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 Library General Public
14 // License along with this library; if not, write to the
15 // Free Software Foundation, Inc., 59 Temple Place - Suite 330,
16 // Boston, MA 02111-1307, USA.
28 /// Default constructor. Does not initialize at all.
29 /// If you need them zero initialized, SGQuat::zeros()
32 /// Initialize with nans in the debug build, that will guarantee to have
33 /// a fast uninitialized default constructor in the release but shows up
34 /// uninitialized values in the debug build very fast ...
36 for (unsigned i = 0; i < 4; ++i)
37 _data[i] = SGLimits<T>::quiet_NaN();
40 /// Constructor. Initialize by the given values
41 SGQuat(T _x, T _y, T _z, T _w)
42 { x() = _x; y() = _y; z() = _z; w() = _w; }
43 /// Constructor. Initialize by the content of a plain array,
44 /// make sure it has at least 4 elements
45 explicit SGQuat(const T* d)
46 { _data[0] = d[0]; _data[1] = d[1]; _data[2] = d[2]; _data[3] = d[3]; }
48 /// Return a unit quaternion
49 static SGQuat unit(void)
50 { return fromRealImag(1, SGVec3<T>(0)); }
52 /// Return a quaternion from euler angles
53 static SGQuat fromEulerRad(T z, T y, T x)
56 T zd2 = T(0.5)*z; T yd2 = T(0.5)*y; T xd2 = T(0.5)*x;
57 T Szd2 = sin(zd2); T Syd2 = sin(yd2); T Sxd2 = sin(xd2);
58 T Czd2 = cos(zd2); T Cyd2 = cos(yd2); T Cxd2 = cos(xd2);
59 T Cxd2Czd2 = Cxd2*Czd2; T Cxd2Szd2 = Cxd2*Szd2;
60 T Sxd2Szd2 = Sxd2*Szd2; T Sxd2Czd2 = Sxd2*Czd2;
61 q.w() = Cxd2Czd2*Cyd2 + Sxd2Szd2*Syd2;
62 q.x() = Sxd2Czd2*Cyd2 - Cxd2Szd2*Syd2;
63 q.y() = Cxd2Czd2*Syd2 + Sxd2Szd2*Cyd2;
64 q.z() = Cxd2Szd2*Cyd2 - Sxd2Czd2*Syd2;
68 /// Return a quaternion from euler angles in degrees
69 static SGQuat fromEulerDeg(T z, T y, T x)
71 return fromEulerRad(SGMisc<T>::deg2rad(z), SGMisc<T>::deg2rad(y),
72 SGMisc<T>::deg2rad(x));
75 /// Return a quaternion from euler angles
76 static SGQuat fromYawPitchRoll(T y, T p, T r)
77 { return fromEulerRad(y, p, r); }
79 /// Return a quaternion from euler angles
80 static SGQuat fromYawPitchRollDeg(T y, T p, T r)
81 { return fromEulerDeg(y, p, r); }
83 /// Return a quaternion from euler angles
84 static SGQuat fromHeadAttBank(T h, T a, T b)
85 { return fromEulerRad(h, a, b); }
87 /// Return a quaternion from euler angles
88 static SGQuat fromHeadAttBankDeg(T h, T a, T b)
89 { return fromEulerDeg(h, a, b); }
91 /// Return a quaternion rotation the the horizontal local frame from given
92 /// longitude and latitude
93 static SGQuat fromLonLatRad(T lon, T lat)
97 T yd2 = T(-0.25)*SGMisc<value_type>::pi() - T(0.5)*lat;
109 /// Return a quaternion rotation the the horizontal local frame from given
110 /// longitude and latitude
111 static SGQuat fromLonLatDeg(T lon, T lat)
112 { return fromLonLatRad(SGMisc<T>::deg2rad(lon), SGMisc<T>::deg2rad(lat)); }
114 /// Create a quaternion from the angle axis representation
115 static SGQuat fromAngleAxis(T angle, const SGVec3<T>& axis)
117 T angle2 = 0.5*angle;
118 return fromRealImag(cos(angle2), T(sin(angle2))*axis);
121 /// Create a quaternion from the angle axis representation
122 static SGQuat fromAngleAxisDeg(T angle, const SGVec3<T>& axis)
123 { return fromAngleAxis(SGMisc<T>::deg2rad(angle), axis); }
125 /// Create a quaternion from the angle axis representation where the angle
126 /// is stored in the axis' length
127 static SGQuat fromAngleAxis(const SGVec3<T>& axis)
