1 // SPDX-License-Identifier: LGPL-2.1-or-later
2 //
3 // SPDX-FileCopyrightText: 2006-2007 Torsten Rahn <tackat@kde.org>
4 // SPDX-FileCopyrightText: 2007 Inge Wallin <ingwa@kde.org>
5 // SPDX-FileCopyrightText: 2011 Bernhard Beschow <bbeschow@cs.tu-berlin.de>
6 //
7
8 #include "Quaternion.h"
9
10 using namespace std;
11
12 #include <QString>
13 #include <QDebug>
14
15
16 using namespace Marble;
17
Quaternion()18 Quaternion::Quaternion()
19 {
20 // like in libeigen we keep the quaternion uninitialized
21 // set( 1.0, 0.0, 0.0, 0.0 );
22 }
23
Quaternion(qreal w,qreal x,qreal y,qreal z)24 Quaternion::Quaternion(qreal w, qreal x, qreal y, qreal z)
25 {
26 v[Q_W] = w;
27 v[Q_X] = x;
28 v[Q_Y] = y;
29 v[Q_Z] = z;
30 }
31
fromSpherical(qreal lon,qreal lat)32 Quaternion Quaternion::fromSpherical(qreal lon, qreal lat)
33 {
34 const qreal w = 0.0;
35 const qreal x = cos(lat) * sin(lon);
36 const qreal y = sin(lat);
37 const qreal z = cos(lat) * cos(lon);
38
39 return Quaternion( w, x, y, z );
40 }
41
getSpherical(qreal & lon,qreal & lat) const42 void Quaternion::getSpherical(qreal &lon, qreal &lat) const
43 {
44 qreal y = v[Q_Y];
45 if ( y > 1.0 )
46 y = 1.0;
47 else if ( y < -1.0 )
48 y = -1.0;
49
50 lat = asin( y );
51
52 if(v[Q_X] * v[Q_X] + v[Q_Z] * v[Q_Z] > 0.00005)
53 lon = atan2(v[Q_X], v[Q_Z]);
54 else
55 lon = 0.0;
56 }
57
normalize()58 void Quaternion::normalize()
59 {
60 (*this) *= 1.0 / length();
61 }
62
length() const63 qreal Quaternion::length() const
64 {
65 return sqrt(v[Q_W] * v[Q_W] + v[Q_X] * v[Q_X] + v[Q_Y] * v[Q_Y] + v[Q_Z] * v[Q_Z]);
66 }
67
operator *=(qreal mult)68 Quaternion& Quaternion::operator*=(qreal mult)
69 {
70 (*this) = (*this) * mult;
71
72 return *this;
73 }
74
inverse() const75 Quaternion Quaternion::inverse() const
76 {
77 Quaternion inverse( v[Q_W], -v[Q_X], -v[Q_Y], -v[Q_Z] );
78 inverse.normalize();
79
80 return inverse;
81 }
82
log() const83 Quaternion Quaternion::log() const
84 {
85 double const qlen = length();
86 double const vlen = sqrt(v[Q_X]*v[Q_X] + v[Q_Y]*v[Q_Y] + v[Q_Z]*v[Q_Z]);
87 double const a = acos(v[Q_W]/qlen) / vlen;
88 return Quaternion(std::log(qlen), v[Q_X] * a, v[Q_Y] * a, v[Q_Z] * a);
89 }
90
exp() const91 Quaternion Quaternion::exp() const
92 {
93 double const vlen = sqrt(v[Q_X]*v[Q_X] + v[Q_Y]*v[Q_Y] + v[Q_Z]*v[Q_Z]);
94 double const s = std::exp(v[Q_W]);
95 double const a = s * sin(vlen) / vlen;
96 return Quaternion(s * cos(vlen), v[Q_X] * a, v[Q_Y] * a, v[Q_Z] * a);
97 }
98
fromEuler(qreal pitch,qreal yaw,qreal roll)99 Quaternion Quaternion::fromEuler(qreal pitch, qreal yaw, qreal roll)
100 {
101 const qreal cPhi = cos(0.5 * pitch); // also: "heading"
102 const qreal cThe = cos(0.5 * yaw); // also: "attitude"
103 const qreal cPsi = cos(0.5 * roll); // also: "bank"
104
105 const qreal sPhi = sin(0.5 * pitch);
106 const qreal sThe = sin(0.5 * yaw);
107 const qreal sPsi = sin(0.5 * roll);
108
109 const qreal w = cPhi * cThe * cPsi + sPhi * sThe * sPsi;
110 const qreal x = sPhi * cThe * cPsi - cPhi * sThe * sPsi;
111 const qreal y = cPhi * sThe * cPsi + sPhi * cThe * sPsi;
