184 lines
4.7 KiB
C++
184 lines
4.7 KiB
C++
/*
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LA: linear algebra C++ interface library
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Copyright (C) 2008-2020 Jiri Pittner <jiri.pittner@jh-inst.cas.cz> or <jiri@pittnerovi.com>
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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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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#include "quaternion.h"
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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 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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//basically the same code as in normquat2rotmat, but avoiding extra storage
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template<typename T>
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void Quaternion<T>::rotate(T *to, const T *from, Quaternion<T> *grad) const
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{
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//some subexpression eliminations
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{
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T q00= q[0]*q[0];
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T q11= q[1]*q[1];
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T q22= q[2]*q[2];
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T q33= q[3]*q[3];
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to[0] = (q00+q11-q22-q33) * from[0];
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to[1] = (q00+q22-q11-q33) * from[1];
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to[2] = (q00+q33-q11-q22) * from[2];
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}
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T q01= q[0]*q[1];
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T q02= q[0]*q[2];
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T q03= q[0]*q[3];
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T q12= q[1]*q[2];
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T q13= q[1]*q[3];
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T q23= q[2]*q[3];
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T f0=from[0]+from[0];
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T f1=from[1]+from[1];
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T f2=from[2]+from[2];
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to[0] += (q12+q03)*f1;
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to[0] += (q13-q02)*f2;
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to[1] += (q12-q03)*f0;
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to[1] += (q23+q01)*f2;
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to[2] += (q13+q02)*f0;
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to[2] += (q23-q01)*f1;
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/*
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to[0] = (2*q[0]*q[0]-1+2*q[1]*q[1]) * from[0] +
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2*(q[1]*q[2]+q[0]*q[3]) * from[1] +
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2*(q[1]*q[3]-q[0]*q[2]) * from[2];
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to[1] = 2*(q[1]*q[2]-q[0]*q[3]) * from[0] +
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(2*q[0]*q[0]-1+2*q[2]*q[2]) * from[1] +
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2*(q[2]*q[3]+q[0]*q[1]) * from[2];
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to[2] = 2*(q[1]*q[3]+q[0]*q[2]) * from[0] +
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2*(q[2]*q[3]-q[0]*q[1]) * from[1] +
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(2*q[0]*q[0]-1+2*q[3]*q[3]) * from[2];
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*/
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if(grad)
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{
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grad[0][0]= q[0]*f0 + q[3]*f1 - q[2]*f2;
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grad[0][1]= q[1]*f0 + q[2]*f1 + q[3]*f2;
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grad[0][2]= -q[2]*f0 + q[1]*f1 - q[0]*f2;
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grad[0][3]= -q[3]*f0 + q[0]*f1 + q[1]*f2;
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grad[1][0]= -q[3]*f0 + q[0]*f1 + q[1]*f2;
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grad[1][1]= q[2]*f0 - q[1]*f1 + q[0]*f2;
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grad[1][2]= q[1]*f0 + q[2]*f1 + q[3]*2;
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grad[1][3]= -q[0]*f0 - q[3]*f1 + q[2]*f2;
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grad[2][0]= q[2]*f0 - q[1]*f1 + q[0]*f2;
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grad[2][1]= q[3]*f0 - q[0]*f1 - q[1]*f2;
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grad[2][2]= q[0]*f0 + q[3]*f1 - q[2]*f2;
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grad[2][3]= q[1]*f0 + q[2]*f1 + q[3]*f2;
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}
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}
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template<typename T>
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Quaternion<T> Quaternion<T>::rotateby(const Quaternion<T> &rhs)
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{
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//return rhs.inverse() * *this * rhs; //inefficient reference implementation
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Quaternion<T> r;
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r[0]=0;
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rhs.rotate(&r[1],&q[1]);
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return r;
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}
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template<typename T>
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Quaternion<T> Quaternion<T>::rotate_match(T *to, const T *from, const T *match) const
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{
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Quaternion<T> grad[3];
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Quaternion<T>::rotate(to, from, grad);
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Quaternion<T> derivative;
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derivative = grad[0] * (to[0]-match[0]);
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derivative += grad[1] * (to[1]-match[1]);
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derivative += grad[2] * (to[2]-match[2]);
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return derivative;
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}
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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 Quaternion<T>::normquat2euler(T *e) const
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{
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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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template<typename T>
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void Quaternion<T>::axis2normquat(const T *axis, const T &angle)
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{
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T a = (T).5*angle;
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q[0]=cos(a);
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T s=sin(a);
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q[1]=axis[0]*s;
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q[2]=axis[1]*s;
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q[3]=axis[2]*s;
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}
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template<typename T>
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void Quaternion<T>::normquat2axis(T *axis, T &angle) const
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{
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T s = sqrt(q[1]*q[1] + q[2]*q[2] +q[3]*q[3]);
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angle = 2*atan2(s,q[0]);
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s= 1/s;
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axis[0]= q[1]*s;
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axis[1]= q[2]*s;
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axis[2]= q[3]*s;
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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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#define INSTANTIZE2(T) \
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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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#ifndef AVOID_GONIOM_FUNC
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INSTANTIZE2(float)
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#ifndef QUAT_NO_DOUBLE
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INSTANTIZE2(double)
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#endif
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#endif
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