594 lines
16 KiB
C++
594 lines
16 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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#ifndef __VCGLIB_MATRIX33_H
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#define __VCGLIB_MATRIX33_H
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#include <stdio.h>
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#include <vcg/math/matrix44.h>
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#include <vcg/space/point3.h>
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#include <vector>
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namespace vcg {
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template<class S>
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/** @name Matrix33
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Class Matrix33.
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This is the class for definition of a matrix 3x3.
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@param S (Template Parameter) Specifies the ScalarType field.
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*/
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class Matrix33
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{
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public:
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typedef S ScalarType;
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/// Default constructor
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inline Matrix33() {}
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/// Copy constructor
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Matrix33( const Matrix33 & m )
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{
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for(int i=0;i<9;++i)
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a[i] = m.a[i];
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}
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/// create from array
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Matrix33( const S * v )
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{
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for(int i=0;i<9;++i) a[i] = v[i];
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}
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/// create from Matrix44 excluding row and column k
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Matrix33 (const Matrix44<S> & m, const int & k)
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{
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int i,j, r=0, c=0;
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for(i = 0; i< 4;++i)if(i!=k){c=0;
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for(j=0; j < 4;++j)if(j!=k)
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{ (*this)[r][c] = m[i][j]; ++c;}
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++r;
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}
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}
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template <class EigenMatrix33Type>
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void ToEigenMatrix(EigenMatrix33Type & m) const {
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for(int i = 0; i < 3; i++)
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for(int j = 0; j < 3; j++)
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m(i,j)=(*this)[i][j];
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}
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template <class EigenMatrix33Type>
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void FromEigenMatrix(const EigenMatrix33Type & m){
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for(int i = 0; i < 3; i++)
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for(int j = 0; j < 3; j++)
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(*this)[i][j]=m(i,j);
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}
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/// Number of columns
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inline unsigned int ColumnsNumber() const
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{
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return 3;
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};
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/// Number of rows
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inline unsigned int RowsNumber() const
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{
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return 3;
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};
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/// Assignment operator
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Matrix33 & operator = ( const Matrix33 & m )
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{
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for(int i=0;i<9;++i)
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a[i] = m.a[i];
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return *this;
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}
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/// Operatore di indicizzazione
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inline S * operator [] ( const int i )
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{
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return a+i*3;
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}
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/// Operatore const di indicizzazione
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inline const S * operator [] ( const int i ) const
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{
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return a+i*3;
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}
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/// Modificatore somma per matrici 3x3
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Matrix33 & operator += ( const Matrix33 &m )
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{
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for(int i=0;i<9;++i)
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a[i] += m.a[i];
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return *this;
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}
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/// Modificatore sottrazione per matrici 3x3
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Matrix33 & operator -= ( const Matrix33 &m )
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{
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for(int i=0;i<9;++i)
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a[i] -= m.a[i];
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return *this;
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}
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/// Modificatore divisione per scalare
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Matrix33 & operator /= ( const S &s )
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{
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for(int i=0;i<9;++i)
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a[i] /= s;
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return *this;
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}
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/// Modificatore prodotto per matrice
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Matrix33 operator * ( const Matrix33< S> & t ) const
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{
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Matrix33<S> r;
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int i,j;
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for(i=0;i<3;++i)
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for(j=0;j<3;++j)
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r[i][j] = (*this)[i][0]*t[0][j] + (*this)[i][1]*t[1][j] + (*this)[i][2]*t[2][j];
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return r;
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}
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/// Modificatore prodotto per matrice
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void operator *=( const Matrix33< S> & t )
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{
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Matrix33<S> r;
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int i,j;
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for(i=0;i<3;++i)
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for(j=0;j<3;++j)
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r[i][j] = (*this)[i][0]*t[0][j] + (*this)[i][1]*t[1][j] + (*this)[i][2]*t[2][j];
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for(i=0;i<9;++i) this->a[i] = r.a[i];
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}
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/// Modificatore prodotto per costante
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Matrix33 & operator *= ( const S t )
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{
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for(int i=0;i<9;++i)
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a[i] *= t;
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return *this;
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}
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/// Operatore prodotto per costante
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Matrix33 operator * ( const S t ) const
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{
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Matrix33<S> r;
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for(int i=0;i<9;++i)
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r.a[i] = a[i]* t;
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return r;
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}
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/// Operatore sottrazione per matrici 3x3
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Matrix33 operator - ( const Matrix33 &m ) const
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{
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Matrix33<S> r;
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for(int i=0;i<9;++i)
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r.a[i] = a[i] - m.a[i];
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return r;
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}
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/// Operatore sottrazione per matrici 3x3
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Matrix33 operator + ( const Matrix33 &m ) const
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{
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Matrix33<S> r;
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for(int i=0;i<9;++i)
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r.a[i] = a[i] + m.a[i];
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return r;
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}
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/** Operatore per il prodotto matrice-vettore.
