1
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
2
|
// Copyright 2021 Leszek Koltunski //
|
3
|
// //
|
4
|
// This file is part of Magic Cube. //
|
5
|
// //
|
6
|
// Magic Cube is free software: you can redistribute it and/or modify //
|
7
|
// it under the terms of the GNU General Public License as published by //
|
8
|
// the Free Software Foundation, either version 2 of the License, or //
|
9
|
// (at your option) any later version. //
|
10
|
// //
|
11
|
// Magic Cube is distributed in the hope that it will be useful, //
|
12
|
// but WITHOUT ANY WARRANTY; without even the implied warranty of //
|
13
|
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the //
|
14
|
// GNU General Public License for more details. //
|
15
|
// //
|
16
|
// You should have received a copy of the GNU General Public License //
|
17
|
// along with Magic Cube. If not, see <http://www.gnu.org/licenses/>. //
|
18
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
19
|
|
20
|
package org.distorted.helpers;
|
21
|
|
22
|
import org.distorted.library.type.Static4D;
|
23
|
|
24
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
25
|
|
26
|
public class QuatHelper
|
27
|
{
|
28
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
29
|
// return quat1*quat2
|
30
|
|
31
|
public static Static4D quatMultiply( Static4D quat1, Static4D quat2 )
|
32
|
{
|
33
|
float qx = quat1.get0();
|
34
|
float qy = quat1.get1();
|
35
|
float qz = quat1.get2();
|
36
|
float qw = quat1.get3();
|
37
|
|
38
|
float rx = quat2.get0();
|
39
|
float ry = quat2.get1();
|
40
|
float rz = quat2.get2();
|
41
|
float rw = quat2.get3();
|
42
|
|
43
|
float tx = rw*qx - rz*qy + ry*qz + rx*qw;
|
44
|
float ty = rw*qy + rz*qx + ry*qw - rx*qz;
|
45
|
float tz = rw*qz + rz*qw - ry*qx + rx*qy;
|
46
|
float tw = rw*qw - rz*qz - ry*qy - rx*qx;
|
47
|
|
48
|
return new Static4D(tx,ty,tz,tw);
|
49
|
}
|
50
|
|
51
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
52
|
// rotate 'vector' by quat ( i.e. return quat*vector*(quat^-1) )
|
53
|
|
54
|
public static Static4D rotateVectorByQuat(Static4D vector, Static4D quat)
|
55
|
{
|
56
|
float qx = quat.get0();
|
57
|
float qy = quat.get1();
|
58
|
float qz = quat.get2();
|
59
|
float qw = quat.get3();
|
60
|
|
61
|
Static4D quatInverted= new Static4D(-qx,-qy,-qz,qw);
|
62
|
Static4D tmp = quatMultiply(quat,vector);
|
63
|
|
64
|
return quatMultiply(tmp,quatInverted);
|
65
|
}
|
66
|
|
67
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
68
|
// rotate 'vector' by quat^(-1) ( i.e. return (quat^-1)*vector*quat )
|
69
|
|
70
|
public static Static4D rotateVectorByInvertedQuat(Static4D vector, Static4D quat)
|
71
|
{
|
72
|
float qx = quat.get0();
|
73
|
float qy = quat.get1();
|
74
|
float qz = quat.get2();
|
75
|
float qw = quat.get3();
|
76
|
|
77
|
Static4D quatInverted= new Static4D(-qx,-qy,-qz,qw);
|
78
|
Static4D tmp = quatMultiply(quatInverted,vector);
|
79
|
|
80
|
return quatMultiply(tmp,quat);
|
81
|
}
|
82
|
|
83
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
84
|
|
85
|
public static Static4D quatFromDrag(float dragX, float dragY)
|
86
|
{
|
87
|
float axisX = dragY; // inverted X and Y - rotation axis is perpendicular to (dragX,dragY)
|
88
|
float axisY = dragX; // Why not (-dragY, dragX) ? because Y axis is also inverted!
|
89
|
float axisZ = 0;
|
90
|
float axisL = (float)Math.sqrt(axisX*axisX + axisY*axisY + axisZ*axisZ);
|
91
|
|
92
|
if( axisL>0 )
|
93
|
{
|
94
|
axisX /= axisL;
|
95
|
axisY /= axisL;
|
96
|
axisZ /= axisL;
|
97
|
|
98
|
float ratio = axisL;
|
99
|
ratio = ratio - (int)ratio; // the cos() is only valid in (0,Pi)
|
100
|
|
101
|
float cosA = (float)Math.cos(Math.PI*ratio);
|
102
|
float sinA = (float)Math.sqrt(1-cosA*cosA);
|
103
|
|
104
|
return new Static4D(axisX*sinA, axisY*sinA, axisZ*sinA, cosA);
|
105
|
}
|
106
|
|
107
|
return new Static4D(0f, 0f, 0f, 1f);
|
108
|
}
|
109
|
|
110
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
111
|
|
112
|
public static double computeCos(double oldX, double oldY, double newX, double newY, double len1, double len2)
|
113
|
{
|
114
|
double ret= (oldX*newX+oldY*newY) / (len1*len2);
|
115
|
if( ret<-1.0 ) return -1.0;
|
116
|
if( ret> 1.0 ) return 1.0;
|
117
|
|
118
|
return ret;
|
119
|
}
|
120
|
|
121
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
122
|
// sin of (signed!) angle between vectors 'old' and 'new', counterclockwise!
|
123
|
|
124
|
public static double computeSin(double oldX, double oldY, double newX, double newY, double len1, double len2)
|
125
|
{
|
126
|
double ret= (newX*oldY-oldX*newY) / (len1*len2);
|
127
|
if( ret<-1.0 ) return -1.0;
|
128
|
if( ret> 1.0 ) return 1.0;
|
129
|
|
130
|
return ret;
|
131
|
}
|
132
|
|
133
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
134
|
// return quat Q that turns 3D vector A=(ax,ay,az) to another 3D vector B=(bx,by,bz)
|
135
|
// take care of double-cover by ensuring that always Q.get3() >=0
|
136
|
|
137
|
public static Static4D retRotationQuat(float ax, float ay, float az, float bx, float by, float bz)
|
138
|
{
|
139
|
float nx = ay*bz - az*by;
|
140
|
float ny = az*bx - ax*bz;
|
141
|
float nz = ax*by - ay*bx;
|
142
|
|
143
|
float sin = (float)Math.sqrt(nx*nx + ny*ny + nz*nz);
|
144
|
float cos = ax*bx + ay*by + az*bz;
|
145
|
|
146
|
if( sin!=0 )
|
147
|
{
|
148
|
nx /= sin;
|
149
|
ny /= sin;
|
150
|
nz /= sin;
|
151
|
}
|
152
|
|
153
|
// Why sin<=0 and cos>=0 ?
|
154
|
// 0<angle<180 -> 0<halfAngle<90 -> both sin and cos are positive.
|
155
|
// But1: quats work counterclockwise -> negate cos.
|
156
|
// But2: double-cover, we prefer to have the cos positive (so that unit=(0,0,0,1))
|
157
|
// so negate again both cos and sin.
|
158
|
float sinHalf =-(float)Math.sqrt((1-cos)/2);
|
159
|
float cosHalf = (float)Math.sqrt((1+cos)/2);
|
160
|
|
161
|
return new Static4D(nx*sinHalf,ny*sinHalf,nz*sinHalf,cosHalf);
|
162
|
}
|
163
|
}
|