129 T nAxis = norm(axis);
130 if (nAxis <= SGLimits<T>::min())
131 return SGQuat(1, 0, 0, 0);
132 T angle2 = 0.5*nAxis;
133 return fromRealImag(cos(angle2), T(sin(angle2)/nAxis)*axis);
136 /// Return a quaternion from real and imaginary part
137 static SGQuat fromRealImag(T r, const SGVec3<T>& i)
147 /// Return an all zero vector
148 static SGQuat zeros(void)
149 { return SGQuat(0, 0, 0, 0); }
151 /// write the euler angles into the references
152 void getEulerRad(T& zRad, T& yRad, T& xRad) const
154 value_type sqrQW = w()*w();
155 value_type sqrQX = x()*x();
156 value_type sqrQY = y()*y();
157 value_type sqrQZ = z()*z();
159 value_type num = 2*(y()*z() + w()*x());
160 value_type den = sqrQW - sqrQX - sqrQY + sqrQZ;
161 if (fabs(den) < SGLimits<value_type>::min() &&
162 fabs(num) < SGLimits<value_type>::min())
165 xRad = atan2(num, den);
167 value_type tmp = 2*(x()*z() - w()*y());
169 yRad = 0.5*SGMisc<value_type>::pi();
171 yRad = -0.5*SGMisc<value_type>::pi();
175 num = 2*(x()*y() + w()*z());
176 den = sqrQW + sqrQX - sqrQY - sqrQZ;
177 if (fabs(den) < SGLimits<value_type>::min() &&
178 fabs(num) < SGLimits<value_type>::min())
181 value_type psi = atan2(num, den);
183 psi += 2*SGMisc<value_type>::pi();
188 /// write the euler angles in degrees into the references
189 void getEulerDeg(T& zDeg, T& yDeg, T& xDeg) const
191 getEulerRad(zDeg, yDeg, xDeg);
192 zDeg = SGMisc<T>::rad2deg(zDeg);
193 yDeg = SGMisc<T>::rad2deg(yDeg);
194 xDeg = SGMisc<T>::rad2deg(xDeg);
197 /// write the angle axis representation into the references
198 void getAngleAxis(T& angle, SGVec3<T>& axis) const
201 if (nrm < SGLimits<T>::min()) {
203 axis = SGVec3<T>(0, 0, 0);
206 angle = acos(SGMisc<T>::max(-1, SGMisc<T>::min(1, rNrm*w())));
208 if (fabs(sAng) < SGLimits<T>::min())
209 axis = SGVec3<T>(1, 0, 0);
211 axis = (rNrm/sAng)*imag(*this);
216 /// write the angle axis representation into the references
217 void getAngleAxis(SGVec3<T>& axis) const
220 getAngleAxis(angle, axis);
224 /// Access by index, the index is unchecked
225 const T& operator()(unsigned i) const
227 /// Access by index, the index is unchecked
228 T& operator()(unsigned i)
231 /// Access raw data by index, the index is unchecked
232 const T& operator[](unsigned i) const
234 /// Access raw data by index, the index is unchecked
235 T& operator[](unsigned i)
238 /// Access the x component
239 const T& x(void) const
241 /// Access the x component
244 /// Access the y component
245 const T& y(void) const
247 /// Access the y component
250 /// Access the z component
251 const T& z(void) const
253 /// Access the z component
256 /// Access the w component
257 const T& w(void) const
259 /// Access the w component
263 /// Get the data pointer, usefull for interfacing with plib's sg*Vec
264 const T* data(void) const
266 /// Get the data pointer, usefull for interfacing with plib's sg*Vec
270 /// Readonly interface function to ssg's sgQuat/sgdQuat
271 const T (&sg(void) const)[4]
273 /// Interface function to ssg's sgQuat/sgdQuat
278 SGQuat& operator+=(const SGQuat& v)
279 { _data[0]+=v(0);_data[1]+=v(1);_data[2]+=v(2);_data[3]+=v(3);return *this; }
280 /// Inplace subtraction
281 SGQuat& operator-=(const SGQuat& v)
282 { _data[0]-=v(0);_data[1]-=v(1);_data[2]-=v(2);_data[3]-=v(3);return *this; }
283 /// Inplace scalar multiplication
285 SGQuat& operator*=(S s)
