437 lines
13 KiB
C++
437 lines
13 KiB
C++
/****************************************************************************
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* VCGLib o o *
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* Visual and Computer Graphics Library o o *
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* _ O _ *
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* Copyright(C) 2004-2016 \/)\/ *
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* Visual Computing Lab /\/| *
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* ISTI - Italian National Research Council | *
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* \ *
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* All rights reserved. *
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* *
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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 2 of the License, or *
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* (at your option) any later version. *
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* *
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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 (http://www.gnu.org/licenses/gpl.txt) *
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* for more details. *
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* *
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****************************************************************************/
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/****************************************************************************
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History
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$Log: not supported by cvs2svn $
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Revision 1.18 2007/07/03 16:07:09 corsini
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add DCM to Euler Angles method (to implement)
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Revision 1.17 2007/02/06 12:24:07 tarini
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added a missing "Quaternion<S>::" in "FromEulerAngles"
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Revision 1.16 2007/02/05 13:55:21 corsini
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add euler angle to quaternion conversion
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Revision 1.15 2006/06/22 08:00:26 ganovelli
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toMatrix with matrix33 added
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Revision 1.14 2005/04/17 21:57:03 ganovelli
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tolto il const a interpolate
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Revision 1.13 2005/04/15 09:19:50 ponchio
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Typo: Point3 -> Point4
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Revision 1.12 2005/04/14 17:22:34 ponchio
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*** empty log message ***
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Revision 1.11 2005/04/14 11:35:09 ponchio
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*** empty log message ***
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Revision 1.10 2004/12/15 18:45:50 tommyfranken
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*** empty log message ***
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Revision 1.9 2004/10/22 14:35:42 ponchio
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m.element(x, y) -> m[x][y]
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Revision 1.8 2004/10/07 13:54:03 ganovelli
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added SetIdentity
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Revision 1.7 2004/04/07 10:48:37 cignoni
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updated access to matrix44 elements through V() instead simple []
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Revision 1.6 2004/03/25 14:57:49 ponchio
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Microerror. ($LOG$ -> $Log: not supported by cvs2svn $
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Microerror. ($LOG$ -> Revision 1.18 2007/07/03 16:07:09 corsini
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Microerror. ($LOG$ -> add DCM to Euler Angles method (to implement)
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Microerror. ($LOG$ ->
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Microerror. ($LOG$ -> Revision 1.17 2007/02/06 12:24:07 tarini
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Microerror. ($LOG$ -> added a missing "Quaternion<S>::" in "FromEulerAngles"
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Microerror. ($LOG$ ->
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Microerror. ($LOG$ -> Revision 1.16 2007/02/05 13:55:21 corsini
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Microerror. ($LOG$ -> add euler angle to quaternion conversion
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Microerror. ($LOG$ ->
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Microerror. ($LOG$ -> Revision 1.15 2006/06/22 08:00:26 ganovelli
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Microerror. ($LOG$ -> toMatrix with matrix33 added
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Microerror. ($LOG$ ->
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Microerror. ($LOG$ -> Revision 1.14 2005/04/17 21:57:03 ganovelli
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Microerror. ($LOG$ -> tolto il const a interpolate
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Microerror. ($LOG$ ->
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Microerror. ($LOG$ -> Revision 1.13 2005/04/15 09:19:50 ponchio
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Microerror. ($LOG$ -> Typo: Point3 -> Point4
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Microerror. ($LOG$ ->
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Microerror. ($LOG$ -> Revision 1.12 2005/04/14 17:22:34 ponchio
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Microerror. ($LOG$ -> *** empty log message ***
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Microerror. ($LOG$ ->
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Microerror. ($LOG$ -> Revision 1.11 2005/04/14 11:35:09 ponchio
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Microerror. ($LOG$ -> *** empty log message ***
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Microerror. ($LOG$ ->
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Microerror. ($LOG$ -> Revision 1.10 2004/12/15 18:45:50 tommyfranken
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Microerror. ($LOG$ -> *** empty log message ***
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Microerror. ($LOG$ ->
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Microerror. ($LOG$ -> Revision 1.9 2004/10/22 14:35:42 ponchio
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Microerror. ($LOG$ -> m.element(x, y) -> m[x][y]
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Microerror. ($LOG$ ->
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Microerror. ($LOG$ -> Revision 1.8 2004/10/07 13:54:03 ganovelli
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Microerror. ($LOG$ -> added SetIdentity
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Microerror. ($LOG$ ->
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Microerror. ($LOG$ -> Revision 1.7 2004/04/07 10:48:37 cignoni
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Microerror. ($LOG$ -> updated access to matrix44 elements through V() instead simple []
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Microerror. ($LOG$ ->
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****************************************************************************/
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#ifndef QUATERNION_H
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#define QUATERNION_H
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#include <vcg/space/point3.h>
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#include <vcg/space/point4.h>
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#include <vcg/math/base.h>
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#include <vcg/math/matrix44.h>
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#include <vcg/math/matrix33.h>
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namespace vcg {
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/** Class quaternion.
