
     */
    public Quaternion(final double[] v) {
        this(0, v);
    }

    /**
     * Returns the conjugate quaternion of the instance.
     *
     * @return the conjugate quaternion
     */
    public Quaternion getConjugate() {
        return new Quaternion(q0, -q1, -q2, -q3);
    }

    /**
     * Returns the Hamilton product of two quaternions.
     *
     * @param q1 First quaternion.
     * @param q2 Second quaternion.
     * @return the product {@code q1} and {@code q2}, in that order.
     */
    public static Quaternion multiply(final Quaternion q1, final Quaternion q2) {
        // Components of the first quaternion.
        final double q1a = q1.getQ0();
        final double q1b = q1.getQ1();
        final double q1c = q1.getQ2();
        final double q1d = q1.getQ3();

        // Components of the second quaternion.
        final double q2a = q2.getQ0();
        final double q2b = q2.getQ1();
        final double q2c = q2.getQ2();
        final double q2d = q2.getQ3();

        // Components of the product.
        final double w = q1a * q2a - q1b * q2b - q1c * q2c - q1d * q2d;
        final double x = q1a * q2b + q1b * q2a + q1c * q2d - q1d * q2c;
        final double y = q1a * q2c - q1b * q2d + q1c * q2a + q1d * q2b;
        final double z = q1a * q2d + q1b * q2c - q1c * q2b + q1d * q2a;

        return new Quaternion(w, x, y, z);
    }

    /**
     * Returns the Hamilton product of the instance by a quaternion.
     *
     * @param q Quaternion.
     * @return the product of this instance with {@code q}, in that order.
     */
    public Quaternion multiply(final Quaternion q) {
        return multiply(this, q);
    }

    /**
     * Computes the sum of two quaternions.
     *
     * @param q1 Quaternion.
     * @param q2 Quaternion.
     * @return the sum of {@code q1} and {@code q2}.
     */
    public static Quaternion add(final Quaternion q1,
                                 final Quaternion q2) {
        return new Quaternion(q1.getQ0() + q2.getQ0(),
                              q1.getQ1() + q2.getQ1(),
                              q1.getQ2() + q2.getQ2(),
                              q1.getQ3() + q2.getQ3());
    }

    /**
     * Computes the sum of the instance and another quaternion.
     *
     * @param q Quaternion.
     * @return the sum of this instance and {@code q}
     */
    public Quaternion add(final Quaternion q) {
        return add(this, q);
    }

    /**
     * Subtracts two quaternions.
     *
     * @param q1 First Quaternion.
     * @param q2 Second quaternion.
     * @return the difference between {@code q1} and {@code q2}.
     */
    public static Quaternion subtract(final Quaternion q1,
                                      final Quaternion q2) {
        return new Quaternion(q1.getQ0() - q2.getQ0(),
                              q1.getQ1() - q2.getQ1(),
                              q1.getQ2() - q2.getQ2(),
                              q1.getQ3() - q2.getQ3());
    }

    /**
     * Subtracts a quaternion from the instance.
     *
     * @param q Quaternion.
     * @return the difference between this instance and {@code q}.
     */
    public Quaternion subtract(final Quaternion q) {
        return subtract(this, q);
    }

    /**
     * Computes the dot-product of two quaternions.
     *
     * @param q1 Quaternion.
     * @param q2 Quaternion.
     * @return the dot product of {@code q1} and {@code q2}.
     */
    public static double dotProduct(final Quaternion q1,
                                    final Quaternion q2) {
        return q1.getQ0() * q2.getQ0() +
            q1.getQ1() * q2.getQ1() +
            q1.getQ2() * q2.getQ2() +
            q1.getQ3() * q2.getQ3();
    }

    /**
     * Computes the dot-product of the instance by a quaternion.
     *
     * @param q Quaternion.
     * @return the dot product of this instance and {@code q}.
     */
    public double dotProduct(final Quaternion q) {
        return dotProduct(this, q);
    }

    /**
     * Computes the norm of the quaternion.
     *
     * @return the norm.
     */
    public double getNorm() {
        return FastMath.sqrt(q0 * q0 +
                             q1 * q1 +
                             q2 * q2 +
                             q3 * q3);
    }

    /**
     * Computes the normalized quaternion (the versor of the instance).
     * The norm of the quaternion must not be zero.
     *
     * @return a normalized quaternion.
     * @throws ZeroException if the norm of the quaternion is zero.
     */
    public Quaternion normalize() {
        final double norm = getNorm();

        if (norm < Precision.SAFE_MIN) {
            throw new ZeroException(LocalizedFormats.NORM, norm);
        }

        return new Quaternion(q0 / norm,
                              q1 / norm,
                              q2 / norm,
                              q3 / norm);
    }

