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Java™ Binding for the OpenGL® API
/**
* Copyright 2010 JogAmp Community. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without modification, are
* permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice, this list of
* conditions and the following disclaimer.
*
* 2. 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 JogAmp Community ``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 JogAmp Community 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.
*
* The views and conclusions contained in the software and documentation are those of the
* authors and should not be interpreted as representing official policies, either expressed
* or implied, of JogAmp Community.
*/
package com.jogamp.opengl.math;
public class Quaternion {
protected float x, y, z, w;
public Quaternion() {
setIdentity();
}
public Quaternion(Quaternion q) {
x = q.x;
y = q.y;
z = q.z;
w = q.w;
}
public Quaternion(float x, float y, float z, float w) {
this.x = x;
this.y = y;
this.z = z;
this.w = w;
}
/**
* Constructor to create a rotation based quaternion from two vectors
*
* @param vector1
* @param vector2
*/
public Quaternion(float[] vector1, float[] vector2) {
final float theta = FloatUtil.acos(VectorUtil.dot(vector1, vector2));
final float[] cross = VectorUtil.cross(vector1, vector2);
fromAxis(cross, theta);
}
/***
* Constructor to create a rotation based quaternion from axis vector and angle
* @param vector axis vector
* @param angle rotation angle (rads)
* @see #fromAxis(float[], float)
*/
public Quaternion(float[] vector, float angle) {
fromAxis(vector, angle);
}
/***
* Initialize this quaternion with given axis vector and rotation angle
*
* @param vector axis vector
* @param angle rotation angle (rads)
*/
public void fromAxis(float[] vector, float angle) {
final float halfangle = angle * 0.5f;
final float sin = FloatUtil.sin(halfangle);
final float[] nv = VectorUtil.normalize(vector);
x = (nv[0] * sin);
y = (nv[1] * sin);
z = (nv[2] * sin);
w = FloatUtil.cos(halfangle);
}
/**
* Transform the rotational quaternion to axis based rotation angles
*
* @return new float[4] with ,theta,Rx,Ry,Rz
*/
public float[] toAxis() {
final float[] vec = new float[4];
final float scale = FloatUtil.sqrt(x * x + y * y + z * z);
vec[0] = FloatUtil.acos(w) * 2.0f;
vec[1] = x / scale;
vec[2] = y / scale;
vec[3] = z / scale;
return vec;
}
public float getW() {
return w;
}
public void setW(float w) {
this.w = w;
}
public float getX() {
return x;
}
public void setX(float x) {
this.x = x;
}
public float getY() {
return y;
}
public void setY(float y) {
this.y = y;
}
public float getZ() {
return z;
}
public void setZ(float z) {
this.z = z;
}
/**
* Add a quaternion
*
* @param q quaternion
*/
public void add(Quaternion q) {
x += q.x;
y += q.y;
z += q.z;
}
/**
* Subtract a quaternion
*
* @param q quaternion
*/
public void subtract(Quaternion q) {
x -= q.x;
y -= q.y;
z -= q.z;
}
/**
* Divide a quaternion by a constant
*
* @param n a float to divide by
*/
public void divide(float n) {
x /= n;
y /= n;
z /= n;
}
/**
* Multiply this quaternion by the param quaternion
*
* @param q a quaternion to multiply with
*/
public void mult(Quaternion q) {
final float w1 = w * q.w - x * q.x - y * q.y - z * q.z;
final float x1 = w * q.x + x * q.w + y * q.z - z * q.y;
final float y1 = w * q.y - x * q.z + y * q.w + z * q.x;
final float z1 = w * q.z + x * q.y - y * q.x + z * q.w;
w = w1;
x = x1;
y = y1;
z = z1;
}
/**
* Multiply a quaternion by a constant
*
* @param n a float constant
*/
public void mult(float n) {
x *= n;
y *= n;
z *= n;
}
/***
* Rotate given vector by this quaternion
*
* @param vector input vector
* @return rotated vector
*/
public float[] mult(float[] vector) {
// TODO : optimize
final float[] res = new float[3];
final Quaternion a = new Quaternion(vector[0], vector[1], vector[2], 0.0f);
final Quaternion b = new Quaternion(this);
final Quaternion c = new Quaternion(this);
b.inverse();
a.mult(b);
c.mult(a);
res[0] = c.x;
res[1] = c.y;
res[2] = c.z;
return res;
}
/**
* Normalize a quaternion required if to be used as a rotational quaternion
*/
public void normalize() {
final float norme = (float) FloatUtil.sqrt(w * w + x * x + y * y + z * z);
if (norme == 0.0f) {
setIdentity();
} else {
final float recip = 1.0f / norme;
w *= recip;
x *= recip;
y *= recip;
z *= recip;
}
}
/**
* Invert the quaternion If rotational, will produce a the inverse rotation
*/
public void inverse() {
final float norm = w * w + x * x + y * y + z * z;
final float recip = 1.0f / norm;
w *= recip;
x = -1 * x * recip;
y = -1 * y * recip;
z = -1 * z * recip;
}
/**
* Transform this quaternion to a 4x4 column matrix representing the
* rotation
*
* @return new float[16] column matrix 4x4
*/
public float[] toMatrix() {
final float[] matrix = new float[16];
matrix[0] = 1.0f - 2 * y * y - 2 * z * z;
matrix[1] = 2 * x * y + 2 * w * z;
matrix[2] = 2 * x * z - 2 * w * y;
matrix[3] = 0;
matrix[4] = 2 * x * y - 2 * w * z;
matrix[5] = 1.0f - 2 * x * x - 2 * z * z;
matrix[6] = 2 * y * z + 2 * w * x;
matrix[7] = 0;
matrix[8] = 2 * x * z + 2 * w * y;
matrix[9] = 2 * y * z - 2 * w * x;
matrix[10] = 1.0f - 2 * x * x - 2 * y * y;
matrix[11] = 0;
matrix[12] = 0;
matrix[13] = 0;
matrix[14] = 0;
matrix[15] = 1;
return matrix;
}
/**
* Set this quaternion from a Sphereical interpolation of two param
* quaternion, used mostly for rotational animation.