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A quaternion is a point in the unit sphere in four dimension: all
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rotations in three-dimensional space can be represented by a quaternion.
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*/
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template<class S> class Quaternion: public Point4<S> {
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public:
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Quaternion() {}
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Quaternion(const S v0, const S v1, const S v2, const S v3): Point4<S>(v0,v1,v2,v3){}
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Quaternion(const Point4<S> p) : Point4<S>(p) {}
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Quaternion(const S phi, const Point3<S> &a);
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Quaternion operator*(const S &s) const;
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//Quaternion &operator*=(S d);
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Quaternion operator*(const Quaternion &q) const;
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Quaternion &operator*=(const Quaternion &q);
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void Invert();
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Quaternion<S> Inverse() const;
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void SetIdentity();
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void FromAxis(const S phi, const Point3<S> &a);
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void ToAxis(S &phi, Point3<S> &a ) const;
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///warning m must be a rotation matrix, result is unpredictable otherwise
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void FromMatrix(const Matrix44<S> &m);
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void FromMatrix(const Matrix33<S> &m);
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void ToMatrix(Matrix44<S> &m) const;
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void ToMatrix(Matrix33<S> &m) const;
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void ToEulerAngles(S &alpha, S &beta, S &gamma) const;
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void FromEulerAngles(S alpha, S beta, S gamma);
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Point3<S> Rotate(const Point3<S> vec) const;
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//duplicated ... because of gcc new confoming to ISO template derived classes
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//do no 'see' parent members (unless explicitly specified)
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const S & V ( const int i ) const { assert(i>=0 && i<4); return Point4<S>::V(i); }
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S & V ( const int i ) { assert(i>=0 && i<4); return Point4<S>::V(i); }
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/// constuctor that imports from different Quaternion types
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template <class Q>
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static inline Quaternion Construct( const Quaternion<Q> & b )
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{
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return Quaternion(S(b[0]),S(b[1]),S(b[2]),S(b[3]));
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}
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private:
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};
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/*template<classS, class M> void QuaternionToMatrix(Quaternion<S> &s, M &m);
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template<classS, class M> void MatrixtoQuaternion(M &m, Quaternion<S> &s);*/
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template <class S> Quaternion<S> Interpolate( Quaternion<S> a, Quaternion<S> b, double t);
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template <class S> Quaternion<S> &Invert(Quaternion<S> &q);
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template <class S> Quaternion<S> Inverse(const Quaternion<S> &q);
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//Implementation
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template <class S>
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void Quaternion<S>::SetIdentity(){
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FromAxis(0, Point3<S>(1, 0, 0));
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}
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template <class S> Quaternion<S>::Quaternion(const S phi, const Point3<S> &a) {
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FromAxis(phi, a);
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}
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template <class S> Quaternion<S> Quaternion<S>::operator*(const S &s) const {
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return (Quaternion(V(0)*s,V(1)*s,V(2)*s,V(3)*s));
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}
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template <class S> Quaternion<S> Quaternion<S>::operator*(const Quaternion &q) const {
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Point3<S> t1(V(1), V(2), V(3));
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Point3<S> t2(q.V(1), q.V(2), q.V(3));
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S d = t2.dot(t1);
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Point3<S> t3 = t1 ^ t2;
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t1 *= q.V(0);
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t2 *= V(0);
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Point3<S> tf = t1 + t2 +t3;
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Quaternion<S> t;
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t.V(0) = V(0) * q.V(0) - d;
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t.V(1) = tf[0];
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t.V(2) = tf[1];
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t.V(3) = tf[2];
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return t;
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}
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template <class S> Quaternion<S> &Quaternion<S>::operator*=(const Quaternion &q) {
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S ww = V(0) * q.V(0) - V(1) * q.V(1) - V(2) * q.V(2) - V(3) * q.V(3);
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S xx = V(0) * q.V(1) + V(1) * q.V(0) + V(2) * q.V(3) - V(3) * q.V(2);
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S yy = V(0) * q.V(2) - V(1) * q.V(3) + V(2) * q.V(0) + V(3) * q.V(1);
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V(0) = ww;
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V(1) = xx;
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V(2) = yy;
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V(3) = V(0) * q.V(3) + V(1) * q.V(2) - V(2) * q.V(1) + V(3) * q.V(0);
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return *this;
