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.
27 /// Default constructor. Does not initialize at all.
28 /// If you need them zero initialized, SGQuat::zeros()
31 /// Initialize with nans in the debug build, that will guarantee to have
32 /// a fast uninitialized default constructor in the release but shows up
33 /// uninitialized values in the debug build very fast ...
35 for (unsigned i = 0; i < 4; ++i)
36 _data[i] = SGLimits<T>::quiet_NaN();
39 /// Constructor. Initialize by the given values
40 SGQuat(T _x, T _y, T _z, T _w)
41 { x() = _x; y() = _y; z() = _z; w() = _w; }
42 /// Constructor. Initialize by the content of a plain array,
43 /// make sure it has at least 4 elements
44 explicit SGQuat(const T* d)
45 { _data[0] = d[0]; _data[1] = d[1]; _data[2] = d[2]; _data[3] = d[3]; }
47 /// Return a unit quaternion
48 static SGQuat unit(void)
49 { return fromRealImag(1, SGVec3<T>(0)); }
51 /// Return a quaternion from euler angles
52 static SGQuat fromEulerRad(T z, T y, T x)
55 T zd2 = T(0.5)*z; T yd2 = T(0.5)*y; T xd2 = T(0.5)*x;
56 T Szd2 = sin(zd2); T Syd2 = sin(yd2); T Sxd2 = sin(xd2);
57 T Czd2 = cos(zd2); T Cyd2 = cos(yd2); T Cxd2 = cos(xd2);
58 T Cxd2Czd2 = Cxd2*Czd2; T Cxd2Szd2 = Cxd2*Szd2;
59 T Sxd2Szd2 = Sxd2*Szd2; T Sxd2Czd2 = Sxd2*Czd2;
60 q.w() = Cxd2Czd2*Cyd2 + Sxd2Szd2*Syd2;
61 q.x() = Sxd2Czd2*Cyd2 - Cxd2Szd2*Syd2;
62 q.y() = Cxd2Czd2*Syd2 + Sxd2Szd2*Cyd2;
63 q.z() = Cxd2Szd2*Cyd2 - Sxd2Czd2*Syd2;
67 /// Return a quaternion from euler angles in degrees
68 static SGQuat fromEulerDeg(T z, T y, T x)
70 return fromEulerRad(SGMisc<T>::deg2rad(z), SGMisc<T>::deg2rad(y),
71 SGMisc<T>::deg2rad(x));
74 /// Return a quaternion from euler angles
75 static SGQuat fromYawPitchRoll(T y, T p, T r)
76 { return fromEulerRad(y, p, r); }
78 /// Return a quaternion from euler angles
79 static SGQuat fromYawPitchRollDeg(T y, T p, T r)
80 { return fromEulerDeg(y, p, r); }
82 /// Return a quaternion from euler angles
83 static SGQuat fromHeadAttBank(T h, T a, T b)
84 { return fromEulerRad(h, a, b); }
86 /// Return a quaternion from euler angles
87 static SGQuat fromHeadAttBankDeg(T h, T a, T b)
88 { return fromEulerDeg(h, a, b); }
90 /// Return a quaternion rotation the the horizontal local frame from given
91 /// longitude and latitude
92 static SGQuat fromLonLatRad(T lon, T lat)
96 T yd2 = T(-0.25)*SGMisc<value_type>::pi() - T(0.5)*lat;
108 /// Return a quaternion rotation the the horizontal local frame from given
109 /// longitude and latitude
110 static SGQuat fromLonLatDeg(T lon, T lat)
111 { return fromLonLatRad(SGMisc<T>::deg2rad(lon), SGMisc<T>::deg2rad(lat)); }
113 /// Create a quaternion from the angle axis representation
114 static SGQuat fromAngleAxis(T angle, const SGVec3<T>& axis)
116 T angle2 = 0.5*angle;
117 return fromRealImag(cos(angle2), T(sin(angle2))*axis);
120 /// Create a quaternion from the angle axis representation
121 static SGQuat fromAngleAxisDeg(T angle, const SGVec3<T>& axis)
122 { return fromAngleAxis(SGMisc<T>::deg2rad(angle), axis); }
124 /// Create a quaternion from the angle axis representation where the angle
125 /// is stored in the axis' length
126 static SGQuat fromAngleAxis(const SGVec3<T>& axis)
128 T nAxis = norm(axis);
129 if (nAxis <= SGLimits<T>::min())
130 return SGQuat(1, 0, 0, 0);
131 T angle2 = 0.5*nAxis;
