389 lines
12 KiB
C++
389 lines
12 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 \/)\/ *
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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 1.16 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 1.16 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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/** Classe 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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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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void FromMatrix(Matrix44<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 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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};
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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 * 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> 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> void Quaternion<S>::ToMatrix(Matrix44<S> &m) const {
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S q00 = V(1)*V(1);
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S q01 = V(1)*V(2);
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S q02 = V(1)*V(3);
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S q03 = V(1)*V(0);
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S q11 = V(2)*V(2);
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S q12 = V(2)*V(3);
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S q13 = V(2)*V(0);
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S q22 = V(3)*V(3);
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S q23 = V(3)*V(0);
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m[0][0] = (S)(1.0-(q11 + q22)*2.0);
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m[1][0] = (S)((q01 - q23)*2.0);
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m[2][0] = (S)((q02 + q13)*2.0);
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m[3][0] = (S)0.0;
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m[0][1] = (S)((q01 + q23)*2.0);
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m[1][1] = (S)(1.0-(q22 + q00)*2.0);
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m[2][1] = (S)((q12 - q03)*2.0);
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m[3][1] = (S)0.0;
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m[0][2] = (S)((q02 - q13)*2.0);
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m[1][2] = (S)((q12 + q03)*2.0);
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m[2][2] = (S)(1.0-(q11 + q00)*2.0);
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m[3][2] = (S)0.0;
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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][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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S q00 = V(1)*V(1);
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S q01 = V(1)*V(2);
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S q02 = V(1)*V(3);
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S q03 = V(1)*V(0);
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S q11 = V(2)*V(2);
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S q12 = V(2)*V(3);
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S q13 = V(2)*V(0);
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S q22 = V(3)*V(3);
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S q23 = V(3)*V(0);
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m[0][0] = (S)(1.0-(q11 + q22)*2.0);
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m[1][0] = (S)((q01 - q23)*2.0);
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m[2][0] = (S)((q02 + q13)*2.0);
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m[0][1] = (S)((q01 + q23)*2.0);
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m[1][1] = (S)(1.0-(q22 + q00)*2.0);
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m[2][1] = (S)((q12 - q03)*2.0);
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m[0][2] = (S)((q02 - q13)*2.0);
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m[1][2] = (S)((q12 + q03)*2.0);
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m[2][2] = (S)(1.0-(q11 + q00)*2.0);
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}
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///warning m deve essere una matrice di rotazione pena il disastro.
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template <class S> void Quaternion<S>::FromMatrix(Matrix44<S> &m) {
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S Sc;
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S t = (m.V()[0] + m.V()[5] + m.V()[10] + (S)1.0);
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if(t > 0) {
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Sc = (S)0.5 / math::Sqrt(t);
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V(0) = (S)0.25 / Sc;
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V(1) = ( m.V()[9] - m.V()[6] ) * Sc;
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V(2) = ( m.V()[2] - m.V()[8] ) * Sc;
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V(3) = ( m.V()[4] - m.V()[1] ) * Sc;
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} else {
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if(m.V()[0] > m.V()[5] && m.V()[0] > m.V()[10]) {
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Sc = math::Sqrt( (S)1.0 + m.V()[0] - m.V()[5] - m.V()[10] ) * (S)2.0;
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V(1) = (S)0.5 / Sc;
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V(2) = (m.V()[1] + m.V()[4] ) / Sc;
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V(3) = (m.V()[2] + m.V()[8] ) / Sc;
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V(0) = (m.V()[6] + m.V()[9] ) / Sc;
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} else if( m.V()[5] > m.V()[10]) {
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Sc = math::Sqrt( (S)1.0 + m.V()[5] - m.V()[0] - m.V()[10] ) * (S)2.0;
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V(1) = (m.V()[1] + m.V()[4] ) / Sc;
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V(2) = (S)0.5 / Sc;
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V(3) = (m.V()[6] + m.V()[9] ) / Sc;
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V(0) = (m.V()[2] + m.V()[8] ) / Sc;
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} else {
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Sc = math::Sqrt( (S)1.0 + m.V()[10] - m.V()[0] - m.V()[5] ) * (S)2.0;
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V(1) = (m.V()[2] + m.V()[8] ) / Sc;
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V(2) = (m.V()[6] + m.V()[9] ) / Sc;
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V(3) = (S)0.5 / Sc;
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V(0) = (m.V()[1] + m.V()[4] ) / Sc;
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}
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}
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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 = cos(alpha / 2.0);
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S cosbeta = cos(beta / 2.0);
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S cosgamma = cos(gamma / 2.0);
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S sinalpha = sin(alpha / 2.0);
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S sinbeta = sin(beta / 2.0);
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S singamma = 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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} // end namespace
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#endif
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