1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
|
/*
* 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; version 2 of the License.
*
* 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_10;
public class AltosQuaternion {
double r; /* real bit */
double x, y, z; /* imaginary bits */
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 (this.r * this.r +
this.x * this.x +
this.y * this.y +
this.z * this.z);
}
public AltosQuaternion scale(double b) {
return new AltosQuaternion(
this.r * b,
this.x * b,
this.y * b,
this.z * b);
}
public AltosQuaternion normalize() {
double n = normal();
if (n <= 0)
return this;
return scale(1/Math.sqrt(n));
}
public double dot(AltosQuaternion b) {
return (this.r * b.r +
this.x * b.x +
this.y * b.y +
this.z * b.z);
}
public AltosQuaternion rotate(AltosQuaternion b) {
return (b.multiply(this)).multiply(b.conjugate());
}
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) {
this.r = q.r;
this.x = q.x;
this.y = q.y;
this.z = q.z;
}
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 half_euler(double x, double y, double z) {
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);
}
}
|
