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jiri
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@ -17,19 +17,45 @@
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*/
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#include "quaternion.h"
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#include <math.h>
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template<>
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double Quaternion<double>::norm(void) const
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//do not replicate this code in each object file, therefore not in .h
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//and instantize the templates for the types needed
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template<typename T>
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const Quaternion<T> Quaternion<T>::operator*(const Quaternion<T> &rhs) const
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{
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return sqrt(this->normsqr());
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}
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return Quaternion<T>
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(
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this->q[0]*rhs.q[0]-this->q[1]*rhs.q[1]-this->q[2]*rhs.q[2]-this->q[3]*rhs.q[3],
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this->q[0]*rhs.q[1]+this->q[1]*rhs.q[0]+this->q[2]*rhs.q[3]-this->q[3]*rhs.q[2],
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this->q[0]*rhs.q[2]+this->q[2]*rhs.q[0]+this->q[3]*rhs.q[1]-this->q[1]*rhs.q[3],
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this->q[0]*rhs.q[3]+this->q[3]*rhs.q[0]+this->q[1]*rhs.q[2]-this->q[2]*rhs.q[1]
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);
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};
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template<>
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float Quaternion<float>::norm(void) const
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//optionally skip this for microcontrollers if not needed
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//note that C++ standard headers should use float version of the functions for T=float
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#ifndef AVOID_GONIOM_FUNC
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template<typename T>
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void normquat2euler(const Quaternion<T> &q, T (&e)[3])
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{
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return sqrtf(this->normsqr());
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e[0]= atan2(2*q[1]*q[2]-2*q[0]*q[3],2*q[0]*q[0]+2*q[1]*q[1]-1);
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e[1]= -asin(2*q[1]*q[3]+2*q[0]*q[2]);
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e[2]= atan2(2*q[2]*q[3]-2*q[0]*q[1],2*q[0]*q[0]+2*q[3]*q[3]-1);
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}
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#endif
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//force instantization
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#define INSTANTIZE(T) \
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template class Quaternion<T>; \
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template void normquat2euler(const Quaternion<T> &q, T (&e)[3]); \
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INSTANTIZE(float)
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#ifndef QUAT_NO_DOUBLE
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INSTANTIZE(double)
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#endif
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96
quaternion.h
96
quaternion.h
@ -15,11 +15,18 @@
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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//this actually should be compilable separately from LA as well as being a part of LA
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#ifndef _QUATERNION_H_
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#define _QUATERNION_H_
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#include <stdlib.h>
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#include <iostream>
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#include <complex>
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#include <cstring>
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#include <math.h>
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template <typename T>
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class Quaternion
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@ -29,13 +36,15 @@ public:
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T q[4];
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//
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Quaternion(void) {};
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Quaternion(const T x, const T u=0, const T v=0, const T w=0) {q[0]=x; q[1]=u; q[2]=v; q[3]=w;}; //quaternion from real
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Quaternion(const T x, const T u=0, const T v=0, const T w=0) {q[0]=x; q[1]=u; q[2]=v; q[3]=w;}; //quaternion from real(s)
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Quaternion(const std::complex<T> &rhs) {q[0]=rhs.real(); q[1]=rhs.imag(); q[2]=0; q[3]=0;} //quaternion from complex
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explicit Quaternion(const T* x) {memcpy(q,x,4*sizeof(T));}
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//compiler generates default copy constructor and assignment operator
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//formal indexing
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const T operator[](const int i) const {return this->q[i];};
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T operator[](const int i) {return this->q[i];};
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T& operator[](const int i) {return this->q[i];};
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//operations of quaternions with scalars
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Quaternion& operator=(const T x) {q[0]=x; memset(&q[1],0,3*sizeof(T)); return *this;}; //quaternion from real
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@ -49,24 +58,17 @@ public:
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const Quaternion operator/(const T rhs) const {return Quaternion(*this) /= rhs;};
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//quaternion algebra
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const Quaternion operator-() const {Quaternion r(*this); r.q[0]= -r.q[0]; r.q[1]= -r.q[1]; r.q[2]= -r.q[2]; r.q[3]= -r.q[3]; return r;}; //unary minus
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Quaternion& operator+=(const Quaternion &rhs) {this->q[0]+=rhs.q[0];this->q[1]+=rhs.q[1];this->q[2]+=rhs.q[2];this->q[3]+=rhs.q[3]; return *this;};
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Quaternion& operator-=(const Quaternion &rhs) {this->q[0]-=rhs.q[0];this->q[1]-=rhs.q[1];this->q[2]-=rhs.q[2];this->q[3]-=rhs.q[3]; return *this;};
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const Quaternion operator+(const Quaternion &rhs) const {return Quaternion(*this) += rhs;};
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const Quaternion operator-(const Quaternion &rhs) const {return Quaternion(*this) -= rhs;};
