1 // Copyright (C) 2006 Mathias Froehlich - Mathias.Froehlich@web.de
3 // This library is free software; you can redistribute it and/or
4 // modify it under the terms of the GNU Library General Public
5 // License as published by the Free Software Foundation; either
6 // version 2 of the License, or (at your option) any later version.
8 // This library is distributed in the hope that it will be useful,
9 // but WITHOUT ANY WARRANTY; without even the implied warranty of
10 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
11 // Library General Public License for more details.
13 // You should have received a copy of the GNU General Public License
14 // along with this program; if not, write to the Free Software
15 // Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
36 /// Default constructor. Does not initialize at all.
37 /// If you need them zero initialized, SGQuat::zeros()
40 /// Initialize with nans in the debug build, that will guarantee to have
41 /// a fast uninitialized default constructor in the release but shows up
42 /// uninitialized values in the debug build very fast ...
44 for (unsigned i = 0; i < 4; ++i)
45 _data[i] = SGLimits<T>::quiet_NaN();
48 /// Constructor. Initialize by the given values
49 SGQuat(T _x, T _y, T _z, T _w)
50 { x() = _x; y() = _y; z() = _z; w() = _w; }
51 /// Constructor. Initialize by the content of a plain array,
52 /// make sure it has at least 4 elements
53 explicit SGQuat(const T* d)
54 { _data[0] = d[0]; _data[1] = d[1]; _data[2] = d[2]; _data[3] = d[3]; }
56 /// Return a unit quaternion
57 static SGQuat unit(void)
58 { return fromRealImag(1, SGVec3<T>(0)); }
60 /// Return a quaternion from euler angles
61 static SGQuat fromEulerRad(T z, T y, T x)
64 T zd2 = T(0.5)*z; T yd2 = T(0.5)*y; T xd2 = T(0.5)*x;
65 T Szd2 = sin(zd2); T Syd2 = sin(yd2); T Sxd2 = sin(xd2);
66 T Czd2 = cos(zd2); T Cyd2 = cos(yd2); T Cxd2 = cos(xd2);
67 T Cxd2Czd2 = Cxd2*Czd2; T Cxd2Szd2 = Cxd2*Szd2;
68 T Sxd2Szd2 = Sxd2*Szd2; T Sxd2Czd2 = Sxd2*Czd2;
69 q.w() = Cxd2Czd2*Cyd2 + Sxd2Szd2*Syd2;
70 q.x() = Sxd2Czd2*Cyd2 - Cxd2Szd2*Syd2;
71 q.y() = Cxd2Czd2*Syd2 + Sxd2Szd2*Cyd2;
72 q.z() = Cxd2Szd2*Cyd2 - Sxd2Czd2*Syd2;
76 /// Return a quaternion from euler angles in degrees
77 static SGQuat fromEulerDeg(T z, T y, T x)
79 return fromEulerRad(SGMisc<T>::deg2rad(z), SGMisc<T>::deg2rad(y),
80 SGMisc<T>::deg2rad(x));
83 /// Return a quaternion from euler angles
84 static SGQuat fromYawPitchRoll(T y, T p, T r)
85 { return fromEulerRad(y, p, r); }
87 /// Return a quaternion from euler angles
88 static SGQuat fromYawPitchRollDeg(T y, T p, T r)
89 { return fromEulerDeg(y, p, r); }
91 /// Return a quaternion from euler angles
92 static SGQuat fromHeadAttBank(T h, T a, T b)
93 { return fromEulerRad(h, a, b); }
95 /// Return a quaternion from euler angles
96 static SGQuat fromHeadAttBankDeg(T h, T a, T b)
97 { return fromEulerDeg(h, a, b); }
99 /// Return a quaternion rotation the the horizontal local frame from given
100 /// longitude and latitude
101 static SGQuat fromLonLatRad(T lon, T lat)
105 T yd2 = T(-0.25)*SGMisc<value_type>::pi() - T(0.5)*lat;
117 /// Return a quaternion rotation the the horizontal local frame from given
118 /// longitude and latitude
119 static SGQuat fromLonLatDeg(T lon, T lat)
120 { return fromLonLatRad(SGMisc<T>::deg2rad(lon), SGMisc<T>::deg2rad(lat)); }
122 /// Return a quaternion rotation the the horizontal local frame from given
123 /// longitude and latitude
124 static SGQuat fromLonLat(const SGGeod& geod)