    /**
     * {@inheritDoc}
     */
    @Override
    public boolean equals(Object other) {
        if (this == other) {
            return true;
        }
        if (other instanceof Quaternion) {
            final Quaternion q = (Quaternion) other;
            return q0 == q.getQ0() &&
                q1 == q.getQ1() &&
                q2 == q.getQ2() &&
                q3 == q.getQ3();
        }

        return false;
    }

    /**
     * {@inheritDoc}
     */
    @Override
    public int hashCode() {
        // "Effective Java" (second edition, p. 47).
        int result = 17;
        for (double comp : new double[] { q0, q1, q2, q3 }) {
            final int c = MathUtils.hash(comp);
            result = 31 * result + c;
        }
        return result;
    }

    /**
     * Checks whether this instance is equal to another quaternion
     * within a given tolerance.
     *
     * @param q Quaternion with which to compare the current quaternion.
     * @param eps Tolerance.
     * @return {@code true} if the each of the components are equal
     * within the allowed absolute error.
     */
    public boolean equals(final Quaternion q,
                          final double eps) {
        return Precision.equals(q0, q.getQ0(), eps) &&
            Precision.equals(q1, q.getQ1(), eps) &&
            Precision.equals(q2, q.getQ2(), eps) &&
            Precision.equals(q3, q.getQ3(), eps);
    }

    /**
     * Checks whether the instance is a unit quaternion within a given
     * tolerance.
     *
     * @param eps Tolerance (absolute error).
     * @return {@code true} if the norm is 1 within the given tolerance,
     * {@code false} otherwise
     */
    public boolean isUnitQuaternion(double eps) {
        return Precision.equals(getNorm(), 1d, eps);
    }

    /**
     * Checks whether the instance is a pure quaternion within a given
     * tolerance.
     *
     * @param eps Tolerance (absolute error).
     * @return {@code true} if the scalar part of the quaternion is zero.
     */
    public boolean isPureQuaternion(double eps) {
        return FastMath.abs(getQ0()) <= eps;
    }

    /**
     * Returns the polar form of the quaternion.
     *
     * @return the unit quaternion with positive scalar part.
     */
    public Quaternion getPositivePolarForm() {
        if (getQ0() < 0) {
            final Quaternion unitQ = normalize();
            // The quaternion of rotation (normalized quaternion) q and -q
            // are equivalent (i.e. represent the same rotation).
            return new Quaternion(-unitQ.getQ0(),
                                  -unitQ.getQ1(),
                                  -unitQ.getQ2(),
                                  -unitQ.getQ3());
        } else {
            return this.normalize();
        }
    }

    /**
     * Returns the inverse of this instance.
     * The norm of the quaternion must not be zero.
     *
     * @return the inverse.
     * @throws ZeroException if the norm (squared) of the quaternion is zero.
     */
    public Quaternion getInverse() {
        final double squareNorm = q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3;
        if (squareNorm < Precision.SAFE_MIN) {
            throw new ZeroException(LocalizedFormats.NORM, squareNorm);
        }

        return new Quaternion(q0 / squareNorm,
                              -q1 / squareNorm,
                              -q2 / squareNorm,
                              -q3 / squareNorm);
    }

    /**
     * Gets the first component of the quaternion (scalar part).
     *
     * @return the scalar part.
     */
    public double getQ0() {
        return q0;
    }

    /**
     * Gets the second component of the quaternion (first component
     * of the vector part).
     *
     * @return the first component of the vector part.
     */
    public double getQ1() {
        return q1;
    }

    /**
     * Gets the third component of the quaternion (second component
     * of the vector part).
     *
     * @return the second component of the vector part.
     */
    public double getQ2() {
        return q2;
    }

    /**
     * Gets the fourth component of the quaternion (third component
     * of the vector part).
     *
     * @return the third component of the vector part.
     */
    public double getQ3() {
        return q3;
    }

    /**
     * Gets the scalar part of the quaternion.
     *
     * @return the scalar part.
     * @see #getQ0()
     */
    public double getScalarPart() {
        return getQ0();
    }

    /**
     * Gets the three components of the vector part of the quaternion.
     *
     * @return the vector part.
     * @see #getQ1()
     * @see #getQ2()
     * @see #getQ3()
     */
    public double[] getVectorPart() {
        return new double[] { getQ1(), getQ2(), getQ3() };
    }

    /**
     * Multiplies the instance by a scalar.
     *
     * @param alpha Scalar factor.
     * @return a scaled quaternion.
     */
    public Quaternion multiply(final double alpha) {
        return new Quaternion(alpha * q0,
                              alpha * q1,
                              alpha * q2,
                              alpha * q3);
    }

    /**
     * {@inheritDoc}
     */
    @Override
    public String toString() {
        final String sp = " ";
        final StringBuilder s = new StringBuilder();
        s.append("[")
            .append(q0).append(sp)
            .append(q1).append(sp)
            .append(q2).append(sp)
            .append(q3)
            .append("]");

        return s.toString();
    }
}

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