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/*
* Copyright © 2014 Keith Packard <keithp@keithp.com>
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.
*/
package org.altusmetrum.altoslib_13;
public class AltosQuaternion {
double r; /* real bit */
double x, y, z; /* imaginary bits */
/* Multiply by b */
public AltosQuaternion multiply(AltosQuaternion b) {
return new AltosQuaternion(
this.r * b.r - this.x * b.x - this.y * b.y - this.z * b.z,
this.r * b.x + this.x * b.r + this.y * b.z - this.z * b.y,
this.r * b.y - this.x * b.z + this.y * b.r + this.z * b.x,
this.r * b.z + this.x * b.y - this.y * b.x + this.z * b.r);
}
public AltosQuaternion conjugate() {
return new AltosQuaternion(this.r,
-this.x,
-this.y,
-this.z);
}
public double normal() {
return Math.sqrt(this.r * this.r +
this.x * this.x +
this.y * this.y +
this.z * this.z);
}
/* Scale by a real value */
public AltosQuaternion scale(double b) {
return new AltosQuaternion(this.r * b,
this.x * b,
this.y * b,
this.z * b);
}
/* Divide by the length to end up with a quaternion of length 1 */
public AltosQuaternion normalize() {
double n = normal();
if (n <= 0)
return this;
return scale(1/n);
}
/* dot product */
public double dot(AltosQuaternion b) {
return (this.r * b.r +
this.x * b.x +
this.y * b.y +
this.z * b.z);
}
/* Rotate 'this' by 'b' */
public AltosQuaternion rotate(AltosQuaternion b) {
return (b.multiply(this)).multiply(b.conjugate());
}
/* Given two vectors (this and b), compute a quaternion
* representing the rotation between them
*/
public AltosQuaternion vectors_to_rotation(AltosQuaternion b) {
/*
* The cross product will point orthogonally to the two
* vectors, forming our rotation axis. The length will be
* sin(θ), so these values are already multiplied by that.
*/
double x = this.y * b.z - this.z * b.y;
double y = this.z * b.x - this.x * b.z;
double z = this.x * b.y - this.y * b.x;
double s_2 = x*x + y*y + z*z;
double s = Math.sqrt(s_2);
/* cos(θ) = a · b / (|a| |b|).
*
* a and b are both unit vectors, so the divisor is one
*/
double c = this.x*b.x + this.y*b.y + this.z*b.z;
double c_half = Math.sqrt ((1 + c) / 2);
double s_half = Math.sqrt ((1 - c) / 2);
/*
* Divide out the sine factor from the
* cross product, then multiply in the
* half sine factor needed for the quaternion
*/
double s_scale = s_half / s;
AltosQuaternion r = new AltosQuaternion(c_half,
x * s_scale,
y * s_scale,
z * s_scale);
return r.normalize();
}
public AltosQuaternion(double r, double x, double y, double z) {
this.r = r;
this.x = x;
this.y = y;
this.z = z;
}
public AltosQuaternion(AltosQuaternion q) {
r = q.r;
x = q.x;
y = q.y;
z = q.z;
}
public AltosQuaternion() {
r = 1;
x = 0;
y = 0;
z = 0;
}
static public AltosQuaternion vector(double x, double y, double z) {
return new AltosQuaternion(0, x, y, z);
}
static public AltosQuaternion rotation(double x, double y, double z,
double s, double c) {
return new AltosQuaternion(c,
s*x,
s*y,
s*z);
}
static public AltosQuaternion zero_rotation() {
return new AltosQuaternion(1, 0, 0, 0);
}
static public AltosQuaternion euler(double x, double y, double z) {
/* Halve the euler angles */
x = x / 2.0;
y = y / 2.0;
z = z / 2.0;
double s_x = Math.sin(x), c_x = Math.cos(x);
double s_y = Math.sin(y), c_y = Math.cos(y);
double s_z = Math.sin(z), c_z = Math.cos(z);;
return new AltosQuaternion(c_x * c_y * c_z + s_x * s_y * s_z,
s_x * c_y * c_z - c_x * s_y * s_z,
c_x * s_y * c_z + s_x * c_y * s_z,
c_x * c_y * s_z - s_x * s_y * c_z);
}
}
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