125 { return fromLonLatRad(geod.getLongitudeRad(), geod.getLatitudeRad()); }
127 /// Create a quaternion from the angle axis representation
128 static SGQuat fromAngleAxis(T angle, const SGVec3<T>& axis)
130 T angle2 = 0.5*angle;
131 return fromRealImag(cos(angle2), T(sin(angle2))*axis);
134 /// Create a quaternion from the angle axis representation
135 static SGQuat fromAngleAxisDeg(T angle, const SGVec3<T>& axis)
136 { return fromAngleAxis(SGMisc<T>::deg2rad(angle), axis); }
138 /// Create a quaternion from the angle axis representation where the angle
139 /// is stored in the axis' length
140 static SGQuat fromAngleAxis(const SGVec3<T>& axis)
142 T nAxis = norm(axis);
143 if (nAxis <= SGLimits<T>::min())
144 return SGQuat(1, 0, 0, 0);
145 T angle2 = 0.5*nAxis;
146 return fromRealImag(cos(angle2), T(sin(angle2)/nAxis)*axis);
149 /// Return a quaternion from real and imaginary part
150 static SGQuat fromRealImag(T r, const SGVec3<T>& i)
160 /// Return an all zero vector
161 static SGQuat zeros(void)
162 { return SGQuat(0, 0, 0, 0); }
164 /// write the euler angles into the references
165 void getEulerRad(T& zRad, T& yRad, T& xRad) const
167 value_type sqrQW = w()*w();
168 value_type sqrQX = x()*x();
169 value_type sqrQY = y()*y();
170 value_type sqrQZ = z()*z();
172 value_type num = 2*(y()*z() + w()*x());
173 value_type den = sqrQW - sqrQX - sqrQY + sqrQZ;
174 if (fabs(den) < SGLimits<value_type>::min() &&
175 fabs(num) < SGLimits<value_type>::min())
178 xRad = atan2(num, den);
180 value_type tmp = 2*(x()*z() - w()*y());
182 yRad = 0.5*SGMisc<value_type>::pi();
184 yRad = -0.5*SGMisc<value_type>::pi();
188 num = 2*(x()*y() + w()*z());
189 den = sqrQW + sqrQX - sqrQY - sqrQZ;
190 if (fabs(den) < SGLimits<value_type>::min() &&
191 fabs(num) < SGLimits<value_type>::min())
194 value_type psi = atan2(num, den);
196 psi += 2*SGMisc<value_type>::pi();
201 /// write the euler angles in degrees into the references
202 void getEulerDeg(T& zDeg, T& yDeg, T& xDeg) const
204 getEulerRad(zDeg, yDeg, xDeg);
205 zDeg = SGMisc<T>::rad2deg(zDeg);
206 yDeg = SGMisc<T>::rad2deg(yDeg);
207 xDeg = SGMisc<T>::rad2deg(xDeg);
210 /// write the angle axis representation into the references
211 void getAngleAxis(T& angle, SGVec3<T>& axis) const
214 if (nrm < SGLimits<T>::min()) {
216 axis = SGVec3<T>(0, 0, 0);
219 angle = acos(SGMisc<T>::max(-1, SGMisc<T>::min(1, rNrm*w())));
221 if (fabs(sAng) < SGLimits<T>::min())
222 axis = SGVec3<T>(1, 0, 0);
224 axis = (rNrm/sAng)*imag(*this);
229 /// write the angle axis representation into the references
230 void getAngleAxis(SGVec3<T>& axis) const
233 getAngleAxis(angle, axis);
237 /// Access by index, the index is unchecked
238 const T& operator()(unsigned i) const
240 /// Access by index, the index is unchecked
241 T& operator()(unsigned i)
244 /// Access raw data by index, the index is unchecked
245 const T& operator[](unsigned i) const
247 /// Access raw data by index, the index is unchecked
248 T& operator[](unsigned i)
251 /// Access the x component
252 const T& x(void) const
254 /// Access the x component
257 /// Access the y component
258 const T& y(void) const
260 /// Access the y component
263 /// Access the z component
264 const T& z(void) const
266 /// Access the z component
269 /// Access the w component
270 const T& w(void) const
272 /// Access the w component
276 /// Get the data pointer, usefull for interfacing with plib's sg*Vec
277 const T* data(void) const
279 /// Get the data pointer, usefull for interfacing with plib's sg*Vec
283 /// Readonly interface function to ssg's sgQuat/sgdQuat