286 { _data[0] *= s; _data[1] *= s; _data[2] *= s; _data[3] *= s; return *this; }
287 /// Inplace scalar multiplication by 1/s
289 SGQuat& operator/=(S s)
290 { return operator*=(1/T(s)); }
291 /// Inplace quaternion multiplication
292 SGQuat& operator*=(const SGQuat& v);
294 /// Transform a vector from the current coordinate frame to a coordinate
295 /// frame rotated with the quaternion
296 SGVec3<T> transform(const SGVec3<T>& v) const
298 value_type r = 2/dot(*this, *this);
299 SGVec3<T> qimag = imag(*this);
300 value_type qr = real(*this);
301 return (r*qr*qr - 1)*v + (r*dot(qimag, v))*qimag - (r*qr)*cross(qimag, v);
303 /// Transform a vector from the coordinate frame rotated with the quaternion
304 /// to the current coordinate frame
305 SGVec3<T> backTransform(const SGVec3<T>& v) const
307 value_type r = 2/dot(*this, *this);
308 SGVec3<T> qimag = imag(*this);
309 value_type qr = real(*this);
310 return (r*qr*qr - 1)*v + (r*dot(qimag, v))*qimag + (r*qr)*cross(qimag, v);
313 /// Rotate a given vector with the quaternion
314 SGVec3<T> rotate(const SGVec3<T>& v) const
315 { return backTransform(v); }
316 /// Rotate a given vector with the inverse quaternion
317 SGVec3<T> rotateBack(const SGVec3<T>& v) const
318 { return transform(v); }
320 /// Return the time derivative of the quaternion given the angular velocity
322 derivative(const SGVec3<T>& angVel)
326 deriv.w() = 0.5*(-x()*angVel(0) - y()*angVel(1) - z()*angVel(2));
327 deriv.x() = 0.5*( w()*angVel(0) - z()*angVel(1) + y()*angVel(2));
328 deriv.y() = 0.5*( z()*angVel(0) + w()*angVel(1) - x()*angVel(2));
329 deriv.z() = 0.5*(-y()*angVel(0) + x()*angVel(1) + w()*angVel(2));
339 /// Unary +, do nothing ...
343 operator+(const SGQuat<T>& v)
346 /// Unary -, do nearly nothing
350 operator-(const SGQuat<T>& v)
351 { return SGQuat<T>(-v(0), -v(1), -v(2), -v(3)); }
357 operator+(const SGQuat<T>& v1, const SGQuat<T>& v2)
358 { return SGQuat<T>(v1(0)+v2(0), v1(1)+v2(1), v1(2)+v2(2), v1(3)+v2(3)); }
364 operator-(const SGQuat<T>& v1, const SGQuat<T>& v2)
365 { return SGQuat<T>(v1(0)-v2(0), v1(1)-v2(1), v1(2)-v2(2), v1(3)-v2(3)); }
367 /// Scalar multiplication
368 template<typename S, typename T>
371 operator*(S s, const SGQuat<T>& v)
372 { return SGQuat<T>(s*v(0), s*v(1), s*v(2), s*v(3)); }
374 /// Scalar multiplication
375 template<typename S, typename T>
378 operator*(const SGQuat<T>& v, S s)
379 { return SGQuat<T>(s*v(0), s*v(1), s*v(2), s*v(3)); }
381 /// Quaterion multiplication
385 operator*(const SGQuat<T>& v1, const SGQuat<T>& v2)
388 v.x() = v1.w()*v2.x() + v1.x()*v2.w() + v1.y()*v2.z() - v1.z()*v2.y();
389 v.y() = v1.w()*v2.y() - v1.x()*v2.z() + v1.y()*v2.w() + v1.z()*v2.x();
390 v.z() = v1.w()*v2.z() + v1.x()*v2.y() - v1.y()*v2.x() + v1.z()*v2.w();
391 v.w() = v1.w()*v2.w() - v1.x()*v2.x() - v1.y()*v2.y() - v1.z()*v2.z();
395 /// Now define the inplace multiplication
399 SGQuat<T>::operator*=(const SGQuat& v)
400 { (*this) = (*this)*v; return *this; }
402 /// The conjugate of the quaternion, this is also the
403 /// inverse for normalized quaternions
407 conj(const SGQuat<T>& v)
408 { return SGQuat<T>(-v(0), -v(1), -v(2), v(3)); }
410 /// The conjugate of the quaternion, this is also the
411 /// inverse for normalized quaternions
415 inverse(const SGQuat<T>& v)
416 { return (1/dot(v, v))*SGQuat<T>(-v(0), -v(1), -v(2), v(3)); }
418 /// The imagniary part of the quaternion