132 return fromRealImag(cos(angle2), T(sin(angle2)/nAxis)*axis);
135 /// Return a quaternion from real and imaginary part
136 static SGQuat fromRealImag(T r, const SGVec3<T>& i)
146 /// Return an all zero vector
147 static SGQuat zeros(void)
148 { return SGQuat(0, 0, 0, 0); }
150 /// write the euler angles into the references
151 void getEulerRad(T& zRad, T& yRad, T& xRad) const
153 value_type sqrQW = w()*w();
154 value_type sqrQX = x()*x();
155 value_type sqrQY = y()*y();
156 value_type sqrQZ = z()*z();
158 value_type num = 2*(y()*z() + w()*x());
159 value_type den = sqrQW - sqrQX - sqrQY + sqrQZ;
160 if (fabs(den) < SGLimits<value_type>::min() &&
161 fabs(num) < SGLimits<value_type>::min())
164 xRad = atan2(num, den);
166 value_type tmp = 2*(x()*z() - w()*y());
168 yRad = 0.5*SGMisc<value_type>::pi();
170 yRad = -0.5*SGMisc<value_type>::pi();
174 num = 2*(x()*y() + w()*z());
175 den = sqrQW + sqrQX - sqrQY - sqrQZ;
176 if (fabs(den) < SGLimits<value_type>::min() &&
177 fabs(num) < SGLimits<value_type>::min())
180 value_type psi = atan2(num, den);
182 psi += 2*SGMisc<value_type>::pi();
187 /// write the euler angles in degrees into the references
188 void getEulerDeg(T& zDeg, T& yDeg, T& xDeg) const
190 getEulerRad(zDeg, yDeg, xDeg);
191 zDeg = SGMisc<T>::rad2deg(zDeg);
192 yDeg = SGMisc<T>::rad2deg(yDeg);
193 xDeg = SGMisc<T>::rad2deg(xDeg);
196 /// write the angle axis representation into the references
197 void getAngleAxis(T& angle, SGVec3<T>& axis) const
200 if (nrm < SGLimits<T>::min()) {
202 axis = SGVec3<T>(0, 0, 0);
205 angle = acos(SGMisc<T>::max(-1, SGMisc<T>::min(1, rNrm*w())));
207 if (fabs(sAng) < SGLimits<T>::min())
208 axis = SGVec3<T>(1, 0, 0);
210 axis = (rNrm/sAng)*imag(*this);
215 /// write the angle axis representation into the references
216 void getAngleAxis(SGVec3<T>& axis) const
219 getAngleAxis(angle, axis);
223 /// Access by index, the index is unchecked
224 const T& operator()(unsigned i) const
226 /// Access by index, the index is unchecked
227 T& operator()(unsigned i)
230 /// Access raw data by index, the index is unchecked
231 const T& operator[](unsigned i) const
233 /// Access raw data by index, the index is unchecked
234 T& operator[](unsigned i)
237 /// Access the x component
238 const T& x(void) const
240 /// Access the x component
243 /// Access the y component
244 const T& y(void) const
246 /// Access the y component
249 /// Access the z component
250 const T& z(void) const
252 /// Access the z component
255 /// Access the w component
256 const T& w(void) const
258 /// Access the w component
262 /// Get the data pointer, usefull for interfacing with plib's sg*Vec
263 const T* data(void) const
265 /// Get the data pointer, usefull for interfacing with plib's sg*Vec
269 /// Readonly interface function to ssg's sgQuat/sgdQuat
270 const T (&sg(void) const)[4]
272 /// Interface function to ssg's sgQuat/sgdQuat
277 SGQuat& operator+=(const SGQuat& v)
278 { _data[0]+=v(0);_data[1]+=v(1);_data[2]+=v(2);_data[3]+=v(3);return *this; }
279 /// Inplace subtraction
280 SGQuat& operator-=(const SGQuat& v)
281 { _data[0]-=v(0);_data[1]-=v(1);_data[2]-=v(2);_data[3]-=v(3);return *this; }
282 /// Inplace scalar multiplication
284 SGQuat& operator*=(S s)
285 { _data[0] *= s; _data[1] *= s; _data[2] *= s; _data[3] *= s; return *this; }
286 /// Inplace scalar multiplication by 1/s