112 const qreal z = cPhi * cThe * sPsi - sPhi * sThe * cPsi;
113
114 return Quaternion( w, x, y, z );
115 }
116
pitch() const117 qreal Quaternion::pitch() const // "heading", phi
118 {
119 return atan2( 2.0*(v[Q_X]*v[Q_W]-v[Q_Y]*v[Q_Z]),
120 ( 1.0 - 2.0*(v[Q_X]*v[Q_X]+v[Q_Z]*v[Q_Z]) ) );
121 }
122
yaw() const123 qreal Quaternion::yaw() const // "attitude", theta
124 {
125 return atan2( 2.0*(v[Q_Y]*v[Q_W]-v[Q_X]*v[Q_Z]),
126 ( 1.0 - 2.0*(v[Q_Y]*v[Q_Y]+v[Q_Z]*v[Q_Z]) ) );
127 }
128
roll() const129 qreal Quaternion::roll() const // "bank", psi
130 {
131 return asin(2.0*(v[Q_X]*v[Q_Y]+v[Q_Z]*v[Q_W]));
132 }
133
134 #ifndef QT_NO_DEBUG_STREAM
operator <<(QDebug debug,const Quaternion & q)135 QDebug operator<<(QDebug debug, const Quaternion &q)
136 {
137 QString quatdisplay = QString("Quaternion: w= %1, x= %2, y= %3, z= %4, |q|= %5" )
138 .arg(q.v[Q_W]).arg(q.v[Q_X]).arg(q.v[Q_Y]).arg(q.v[Q_Z]).arg(q.length());
139
140 debug << quatdisplay;
141
142 return debug;
143 }
144 #endif
145
operator *=(const Quaternion & q)146 Quaternion& Quaternion::operator*=(const Quaternion &q)
147 {
148 (*this) = (*this) * q;
149
150 return *this;
151 }
152
operator ==(const Quaternion & q) const153 bool Quaternion::operator==(const Quaternion &q) const
154 {
155
156 return ( v[Q_W] == q.v[Q_W]
157 && v[Q_X] == q.v[Q_X]
158 && v[Q_Y] == q.v[Q_Y]
159 && v[Q_Z] == q.v[Q_Z] );
160 }
161
operator *(const Quaternion & q) const162 Quaternion Quaternion::operator*(const Quaternion &q) const
163 {
164 const qreal w = v[Q_W] * q.v[Q_W] - v[Q_X] * q.v[Q_X] - v[Q_Y] * q.v[Q_Y] - v[Q_Z] * q.v[Q_Z];
165 const qreal x = v[Q_W] * q.v[Q_X] + v[Q_X] * q.v[Q_W] + v[Q_Y] * q.v[Q_Z] - v[Q_Z] * q.v[Q_Y];
166 const qreal y = v[Q_W] * q.v[Q_Y] - v[Q_X] * q.v[Q_Z] + v[Q_Y] * q.v[Q_W] + v[Q_Z] * q.v[Q_X];
167 const qreal z = v[Q_W] * q.v[Q_Z] + v[Q_X] * q.v[Q_Y] - v[Q_Y] * q.v[Q_X] + v[Q_Z] * q.v[Q_W];
168
169 return Quaternion( w, x, y, z );
170 }
171
operator +(const Quaternion & q) const172 Quaternion Quaternion::operator+(const Quaternion &q) const
173 {
174 return Quaternion(v[Q_W] + q.v[Q_W],
175 v[Q_X] + q.v[Q_X],
176 v[Q_Y] + q.v[Q_Y],
177 v[Q_Z] + q.v[Q_Z]);
178 }
179
operator *(qreal factor) const180 Quaternion Quaternion::operator*(qreal factor) const
181 {
182 return Quaternion( v[Q_W] * factor, v[Q_X] * factor, v[Q_Y] * factor, v[Q_Z] * factor );
183 }
184
rotateAroundAxis(const Quaternion & q)185 void Quaternion::rotateAroundAxis(const Quaternion &q)
186 {
187 const qreal w = + v[Q_X] * q.v[Q_X] + v[Q_Y] * q.v[Q_Y] + v[Q_Z] * q.v[Q_Z];
188 const qreal x = + v[Q_X] * q.v[Q_W] - v[Q_Y] * q.v[Q_Z] + v[Q_Z] * q.v[Q_Y];
189 const qreal y = + v[Q_X] * q.v[Q_Z] + v[Q_Y] * q.v[Q_W] - v[Q_Z] * q.v[Q_X];
190 const qreal z = - v[Q_X] * q.v[Q_Y] + v[Q_Y] * q.v[Q_X] + v[Q_Z] * q.v[Q_W];
191
192 (*this) = q * Quaternion( w, x, y, z );
193 }
194
slerp(const Quaternion & q1,const Quaternion & q2,qreal t)195 Quaternion Quaternion::slerp(const Quaternion &q1, const Quaternion &q2, qreal t)
196 {
197 qreal p1;
198 qreal p2;
199
200 // Let alpha be the angle between the two quaternions.