422 real(const SGQuat<T>& v)
425 /// The imagniary part of the quaternion
429 imag(const SGQuat<T>& v)
430 { return SGVec3<T>(v.x(), v.y(), v.z()); }
432 /// Scalar dot product
436 dot(const SGQuat<T>& v1, const SGQuat<T>& v2)
437 { return v1(0)*v2(0) + v1(1)*v2(1) + v1(2)*v2(2) + v1(3)*v2(3); }
439 /// The euclidean norm of the vector, that is what most people call length
443 norm(const SGQuat<T>& v)
444 { return sqrt(dot(v, v)); }
446 /// The euclidean norm of the vector, that is what most people call length
450 length(const SGQuat<T>& v)
451 { return sqrt(dot(v, v)); }
453 /// The 1-norm of the vector, this one is the fastest length function we
454 /// can implement on modern cpu's
458 norm1(const SGQuat<T>& v)
459 { return fabs(v(0)) + fabs(v(1)) + fabs(v(2)) + fabs(v(3)); }
461 /// The euclidean norm of the vector, that is what most people call length
465 normalize(const SGQuat<T>& q)
466 { return (1/norm(q))*q; }
468 /// Return true if exactly the same
472 operator==(const SGQuat<T>& v1, const SGQuat<T>& v2)
473 { return v1(0)==v2(0) && v1(1)==v2(1) && v1(2)==v2(2) && v1(3)==v2(3); }
475 /// Return true if not exactly the same
479 operator!=(const SGQuat<T>& v1, const SGQuat<T>& v2)
480 { return ! (v1 == v2); }
482 /// Return true if equal to the relative tolerance tol
483 /// Note that this is not the same than comparing quaternions to represent
484 /// the same rotation
488 equivalent(const SGQuat<T>& v1, const SGQuat<T>& v2, T tol)
489 { return norm1(v1 - v2) < tol*(norm1(v1) + norm1(v2)); }
491 /// Return true if about equal to roundoff of the underlying type
492 /// Note that this is not the same than comparing quaternions to represent
493 /// the same rotation
497 equivalent(const SGQuat<T>& v1, const SGQuat<T>& v2)
498 { return equivalent(v1, v2, 100*SGLimits<T>::epsilon()); }
504 isNaN(const SGQuat<T>& v)
506 return SGMisc<T>::isNaN(v(0)) || SGMisc<T>::isNaN(v(1))
507 || SGMisc<T>::isNaN(v(2)) || SGMisc<T>::isNaN(v(3));
511 /// quaternion interpolation for t in [0,1] interpolate between src (=0)
516 interpolate(T t, const SGQuat<T>& src, const SGQuat<T>& dst)
518 T cosPhi = dot(src, dst);
519 // need to take the shorter way ...
520 int signCosPhi = SGMisc<T>::sign(cosPhi);
521 // cosPhi must be corrected for that sign
522 cosPhi = fabs(cosPhi);
524 // first opportunity to fail - make sure acos will succeed later -
529 // now the half angle between the orientations
532 // need the scales now, if the angle is very small, do linear interpolation
533 // to avoid instabilities
535 if (fabs(o) < SGLimits<T>::epsilon()) {
539 // note that we can give a positive lower bound for sin(o) here
542 scale0 = sin((1 - t)*o)*so;
543 scale1 = sin(t*o)*so;
546 return scale0*src + signCosPhi*scale1*dst;
549 /// Output to an ostream
550 template<typename char_type, typename traits_type, typename T>
552 std::basic_ostream<char_type, traits_type>&
553 operator<<(std::basic_ostream<char_type, traits_type>& s, const SGQuat<T>& v)
554 { return s << "[ " << v(0) << ", " << v(1) << ", " << v(2) << ", " << v(3) << " ]"; }
556 /// Two classes doing actually the same on different types
557 typedef SGQuat<float> SGQuatf;
558 typedef SGQuat<double> SGQuatd;
562 toQuatf(const SGQuatd& v)
563 { return SGQuatf((float)v(0), (float)v(1), (float)v(2), (float)v(3)); }
567 toQuatd(const SGQuatf& v)
568 { return SGQuatd(v(0), v(1), v(2), v(3)); }