288 SGQuat& operator/=(S s)
289 { return operator*=(1/T(s)); }
290 /// Inplace quaternion multiplication
291 SGQuat& operator*=(const SGQuat& v);
293 /// Transform a vector from the current coordinate frame to a coordinate
294 /// frame rotated with the quaternion
295 SGVec3<T> transform(const SGVec3<T>& v) const
297 value_type r = 2/dot(*this, *this);
298 SGVec3<T> qimag = imag(*this);
299 value_type qr = real(*this);
300 return (r*qr*qr - 1)*v + (r*dot(qimag, v))*qimag - (r*qr)*cross(qimag, v);
302 /// Transform a vector from the coordinate frame rotated with the quaternion
303 /// to the current coordinate frame
304 SGVec3<T> backTransform(const SGVec3<T>& v) const
306 value_type r = 2/dot(*this, *this);
307 SGVec3<T> qimag = imag(*this);
308 value_type qr = real(*this);
309 return (r*qr*qr - 1)*v + (r*dot(qimag, v))*qimag + (r*qr)*cross(qimag, v);
312 /// Rotate a given vector with the quaternion
313 SGVec3<T> rotate(const SGVec3<T>& v) const
314 { return backTransform(v); }
315 /// Rotate a given vector with the inverse quaternion
316 SGVec3<T> rotateBack(const SGVec3<T>& v) const
317 { return transform(v); }
319 /// Return the time derivative of the quaternion given the angular velocity
321 derivative(const SGVec3<T>& angVel)
325 deriv.w() = 0.5*(-x()*angVel(0) - y()*angVel(1) - z()*angVel(2));
326 deriv.x() = 0.5*( w()*angVel(0) - z()*angVel(1) + y()*angVel(2));
327 deriv.y() = 0.5*( z()*angVel(0) + w()*angVel(1) - x()*angVel(2));
328 deriv.z() = 0.5*(-y()*angVel(0) + x()*angVel(1) + w()*angVel(2));
338 /// Unary +, do nothing ...
342 operator+(const SGQuat<T>& v)
345 /// Unary -, do nearly nothing
349 operator-(const SGQuat<T>& v)
350 { return SGQuat<T>(-v(0), -v(1), -v(2), -v(3)); }
356 operator+(const SGQuat<T>& v1, const SGQuat<T>& v2)
357 { return SGQuat<T>(v1(0)+v2(0), v1(1)+v2(1), v1(2)+v2(2), v1(3)+v2(3)); }
363 operator-(const SGQuat<T>& v1, const SGQuat<T>& v2)
364 { return SGQuat<T>(v1(0)-v2(0), v1(1)-v2(1), v1(2)-v2(2), v1(3)-v2(3)); }
366 /// Scalar multiplication
367 template<typename S, typename T>
370 operator*(S s, const SGQuat<T>& v)
371 { return SGQuat<T>(s*v(0), s*v(1), s*v(2), s*v(3)); }
373 /// Scalar multiplication
374 template<typename S, typename T>
377 operator*(const SGQuat<T>& v, S s)
378 { return SGQuat<T>(s*v(0), s*v(1), s*v(2), s*v(3)); }
380 /// Quaterion multiplication
384 operator*(const SGQuat<T>& v1, const SGQuat<T>& v2)
387 v.x() = v1.w()*v2.x() + v1.x()*v2.w() + v1.y()*v2.z() - v1.z()*v2.y();
388 v.y() = v1.w()*v2.y() - v1.x()*v2.z() + v1.y()*v2.w() + v1.z()*v2.x();
389 v.z() = v1.w()*v2.z() + v1.x()*v2.y() - v1.y()*v2.x() + v1.z()*v2.w();
390 v.w() = v1.w()*v2.w() - v1.x()*v2.x() - v1.y()*v2.y() - v1.z()*v2.z();
394 /// Now define the inplace multiplication
398 SGQuat<T>::operator*=(const SGQuat& v)
399 { (*this) = (*this)*v; return *this; }
401 /// The conjugate of the quaternion, this is also the
402 /// inverse for normalized quaternions
406 conj(const SGQuat<T>& v)
407 { return SGQuat<T>(-v(0), -v(1), -v(2), v(3)); }
409 /// The conjugate of the quaternion, this is also the
410 /// inverse for normalized quaternions
414 inverse(const SGQuat<T>& v)
415 { return (1/dot(v, v))*SGQuat<T>(-v(0), -v(1), -v(2), v(3)); }
417 /// The imagniary part of the quaternion
421 real(const SGQuat<T>& v)
