Android Open Source - Schooner-3D Quaternion

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License

The source code is released under:

Apache License

Java Source Code

/*
 * Copyright 2012 Dan Mercer//from  w ww.java2s .  c o  m
 * 
 * Licensed 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 com.supermercerbros.gameengine.math;

import com.supermercerbros.gameengine.collision.Point;

/**
 * Represents a rotation. (Although, technically speaking, a quaternion is a
 * four-component complex number with three imaginary parts.) Given an
 * axis-angle rotation, the corresponding quaternion is equal to
 * <code>{cos(theta/2), axis.x * sin(theta/2), axis.y * sin(theta/2), axis.z * sin(theta/2)}</code>
 * . Like {@link Point} objects, Quaternion objects are immutable.
 */
public class Quaternion {
  /**
   * The W-component of the Quaternion.
   */
  final float w;
  /**
   * The X-component of the Quaternion.
   */
  final float x;
  /**
   * The Y-component of the Quaternion.
   */
  final float y;
  /**
   * The Z-component of the Quaternion.
   */
  final float z;
  
  /**
   * Creates a new Quaternion with the given components.
   * 
   * @param w
   *            The W-component of the Quaternion.
   * @param x
   *            The X-component of the Quaternion.
   * @param y
   *            The Y-component of the Quaternion.
   * @param z
   *            The Z-component of the Quaternion.
   */
  public Quaternion(float w, float x, float y, float z) {
    this.w = w;
    this.x = x;
    this.y = y;
    this.z = z;
  }
  
  /**
   * Applies the rotation represented by this Quaternion to the given Point.
   * 
   * @param p
   *            The Point to rotate.
   * @return A new Point at the location of the rotated point.
   * 
   * @see <a
   *      href=http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation
   *      #Using_quaternion_rotations>Quaternion Rotations (Wikipedia)</a>
   */
  public Point rotate(Point p) {
    final float xx = x*x, yy = y*y, zz = z*z;
    final float xy = x*y, yz = y*z, xz = x*z;
    final float xw = x*w, yw = y*w, zw = z*w;
    
    final float rX = p.x * (1 - 2*yy - 2*zz) + p.y * (2*xy - 2*zw) + p.z * (2*xz + 2*yw);
    final float rY = p.x * (2*xy + 2*zw) + p.y * (1 - 2*xx - 2*zz) + p.z * (2*yz - 2*xw);
    final float rZ = p.x * (2*xz - 2*yw) + p.y * (2*yz + 2*xw) + p.z * (1 - 2*xx - 2*yy);
    
    return new Point(rX, rY, rZ);
  }
  
  /**
   * Applies the rotation represented by this Quaternion to the given point.
   * 
   * @param pX The x-coordinate of the Point to rotate.
   * @param pY The y-coordinate of the Point to rotate.
   * @param pZ The z-coordinate of the Point to rotate.
   * 
   * @return A new Point at the location of the rotated point.
   * 
   * @see <a
   *      href=http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation
   *      #Using_quaternion_rotations>Quaternion Rotations (Wikipedia)</a>
   */
  public Point rotate(float pX, float pY, float pZ) {
    final float xx = x*x, yy = y*y, zz = z*z;
    final float xy = x*y, yz = y*z, xz = x*z;
    final float xw = x*w, yw = y*w, zw = z*w;
    
    final float rX = pX * (1 - 2*yy - 2*zz) + pY * (2*xy - 2*zw) + pZ * (2*xz + 2*yw);
    final float rY = pX * (2*xy + 2*zw) + pY * (1 - 2*xx - 2*zz) + pZ * (2*yz - 2*xw);
    final float rZ = pX * (2*xz - 2*yw) + pY * (2*yz + 2*xw) + pZ * (1 - 2*xx - 2*yy);
    
    return new Point(rX, rY, rZ);
  }
  
  public static Point rotate(float qW, float qX, float qY, float qZ, float pX, float pY, float pZ) {
    final float xx = qX*qX, yy = qY*qY, zz = qZ*qZ;
    final float xy = qX*qY, yz = qY*qZ, xz = qX*qZ;
    final float xw = qX*qW, yw = qY*qW, zw = qZ*qW;
    
    final float rX = pX * (1 - 2*yy - 2*zz) + pY * (2*xy - 2*zw) + pZ * (2*xz + 2*yw);
    final float rY = pX * (2*xy + 2*zw) + pY * (1 - 2*xx - 2*zz) + pZ * (2*yz - 2*xw);
    final float rZ = pX * (2*xz - 2*yw) + pY * (2*yz + 2*xw) + pZ * (1 - 2*xx - 2*yy);
    
    return new Point(rX, rY, rZ);
  }
}

Java Source Code List

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