284 const T (&sg(void) const)[4]
286 /// Interface function to ssg's sgQuat/sgdQuat
291 SGQuat& operator+=(const SGQuat& v)
292 { _data[0]+=v(0);_data[1]+=v(1);_data[2]+=v(2);_data[3]+=v(3);return *this; }
293 /// Inplace subtraction
294 SGQuat& operator-=(const SGQuat& v)
295 { _data[0]-=v(0);_data[1]-=v(1);_data[2]-=v(2);_data[3]-=v(3);return *this; }
296 /// Inplace scalar multiplication
298 SGQuat& operator*=(S s)
299 { _data[0] *= s; _data[1] *= s; _data[2] *= s; _data[3] *= s; return *this; }
300 /// Inplace scalar multiplication by 1/s
302 SGQuat& operator/=(S s)
303 { return operator*=(1/T(s)); }
304 /// Inplace quaternion multiplication
305 SGQuat& operator*=(const SGQuat& v);
307 /// Transform a vector from the current coordinate frame to a coordinate
308 /// frame rotated with the quaternion
309 SGVec3<T> transform(const SGVec3<T>& v) const
311 value_type r = 2/dot(*this, *this);
312 SGVec3<T> qimag = imag(*this);
313 value_type qr = real(*this);
314 return (r*qr*qr - 1)*v + (r*dot(qimag, v))*qimag - (r*qr)*cross(qimag, v);
316 /// Transform a vector from the coordinate frame rotated with the quaternion
317 /// to the current coordinate frame
318 SGVec3<T> backTransform(const SGVec3<T>& v) const
320 value_type r = 2/dot(*this, *this);
321 SGVec3<T> qimag = imag(*this);
322 value_type qr = real(*this);
323 return (r*qr*qr - 1)*v + (r*dot(qimag, v))*qimag + (r*qr)*cross(qimag, v);
326 /// Rotate a given vector with the quaternion
327 SGVec3<T> rotate(const SGVec3<T>& v) const
328 { return backTransform(v); }
329 /// Rotate a given vector with the inverse quaternion
330 SGVec3<T> rotateBack(const SGVec3<T>& v) const
331 { return transform(v); }
333 /// Return the time derivative of the quaternion given the angular velocity
335 derivative(const SGVec3<T>& angVel)
339 deriv.w() = 0.5*(-x()*angVel(0) - y()*angVel(1) - z()*angVel(2));
340 deriv.x() = 0.5*( w()*angVel(0) - z()*angVel(1) + y()*angVel(2));
341 deriv.y() = 0.5*( z()*angVel(0) + w()*angVel(1) - x()*angVel(2));
342 deriv.z() = 0.5*(-y()*angVel(0) + x()*angVel(1) + w()*angVel(2));
352 /// Unary +, do nothing ...
356 operator+(const SGQuat<T>& v)
359 /// Unary -, do nearly nothing
363 operator-(const SGQuat<T>& v)
364 { return SGQuat<T>(-v(0), -v(1), -v(2), -v(3)); }
370 operator+(const SGQuat<T>& v1, const SGQuat<T>& v2)
371 { return SGQuat<T>(v1(0)+v2(0), v1(1)+v2(1), v1(2)+v2(2), v1(3)+v2(3)); }
377 operator-(const SGQuat<T>& v1, const SGQuat<T>& v2)
378 { return SGQuat<T>(v1(0)-v2(0), v1(1)-v2(1), v1(2)-v2(2), v1(3)-v2(3)); }
380 /// Scalar multiplication
381 template<typename S, typename T>
384 operator*(S s, const SGQuat<T>& v)
385 { return SGQuat<T>(s*v(0), s*v(1), s*v(2), s*v(3)); }
387 /// Scalar multiplication
388 template<typename S, typename T>
391 operator*(const SGQuat<T>& v, S s)
392 { return SGQuat<T>(s*v(0), s*v(1), s*v(2), s*v(3)); }
394 /// Quaterion multiplication
398 operator*(const SGQuat<T>& v1, const SGQuat<T>& v2)
401 v.x() = v1.w()*v2.x() + v1.x()*v2.w() + v1.y()*v2.z() - v1.z()*v2.y();
402 v.y() = v1.w()*v2.y() - v1.x()*v2.z() + v1.y()*v2.w() + v1.z()*v2.x();
403 v.z() = v1.w()*v2.z() + v1.x()*v2.y() - v1.y()*v2.x() + v1.z()*v2.w();
404 v.w() = v1.w()*v2.w() - v1.x()*v2.x() - v1.y()*v2.y() - v1.z()*v2.z();
408 /// Now define the inplace multiplication
412 SGQuat<T>::operator*=(const SGQuat& v)
413 { (*this) = (*this)*v; return *this; }
415 /// The conjugate of the quaternion, this is also the
416 /// inverse for normalized quaternions
420 conj(const SGQuat<T>& v)
