    001/* ===========================================================
    002 * Orson Charts : a 3D chart library for the Java(tm) platform
    003 * ===========================================================
    004 *
    005 * (C)opyright 2013-2016, by Object Refinery Limited.  All rights reserved.
    006 *
    007 * http://www.object-refinery.com/orsoncharts/index.html
    008 *
    009 * This program is free software: you can redistribute it and/or modify
    010 * it under the terms of the GNU General Public License as published by
    011 * the Free Software Foundation, either version 3 of the License, or
    012 * (at your option) any later version.
    013 *
    014 * This program is distributed in the hope that it will be useful,
    015 * but WITHOUT ANY WARRANTY; without even the implied warranty of
    016 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    017 * GNU General Public License for more details.
    018 *
    019 * You should have received a copy of the GNU General Public License
    020 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
    021 *
    022 * [Oracle and Java are registered trademarks of Oracle and/or its affiliates.
    023 * Other names may be trademarks of their respective owners.]
    024 *
    025 * If you do not wish to be bound by the terms of the GPL, an alternative
    026 * commercial license can be purchased.  For details, please see visit the
    027 * Orson Charts home page:
    028 *
    029 * http://www.object-refinery.com/orsoncharts/index.html
    030 *
    031 */
    032
    033package com.orsoncharts.graphics3d;
    034
    035/**
    036 * A collection of utility methods for 3D geometry.
    037 */
    038public class Utils3D {
    039
    040    private Utils3D() {
    041        // no need to instantiate this class
    042    }
    043
    044    /**
    045     * Returns the length of the vector v.
    046     *
    047     * @param v  the vector ({@code null} not permitted).
    048     *
    049     * @return The length.
    050     */
    051    public static double length(Point3D v) {
    052        return Math.sqrt(v.x * v.x + v.y * v.y + v.z * v.z);
    053    }
    054
    055    /**
    056     * Returns a new vector that is the normalised form of the specified
    057     * vector.
    058     *
    059     * @param v  the vector ({@code null} not permitted).
    060     *
    061     * @return The normalised form of the specified vector.
    062     *
    063     * @since 1.2
    064     */
    065    public static Point3D normalise(Point3D v) {
    066        double length = length(v);
    067        return new Point3D(v.x / length, v.y / length, v.z / length);
    068    }
    069
    070    /**
    071     * Returns the scalar product of two vectors.
    072     *
    073     * @param a  vector A ({@code null} not permitted).
    074     * @param b  vector B ({@code null} not permitted).
    075     *
    076     * @return The scalar product.
    077     */
    078    public static double scalarprod(Point3D a, Point3D b) {
    079        return a.x * b.x + a.y * b.y + a.z * b.z;
    080    }
    081
    082    /**
    083     * Returns the normal vector for the plane defined by three points.
    084     *
    085     * @param a  point A ({@code null} not permitted).
    086     * @param b  point B ({@code null} not permitted).
    087     * @param c  point C ({@code null} not permitted).
    088     *
    089     * @return The normal vector.
    090     */
    091    public static Point3D normal(Point3D a, Point3D b, Point3D c) {
    092        double ax = a.x - c.x;
    093        double ay = a.y - c.y;
    094        double az = a.z - c.z;
    095        double bx = b.x - c.x;
    096        double by = b.y - c.y;
    097        double bz = b.z - c.z;
    098        return new Point3D(ay * bz - az * by, az * bx - ax * bz,
    099                ax * by - ay * bx);
    100    }
    101
    102    /**
    103     * Returns the angle between the two vectors.
    104     *
    105     * @param a  vector A ({@code null} not permitted).
    106     * @param b  vector B ({@code null} not permitted).
    107     *
    108     * @return The (positive) angle in radians.
    109     */
    110    public static double angle(Point3D a, Point3D b) {
    111        double dp = a.x * b.x + a.y * b.y + a.z * b.z;
    112        double alen = length(a);
    113        double blen = length(b);
    114        double c = dp / (alen * blen);
    115        // rounding can cause abs(c) to be greater than one, let's sweep that
    116        // under the carpet...
    117        c = Math.max(-1.0, Math.min(1.0, c));
    118        return Math.acos(c);
    119    }
    120
    121}