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}
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template <class S> void Quaternion<S>::Invert() {
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V(1)*=-1;
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V(2)*=-1;
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V(3)*=-1;
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}
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template <class S> Quaternion<S> Quaternion<S>::Inverse() const{
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return Quaternion<S>( V(0), -V(1), -V(2), -V(3) );
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}
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template <class S> void Quaternion<S>::FromAxis(const S phi, const Point3<S> &a) {
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Point3<S> b = a;
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b.Normalize();
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S s = math::Sin(phi/(S(2.0)));
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V(0) = math::Cos(phi/(S(2.0)));
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V(1) = b[0]*s;
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V(2) = b[1]*s;
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V(3) = b[2]*s;
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}
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template <class S> void Quaternion<S>::ToAxis(S &phi, Point3<S> &a) const {
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S s = math::Asin(V(0))*S(2.0);
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phi = math::Acos(V(0))*S(2.0);
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if(s < 0)
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phi = - phi;
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a.V(0) = V(1);
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a.V(1) = V(2);
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a.V(2) = V(3);
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a.Normalize();
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}
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template <class S> Point3<S> Quaternion<S>::Rotate(const Point3<S> p) const {
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Quaternion<S> co = *this;
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co.Invert();
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Quaternion<S> tmp(0, p.V(0), p.V(1), p.V(2));
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tmp = (*this) * tmp * co;
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return Point3<S>(tmp.V(1), tmp.V(2), tmp.V(3));
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}
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template<class S, class M> void QuaternionToMatrix(const Quaternion<S> &q, M &m) {
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float x2 = q.V(1) + q.V(1);
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float y2 = q.V(2) + q.V(2);
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float z2 = q.V(3) + q.V(3);
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{
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float xx2 = q.V(1) * x2;
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float yy2 = q.V(2) * y2;
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float zz2 = q.V(3) * z2;
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m[0][0] = 1.0f - yy2 - zz2;
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m[1][1] = 1.0f - xx2 - zz2;
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m[2][2] = 1.0f - xx2 - yy2;
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}
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{
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float yz2 = q.V(2) * z2;
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float wx2 = q.V(0) * x2;
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m[1][2] = yz2 - wx2;
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m[2][1] = yz2 + wx2;
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}
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{
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float xy2 = q.V(1) * y2;
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float wz2 = q.V(0) * z2;
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m[0][1] = xy2 - wz2;
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m[1][0] = xy2 + wz2;
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}
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{
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float xz2 = q.V(1) * z2;
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float wy2 = q.V(0) * y2;
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m[2][0] = xz2 - wy2;
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m[0][2] = xz2 + wy2;
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}
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}
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template <class S> void Quaternion<S>::ToMatrix(Matrix44<S> &m) const {
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QuaternionToMatrix<S, Matrix44<S> >(*this, m);
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m[0][3] = (S)0.0;
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m[1][3] = (S)0.0;
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m[2][3] = (S)0.0;
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m[3][0] = (S)0.0;
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m[3][1] = (S)0.0;
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m[3][2] = (S)0.0;
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m[3][3] = (S)1.0;
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}
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template <class S> void Quaternion<S>::ToMatrix(Matrix33<S> &m) const {
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QuaternionToMatrix<S, Matrix33<S> >(*this, m);
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}
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template<class S, class M> void MatrixToQuaternion(const M &m, Quaternion<S> &q) {
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if ( m[0][0] + m[1][1] + m[2][2] > 0.0f ) {
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S t = m[0][0] + m[1][1] + m[2][2] + 1.0f;
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S s = (S)0.5 / math::Sqrt(t);
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q.V(0) = s * t;
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q.V(3) = ( m[1][0] - m[0][1] ) * s;
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q.V(2) = ( m[0][2] - m[2][0] ) * s;
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q.V(1) = ( m[2][1] - m[1][2] ) * s;
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} else if ( m[0][0] > m[1][1] && m[0][0] > m[2][2] ) {
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S t = m[0][0] - m[1][1] - m[2][2] + 1.0f;
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S s = (S)0.5 / math::Sqrt(t);
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q.V(1) = s * t;