*
* Note: Method does not normalize this quaternion!
*
*
* See http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/
* quaternions/slerp/
*
*
* @param a initial quaternion
* @param b target quaternion
* @param t float between 0 and 1 representing interp.
*/
public void slerp(Quaternion a, Quaternion b, float t) {
final float cosom = a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w;
final float t1 = 1.0f - t;
// if the two quaternions are close, just use linear interpolation
if (cosom >= 0.95f) {
x = a.x * t1 + b.x * t;
y = a.y * t1 + b.y * t;
z = a.z * t1 + b.z * t;
w = a.w * t1 + b.w * t;
return;
}
// the quaternions are nearly opposite, we can pick any axis normal to
// a,b
// to do the rotation
if (cosom <= -0.99f) {
x = 0.5f * (a.x + b.x);
y = 0.5f * (a.y + b.y);
z = 0.5f * (a.z + b.z);
w = 0.5f * (a.w + b.w);
return;
}
// cosom is now withion range of acos, do a SLERP
final float sinom = FloatUtil.sqrt(1.0f - cosom * cosom);
final float omega = FloatUtil.acos(cosom);
final float scla = FloatUtil.sin(t1 * omega) / sinom;
final float sclb = FloatUtil.sin(t * omega) / sinom;
x = a.x * scla + b.x * sclb;
y = a.y * scla + b.y * sclb;
z = a.z * scla + b.z * sclb;
w = a.w * scla + b.w * sclb;
}
/**
* Check if this quaternion is empty, ie (0,0,0,1)
*
* @return true if empty, false otherwise
* @deprecated use {@link #isIdentity()} instead
*/
@Deprecated
public boolean isEmpty() {
if (w == 1 && x == 0 && y == 0 && z == 0)
return true;
return false;
}
/**
* Check if this quaternion represents an identity matrix, for rotation.
*
* @return true if it is an identity rep., false otherwise
*/
public boolean isIdentity() {
return w == 1 && x == 0 && y == 0 && z == 0;
}
/***
* Set this quaternion to identity (x=0,y=0,z=0,w=1)
*/
public void setIdentity() {
x = y = z = 0;
w = 1;
}
/**
* compute the quaternion from a 3x3 column matrix
*
* @param m 3x3 column matrix
*/
public void setFromMatrix(float[] m) {
final float T = m[0] + m[4] + m[8] + 1;
if (T > 0) {
final float S = 0.5f / (float) FloatUtil.sqrt(T);
w = 0.25f / S;
x = (m[5] - m[7]) * S;
y = (m[6] - m[2]) * S;
z = (m[1] - m[3]) * S;
} else {
if ((m[0] > m[4]) & (m[0] > m[8])) {
final float S = FloatUtil.sqrt(1.0f + m[0] - m[4] - m[8]) * 2f; // S=4*qx
w = (m[7] - m[5]) / S;
x = 0.25f * S;
y = (m[3] + m[1]) / S;
z = (m[6] + m[2]) / S;
} else if (m[4] > m[8]) {
final float S = FloatUtil.sqrt(1.0f + m[4] - m[0] - m[8]) * 2f; // S=4*qy
w = (m[6] - m[2]) / S;
x = (m[3] + m[1]) / S;
y = 0.25f * S;
z = (m[7] + m[5]) / S;
} else {
final float S = FloatUtil.sqrt(1.0f + m[8] - m[0] - m[4]) * 2f; // S=4*qz
w = (m[3] - m[1]) / S;
x = (m[6] + m[2]) / S;
y = (m[7] + m[5]) / S;
z = 0.25f * S;
}
}
}
/**
* Check if the the 3x3 matrix (param) is in fact an affine rotational
* matrix
*
* @param m 3x3 column matrix
* @return true if representing a rotational matrix, false otherwise
*/
public boolean isRotationMatrix(float[] m) {
final double epsilon = 0.01; // margin to allow for rounding errors
if (FloatUtil.abs(m[0] * m[3] + m[3] * m[4] + m[6] * m[7]) > epsilon)
return false;
if (FloatUtil.abs(m[0] * m[2] + m[3] * m[5] + m[6] * m[8]) > epsilon)
return false;
if (FloatUtil.abs(m[1] * m[2] + m[4] * m[5] + m[7] * m[8]) > epsilon)
return false;
if (FloatUtil.abs(m[0] * m[0] + m[3] * m[3] + m[6] * m[6] - 1) > epsilon)
return false;
if (FloatUtil.abs(m[1] * m[1] + m[4] * m[4] + m[7] * m[7] - 1) > epsilon)
return false;
if (FloatUtil.abs(m[2] * m[2] + m[5] * m[5] + m[8] * m[8] - 1) > epsilon)
return false;
return (FloatUtil.abs(determinant(m) - 1) < epsilon);
}
private float determinant(float[] m) {
return m[0] * m[4] * m[8] + m[3] * m[7] * m[2] + m[6] * m[1] * m[5]
- m[0] * m[7] * m[5] - m[3] * m[1] * m[8] - m[6] * m[4] * m[2];
}
}