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@param v A point in $R^{3}$
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@return Il vettore risultante in $R^{3}$
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*/
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Point3<S> operator * ( const Point3<S> & v ) const
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{
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Point3<S> t;
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t[0] = a[0]*v[0] + a[1]*v[1] + a[2]*v[2];
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t[1] = a[3]*v[0] + a[4]*v[1] + a[5]*v[2];
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t[2] = a[6]*v[0] + a[7]*v[1] + a[8]*v[2];
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return t;
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}
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void OuterProduct(Point3<S> const &p0, Point3<S> const &p1) {
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Point3<S> row;
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row = p1*p0[0];
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a[0] = row[0];a[1] = row[1];a[2] = row[2];
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row = p1*p0[1];
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a[3] = row[0]; a[4] = row[1]; a[5] = row[2];
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row = p1*p0[2];
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a[6] = row[0];a[7] = row[1];a[8] = row[2];
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}
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Matrix33 & SetZero() {
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for(int i=0;i<9;++i) a[i] =0;
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return (*this);
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}
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Matrix33 & SetIdentity() {
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for(int i=0;i<9;++i) a[i] =0;
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a[0]=a[4]=a[8]=1.0;
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return (*this);
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}
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Matrix33 & SetRotateRad(S angle, const Point3<S> & axis )
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{
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S c = cos(angle);
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S s = sin(angle);
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S q = 1-c;
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Point3<S> t = axis;
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t.Normalize();
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a[0] = t[0]*t[0]*q + c;
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a[1] = t[0]*t[1]*q - t[2]*s;
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a[2] = t[0]*t[2]*q + t[1]*s;
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a[3] = t[1]*t[0]*q + t[2]*s;
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a[4] = t[1]*t[1]*q + c;
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a[5] = t[1]*t[2]*q - t[0]*s;
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a[6] = t[2]*t[0]*q -t[1]*s;
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a[7] = t[2]*t[1]*q +t[0]*s;
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a[8] = t[2]*t[2]*q +c;
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return (*this);
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}
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Matrix33 & SetRotateDeg(S angle, const Point3<S> & axis ){
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return SetRotateRad(math::ToRad(angle),axis);
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}
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/// Funzione per eseguire la trasposta della matrice
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Matrix33 & Transpose()
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{
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math::Swap(a[1],a[3]);
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math::Swap(a[2],a[6]);
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math::Swap(a[5],a[7]);
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return *this;
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}
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// for the transistion to eigen
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Matrix33 transpose() const
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{
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Matrix33 res = *this;
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res.Transpose();
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return res;
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}
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void transposeInPlace() { this->Transpose(); }
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/// Funzione per costruire una matrice diagonale dati i tre elem.
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Matrix33 & SetDiagonal(S *v)
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{int i,j;
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for(i=0;i<3;i++)
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for(j=0;j<3;j++)
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if(i==j) (*this)[i][j] = v[i];
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else (*this)[i][j] = 0;
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return *this;
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}
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/// Assegna l'n-simo vettore colonna
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void SetColumn(const int n, S* v){
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assert( (n>=0) && (n<3) );
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a[n]=v[0]; a[n+3]=v[1]; a[n+6]=v[2];
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};
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/// Assegna l'n-simo vettore riga
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void SetRow(const int n, S* v){
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assert( (n>=0) && (n<3) );
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int m=n*3;
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a[m]=v[0]; a[m+1]=v[1]; a[m+2]=v[2];
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};
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/// Assegna l'n-simo vettore colonna
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void SetColumn(const int n, const Point3<S> v){
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assert( (n>=0) && (n<3) );
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a[n]=v[0]; a[n+3]=v[1]; a[n+6]=v[2];
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};
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/// Assegna l'n-simo vettore riga
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void SetRow(const int n, const Point3<S> v){
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assert( (n>=0) && (n<3) );
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int m=n*3;
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a[m]=v[0]; a[m+1]=v[1]; a[m+2]=v[2];
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};
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/// Restituisce l'n-simo vettore colonna
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Point3<S> GetColumn(const int n) const {
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assert( (n>=0) && (n<3) );
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Point3<S> t;
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t[0]=a[n]; t[1]=a[n+3]; t[2]=a[n+6];
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return t;
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};
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/// Restituisce l'n-simo vettore riga
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Point3<S> GetRow(const int n) const {
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assert( (n>=0) && (n<3) );
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Point3<S> t;
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int m=n*3;
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t[0]=a[m]; t[1]=a[m+1]; t[2]=a[m+2];
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return t;
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};
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/// Funzione per il calcolo del determinante
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S Determinant() const
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{
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return a[0]*(a[4]*a[8]-a[5]*a[7]) -
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a[1]*(a[3]*a[8]-a[5]*a[6]) +
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a[2]*(a[3]*a[7]-a[4]*a[6]) ;
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}