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q.V(2) = ( m[1][0] + m[0][1] ) * s;
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q.V(3) = ( m[0][2] + m[2][0] ) * s;
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q.V(0) = ( m[2][1] - m[1][2] ) * s;
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} else if ( m[1][1] > m[2][2] ) {
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S t = - m[0][0] + m[1][1] - m[2][2] + 1.0f;
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S s = (S)0.5 / math::Sqrt(t);
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q.V(2) = s * t;
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q.V(1) = ( m[1][0] + m[0][1] ) * s;
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q.V(0) = ( m[0][2] - m[2][0] ) * s;
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q.V(3) = ( m[2][1] + m[1][2] ) * s;
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} else {
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S t = - m[0][0] - m[1][1] + m[2][2] + 1.0f;
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S s = (S)0.5 / math::Sqrt(t);
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q.V(3) = s * t;
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q.V(0) = ( m[1][0] - m[0][1] ) * s;
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q.V(1) = ( m[0][2] + m[2][0] ) * s;
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q.V(2) = ( m[2][1] + m[1][2] ) * s;
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}
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}
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template <class S> void Quaternion<S>::FromMatrix(const Matrix44<S> &m) {
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MatrixToQuaternion<S, Matrix44<S> >(m, *this);
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}
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template <class S> void Quaternion<S>::FromMatrix(const Matrix33<S> &m) {
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MatrixToQuaternion<S, Matrix33<S> >(m, *this);
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}
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template<class S>
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void Quaternion<S>::ToEulerAngles(S &alpha, S &beta, S &gamma) const
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{
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#define P(a,b,c,d) (2*(V(a)*V(b)+V(c)*V(d)))
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#define M(a,b,c,d) (2*(V(a)*V(b)-V(c)*V(d)))
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alpha = math::Atan2( P(0,1,2,3) , 1-P(1,1,2,2) );
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beta = math::Asin ( M(0,2,3,1) );
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gamma = math::Atan2( P(0,3,1,2) , 1-P(2,2,3,3) );
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#undef P
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#undef M
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}
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template<class S>
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void Quaternion<S>::FromEulerAngles(S alpha, S beta, S gamma)
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{
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S cosalpha = math::Cos(alpha / 2.0);
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S cosbeta = math::Cos(beta / 2.0);
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S cosgamma = math::Cos(gamma / 2.0);
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S sinalpha = math::Sin(alpha / 2.0);
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S sinbeta = math::Sin(beta / 2.0);
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S singamma = math::Sin(gamma / 2.0);
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V(0) = cosalpha * cosbeta * cosgamma + sinalpha * sinbeta * singamma;
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V(1) = sinalpha * cosbeta * cosgamma - cosalpha * sinbeta * singamma;
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V(2) = cosalpha * sinbeta * cosgamma + sinalpha * cosbeta * singamma;
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V(3) = cosalpha * cosbeta * singamma - sinalpha * sinbeta * cosgamma;
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}
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template <class S> Quaternion<S> &Invert(Quaternion<S> &m) {
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m.Invert();
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return m;
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}
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template <class S> Quaternion<S> Inverse(const Quaternion<S> &m) {
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Quaternion<S> a = m;
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a.Invert();
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return a;
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}
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template <class S> Quaternion<S> Interpolate( Quaternion<S> a , Quaternion<S> b , double t) {
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double v = a.V(0) * b.V(0) + a.V(1) * b.V(1) + a.V(2) * b.V(2) + a.V(3) * b.V(3);
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double phi = math::Acos(v);
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if(phi > 0.01) {
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a = a * (math::Sin(phi *(1-t))/math::Sin(phi));
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b = b * (math::Sin(phi * t)/math::Sin(phi));
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}
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Quaternion<S> c;
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c.V(0) = a.V(0) + b.V(0);
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c.V(1) = a.V(1) + b.V(1);
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c.V(2) = a.V(2) + b.V(2);
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c.V(3) = a.V(3) + b.V(3);
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if(v < -0.999) { //almost opposite
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double d = t * (1 - t);
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if(c.V(0) == 0)
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c.V(0) += d;
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else
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c.V(1) += d;
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}
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c.Normalize();
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return c;
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}
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typedef Quaternion<float> Quaternionf;
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typedef Quaternion<double> Quaterniond;
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|
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} // end namespace
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#endif
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