1 |
8fc3b80a
|
Leszek Koltunski
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
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.library.main;
|
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 |
|
|
}
|