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const Quaternion operator*(const Quaternion &rhs) const
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{
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return Quaternion
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(
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this->q[0]*rhs.q[0]-this->q[1]*rhs.q[1]-this->q[2]*rhs.q[2]-this->q[3]*rhs.q[3],
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this->q[0]*rhs.q[1]+this->q[1]*rhs.q[0]+this->q[2]*rhs.q[3]-this->q[3]*rhs.q[2],
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this->q[0]*rhs.q[2]+this->q[2]*rhs.q[0]+this->q[3]*rhs.q[1]-this->q[1]*rhs.q[3],
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this->q[0]*rhs.q[3]+this->q[3]*rhs.q[0]+this->q[1]*rhs.q[2]-this->q[2]*rhs.q[1]
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);
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};
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const Quaternion operator*(const Quaternion &rhs) const;
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Quaternion& conjugateme(void) {q[1] = -q[1]; q[2] = -q[2]; q[3] = -q[3]; return *this;}
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Quaternion conjugate(void) const {return Quaternion(*this).conjugateme();}
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T normsqr(void) const {return q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3];};
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T norm(void) const;
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T norm(void) const {return sqrt(this->normsqr());};
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Quaternion& normalize(bool unique_sign=false) {*this /= this->norm(); if(unique_sign && q[0]<0) *this *= (T)-1; return *this;};
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Quaternion inverse(void) const {return Quaternion(*this).conjugateme()/this->normsqr();};
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const Quaternion operator/(const Quaternion &rhs) const {return *this * rhs.inverse();};
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};
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@ -93,6 +95,74 @@ return s;
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}
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//"euler" or Tait-Bryan angles [corresponding to meul -r -T xyz -d -t -R]
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template<typename T>
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void normquat2euler(const Quaternion<T> &q, T (&e)[3]);
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//the following must be in .h due to the generic M type which is unspecified and can be any type providing [][], either plain C matrix or LA matrix
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//conversion between quanternions and rotation matrices
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//
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template<typename T, typename M>
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void normquat2rotmat(const Quaternion<T> &q, M &a)
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{
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a[0][0] = 2*q[0]*q[0]-1+2*q[1]*q[1];
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a[0][1] = 2*(q[1]*q[2]+q[0]*q[3]);
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a[0][2] = 2*(q[1]*q[3]-q[0]*q[2]);
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a[1][0] = 2*(q[1]*q[2]-q[0]*q[3]);
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a[1][1] = 2*q[0]*q[0]-1+2*q[2]*q[2];
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a[1][2] = 2*(q[2]*q[3]+q[0]*q[1]);
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a[2][0] = 2*(q[1]*q[3]+q[0]*q[2]);
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a[2][1] = 2*(q[2]*q[3]-q[0]*q[1]);
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a[2][2] = 2*q[0]*q[0]-1+2*q[3]*q[3];
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}
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template<typename T, typename M>
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void quat2rotmat(Quaternion<T> q, M &a, const bool already_normalized=false)
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{
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if(!already_normalized) q.normalize();
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normquat2rotmat(q,a);
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}
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//normalized quaternion from rotation matrix
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//convention compatible with the paper on MEMS sensors by Sebastian O.H. Madgwick
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//the rotation matrix correcponds to transpose of (4) in Sarabandi and Thomas paper
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//where the method is described
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template<typename T, typename M>
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void rotmat2normquat(const M &a, Quaternion<T> &q)
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{
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T tr= a[0][0]+a[1][1]+a[2][2];
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if(tr>=0)
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{
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q[0] = (T).5*sqrt((T)1. +tr);
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q[1] = (T).5*sqrt((T)1. +a[0][0]-a[1][1]-a[2][2]);
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q[2] = (T).5*sqrt((T)1. -a[0][0]+a[1][1]-a[2][2]);
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q[3] = (T).5*sqrt((T)1. -a[0][0]-a[1][1]+a[2][2]);
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}
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else
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{
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T a12p = a[0][1]+a[1][0];
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T a12m = a[0][1]-a[1][0];
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T a13p = a[0][2]+a[2][0];
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T a13m = a[0][2]-a[2][0];
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T a23p = a[1][2]+a[2][1];
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T a23m = a[1][2]-a[2][1];
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q[0] = (T).5*sqrt((a23m*a23m+a13m*a13m+a12m*a12m)/((T)3.-tr));
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q[1] = (T).5*sqrt((a23m*a23m+a12p*a12p+a13p*a13p)/((T)3.-a[0][0]+a[1][1]+a[2][2]));
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q[2] = (T).5*sqrt((a13m*a13m+a12p*a12p+a23p*a23p)/((T)3.+a[0][0]-a[1][1]+a[2][2]));
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q[3] = (T).5*sqrt((a12m*a12m+a13p*a13p+a23p*a23p)/((T)3.+a[0][0]+a[1][1]-a[2][2]));
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}
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if(a[1][2]-a[2][1]<0) q[1] = -q[1];
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if(a[2][0]-a[0][2]<0) q[2] = -q[2];
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if(a[0][1]-a[1][0]<0) q[3] = -q[3];
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}
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#endif /* _QUATERNION_H_ */
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