201 qreal cosAlpha = ( q1.v[Q_X] * q2.v[Q_X]
202 + q1.v[Q_Y] * q2.v[Q_Y]
203 + q1.v[Q_Z] * q2.v[Q_Z]
204 + q1.v[Q_W] * q2.v[Q_W] );
205 qreal alpha = acos( cosAlpha );
206 qreal sinAlpha = sin( alpha );
207
208 if ( sinAlpha > 0.0 ) {
209 p1 = sin( ( 1.0 - t ) * alpha ) / sinAlpha;
210 p2 = sin( t * alpha ) / sinAlpha;
211 } else {
212 // both Quaternions are equal
213 p1 = 1.0;
214 p2 = 0.0;
215 }
216
217 const qreal w = p1 * q1.v[Q_W] + p2 * q2.v[Q_W];
218 const qreal x = p1 * q1.v[Q_X] + p2 * q2.v[Q_X];
219 const qreal y = p1 * q1.v[Q_Y] + p2 * q2.v[Q_Y];
220 const qreal z = p1 * q1.v[Q_Z] + p2 * q2.v[Q_Z];
221
222 return Quaternion( w, x, y, z );
223 }
224
nlerp(const Quaternion & q1,const Quaternion & q2,qreal t)225 Quaternion Quaternion::nlerp(const Quaternion &q1, const Quaternion &q2, qreal t)
226 {
227 const qreal p1 = 1.0 - t;
228
229 const qreal w = p1 * q1.v[Q_W] + t * q2.v[Q_W];
230 const qreal x = p1 * q1.v[Q_X] + t * q2.v[Q_X];
231 const qreal y = p1 * q1.v[Q_Y] + t * q2.v[Q_Y];
232 const qreal z = p1 * q1.v[Q_Z] + t * q2.v[Q_Z];
233
234 Quaternion result( w, x, y, z );
235 result.normalize();
236
237 return result;
238 }
239
toMatrix(matrix & m) const240 void Quaternion::toMatrix(matrix &m) const
241 {
242
243 const qreal xy = v[Q_X] * v[Q_Y], xz = v[Q_X] * v[Q_Z];
244 const qreal yy = v[Q_Y] * v[Q_Y], yw = v[Q_Y] * v[Q_W];
245 const qreal zw = v[Q_Z] * v[Q_W], zz = v[Q_Z] * v[Q_Z];
246
247 m[0][0] = 1.0 - 2.0 * (yy + zz);
248 m[0][1] = 2.0 * (xy + zw);
249 m[0][2] = 2.0 * (xz - yw);
250 m[0][3] = 0.0;
251
252 const qreal xx = v[Q_X] * v[Q_X];
253 const qreal xw = v[Q_X] * v[Q_W];
254 const qreal yz = v[Q_Y] * v[Q_Z];
255
256 m[1][0] = 2.0 * (xy - zw);
257 m[1][1] = 1.0 - 2.0 * (xx + zz);
258 m[1][2] = 2.0 * (yz + xw);
259 m[1][3] = 0.0;
260
261 m[2][0] = 2.0 * (xz + yw);
262 m[2][1] = 2.0 * (yz - xw);
263 m[2][2] = 1.0 - 2.0 * (xx + yy);
264 m[2][3] = 0.0;
265 }
266
rotateAroundAxis(const matrix & m)267 void Quaternion::rotateAroundAxis(const matrix &m)
268 {
269 const qreal x = m[0][0] * v[Q_X] + m[1][0] * v[Q_Y] + m[2][0] * v[Q_Z];
270 const qreal y = m[0][1] * v[Q_X] + m[1][1] * v[Q_Y] + m[2][1] * v[Q_Z];
271 const qreal z = m[0][2] * v[Q_X] + m[1][2] * v[Q_Y] + m[2][2] * v[Q_Z];
272
273 v[Q_W] = 1.0;
274 v[Q_X] = x;
275 v[Q_Y] = y;
276 v[Q_Z] = z;
277 }
278