424 /// The imagniary part of the quaternion
428 imag(const SGQuat<T>& v)
429 { return SGVec3<T>(v.x(), v.y(), v.z()); }
431 /// Scalar dot product
435 dot(const SGQuat<T>& v1, const SGQuat<T>& v2)
436 { return v1(0)*v2(0) + v1(1)*v2(1) + v1(2)*v2(2) + v1(3)*v2(3); }
438 /// The euclidean norm of the vector, that is what most people call length
442 norm(const SGQuat<T>& v)
443 { return sqrt(dot(v, v)); }
445 /// The euclidean norm of the vector, that is what most people call length
449 length(const SGQuat<T>& v)
450 { return sqrt(dot(v, v)); }
452 /// The 1-norm of the vector, this one is the fastest length function we
453 /// can implement on modern cpu's
457 norm1(const SGQuat<T>& v)
458 { return fabs(v(0)) + fabs(v(1)) + fabs(v(2)) + fabs(v(3)); }
460 /// The euclidean norm of the vector, that is what most people call length
464 normalize(const SGQuat<T>& q)
465 { return (1/norm(q))*q; }
467 /// Return true if exactly the same
471 operator==(const SGQuat<T>& v1, const SGQuat<T>& v2)
472 { return v1(0)==v2(0) && v1(1)==v2(1) && v1(2)==v2(2) && v1(3)==v2(3); }
474 /// Return true if not exactly the same
478 operator!=(const SGQuat<T>& v1, const SGQuat<T>& v2)
479 { return ! (v1 == v2); }
481 /// Return true if equal to the relative tolerance tol
482 /// Note that this is not the same than comparing quaternions to represent
483 /// the same rotation
487 equivalent(const SGQuat<T>& v1, const SGQuat<T>& v2, T tol)
488 { return norm1(v1 - v2) < tol*(norm1(v1) + norm1(v2)); }
490 /// Return true if about equal to roundoff of the underlying type
491 /// Note that this is not the same than comparing quaternions to represent
492 /// the same rotation
496 equivalent(const SGQuat<T>& v1, const SGQuat<T>& v2)
497 { return equivalent(v1, v2, 100*SGLimits<T>::epsilon()); }
503 isNaN(const SGQuat<T>& v)
505 return SGMisc<T>::isNaN(v(0)) || SGMisc<T>::isNaN(v(1))
506 || SGMisc<T>::isNaN(v(2)) || SGMisc<T>::isNaN(v(3));
510 /// quaternion interpolation for t in [0,1] interpolate between src (=0)
515 interpolate(T t, const SGQuat<T>& src, const SGQuat<T>& dst)
517 T cosPhi = dot(src, dst);
518 // need to take the shorter way ...
519 int signCosPhi = SGMisc<T>::sign(cosPhi);
520 // cosPhi must be corrected for that sign
521 cosPhi = fabs(cosPhi);
523 // first opportunity to fail - make sure acos will succeed later -
528 // now the half angle between the orientations
531 // need the scales now, if the angle is very small, do linear interpolation
532 // to avoid instabilities
534 if (fabs(o) < SGLimits<T>::epsilon()) {
538 // note that we can give a positive lower bound for sin(o) here
541 scale0 = sin((1 - t)*o)*so;
542 scale1 = sin(t*o)*so;
545 return scale0*src + signCosPhi*scale1*dst;
548 /// Output to an ostream
549 template<typename char_type, typename traits_type, typename T>
551 std::basic_ostream<char_type, traits_type>&
552 operator<<(std::basic_ostream<char_type, traits_type>& s, const SGQuat<T>& v)
553 { return s << "[ " << v(0) << ", " << v(1) << ", " << v(2) << ", " << v(3) << " ]"; }
555 /// Two classes doing actually the same on different types
556 typedef SGQuat<float> SGQuatf;
557 typedef SGQuat<double> SGQuatd;
561 toQuatf(const SGQuatd& v)
562 { return SGQuatf((float)v(0), (float)v(1), (float)v(2), (float)v(3)); }
566 toQuatd(const SGQuatf& v)
567 { return SGQuatd(v(0), v(1), v(2), v(3)); }