421 { return SGQuat<T>(-v(0), -v(1), -v(2), v(3)); }
423 /// The conjugate of the quaternion, this is also the
424 /// inverse for normalized quaternions
428 inverse(const SGQuat<T>& v)
429 { return (1/dot(v, v))*SGQuat<T>(-v(0), -v(1), -v(2), v(3)); }
431 /// The imagniary part of the quaternion
435 real(const SGQuat<T>& v)
438 /// The imagniary part of the quaternion
442 imag(const SGQuat<T>& v)
443 { return SGVec3<T>(v.x(), v.y(), v.z()); }
445 /// Scalar dot product
449 dot(const SGQuat<T>& v1, const SGQuat<T>& v2)
450 { return v1(0)*v2(0) + v1(1)*v2(1) + v1(2)*v2(2) + v1(3)*v2(3); }
452 /// The euclidean norm of the vector, that is what most people call length
456 norm(const SGQuat<T>& v)
457 { return sqrt(dot(v, v)); }
459 /// The euclidean norm of the vector, that is what most people call length
463 length(const SGQuat<T>& v)
464 { return sqrt(dot(v, v)); }
466 /// The 1-norm of the vector, this one is the fastest length function we
467 /// can implement on modern cpu's
471 norm1(const SGQuat<T>& v)
472 { return fabs(v(0)) + fabs(v(1)) + fabs(v(2)) + fabs(v(3)); }
474 /// The euclidean norm of the vector, that is what most people call length
478 normalize(const SGQuat<T>& q)
479 { return (1/norm(q))*q; }
481 /// Return true if exactly the same
485 operator==(const SGQuat<T>& v1, const SGQuat<T>& v2)
486 { return v1(0)==v2(0) && v1(1)==v2(1) && v1(2)==v2(2) && v1(3)==v2(3); }
488 /// Return true if not exactly the same
492 operator!=(const SGQuat<T>& v1, const SGQuat<T>& v2)
493 { return ! (v1 == v2); }
495 /// Return true if equal to the relative tolerance tol
496 /// Note that this is not the same than comparing quaternions to represent
497 /// the same rotation
501 equivalent(const SGQuat<T>& v1, const SGQuat<T>& v2, T tol)
502 { return norm1(v1 - v2) < tol*(norm1(v1) + norm1(v2)); }
504 /// Return true if about equal to roundoff of the underlying type
505 /// Note that this is not the same than comparing quaternions to represent
506 /// the same rotation
510 equivalent(const SGQuat<T>& v1, const SGQuat<T>& v2)
511 { return equivalent(v1, v2, 100*SGLimits<T>::epsilon()); }
517 isNaN(const SGQuat<T>& v)
519 return SGMisc<T>::isNaN(v(0)) || SGMisc<T>::isNaN(v(1))
520 || SGMisc<T>::isNaN(v(2)) || SGMisc<T>::isNaN(v(3));
524 /// quaternion interpolation for t in [0,1] interpolate between src (=0)
529 interpolate(T t, const SGQuat<T>& src, const SGQuat<T>& dst)
531 T cosPhi = dot(src, dst);
532 // need to take the shorter way ...
533 int signCosPhi = SGMisc<T>::sign(cosPhi);
534 // cosPhi must be corrected for that sign
535 cosPhi = fabs(cosPhi);
537 // first opportunity to fail - make sure acos will succeed later -
542 // now the half angle between the orientations
545 // need the scales now, if the angle is very small, do linear interpolation
546 // to avoid instabilities
548 if (fabs(o) < SGLimits<T>::epsilon()) {
552 // note that we can give a positive lower bound for sin(o) here
555 scale0 = sin((1 - t)*o)*so;
556 scale1 = sin(t*o)*so;
559 return scale0*src + signCosPhi*scale1*dst;
562 /// Output to an ostream
563 template<typename char_type, typename traits_type, typename T>
565 std::basic_ostream<char_type, traits_type>&
566 operator<<(std::basic_ostream<char_type, traits_type>& s, const SGQuat<T>& v)
567 { return s << "[ " << v(0) << ", " << v(1) << ", " << v(2) << ", " << v(3) << " ]"; }
571 toQuatf(const SGQuatd& v)
572 { return SGQuatf((float)v(0), (float)v(1), (float)v(2), (float)v(3)); }
576 toQuatd(const SGQuatf& v)
577 { return SGQuatd(v(0), v(1), v(2), v(3)); }