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// return the Trace of the matrix i.e. the sum of the diagonal elements
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S Trace() const
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{
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return a[0]+a[4]+a[8];
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}
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/*
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compute the matrix generated by the product of a * b^T
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*/
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void ExternalProduct(const Point3<S> &a, const Point3<S> &b)
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{
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for(int i=0;i<3;++i)
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for(int j=0;j<3;++j)
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(*this)[i][j] = a[i]*b[j];
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}
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/* Compute the Frobenius Norm of the Matrix
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*/
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ScalarType Norm()
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{
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ScalarType SQsum=0;
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for(int i=0;i<3;++i)
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for(int j=0;j<3;++j)
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SQsum += a[i]*a[i];
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return (math::Sqrt(SQsum));
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}
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/*
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It compute the covariance matrix of a set of 3d points. Returns the barycenter
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*/
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template <class STLPOINTCONTAINER >
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void Covariance(const STLPOINTCONTAINER &points, Point3<S> &bp) {
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assert(!points.empty());
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typedef typename STLPOINTCONTAINER::const_iterator PointIte;
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// first cycle: compute the barycenter
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bp.SetZero();
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for( PointIte pi = points.begin(); pi != points.end(); ++pi) bp+= (*pi);
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bp/=points.size();
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// second cycle: compute the covariance matrix
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this->SetZero();
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vcg::Matrix33<ScalarType> A;
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for( PointIte pi = points.begin(); pi != points.end(); ++pi) {
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Point3<S> p = (*pi)-bp;
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A.OuterProduct(p,p);
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(*this)+= A;
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}
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}
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/*
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It compute the cross covariance matrix of two set of 3d points P and X;
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it returns also the barycenters of P and X.
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fonte:
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Besl, McKay
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A method for registration o f 3d Shapes
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IEEE TPAMI Vol 14, No 2 1992
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*/
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template <class STLPOINTCONTAINER >
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void CrossCovariance(const STLPOINTCONTAINER &P, const STLPOINTCONTAINER &X,
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Point3<S> &bp, Point3<S> &bx)
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{
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SetZero();
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assert(P.size()==X.size());
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bx.SetZero();
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bp.SetZero();
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Matrix33<S> tmp;
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typename std::vector <Point3<S> >::const_iterator pi,xi;
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for(pi=P.begin(),xi=X.begin();pi!=P.end();++pi,++xi){
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bp+=*pi;
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bx+=*xi;
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tmp.ExternalProduct(*pi,*xi);
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(*this)+=tmp;
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}
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bp/=P.size();
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bx/=X.size();
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(*this)/=P.size();
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tmp.ExternalProduct(bp,bx);
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(*this)-=tmp;
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}
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template <class STLPOINTCONTAINER, class STLREALCONTAINER>
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void WeightedCrossCovariance(const STLREALCONTAINER & weights,
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const STLPOINTCONTAINER &P,
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const STLPOINTCONTAINER &X,
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Point3<S> &bp,
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Point3<S> &bx)
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{
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SetZero();
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assert(P.size()==X.size());
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bx.SetZero();
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bp.SetZero();
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Matrix33<S> tmp;
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typename std::vector <Point3<S> >::const_iterator pi,xi;
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typename STLREALCONTAINER::const_iterator pw;
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for(pi=P.begin(),xi=X.begin();pi!=P.end();++pi,++xi){
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bp+=(*pi);
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bx+=(*xi);
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}
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bp/=P.size();
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bx/=X.size();
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for(pi=P.begin(),xi=X.begin(),pw = weights.begin();pi!=P.end();++pi,++xi,++pw){
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tmp.ExternalProduct(((*pi)-(bp)),((*xi)-(bp)));
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(*this)+=tmp*(*pw);
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}
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}
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private:
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S a[9];
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};
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///return the tranformation matrix to transform
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///to the frame specified by the three vectors
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template <class S>
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vcg::Matrix33<S> TransformationMatrix(const vcg::Point3<S> dirX,
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const vcg::Point3<S> dirY,
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const vcg::Point3<S> dirZ)
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{
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vcg::Matrix33<S> Trans;
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///it must have right orientation cause of normal
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Trans[0][0]=dirX[0];
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Trans[0][1]=dirX[1];
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Trans[0][2]=dirX[2];
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Trans[1][0]=dirY[0];
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Trans[1][1]=dirY[1];
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Trans[1][2]=dirY[2];
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Trans[2][0]=dirZ[0];
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Trans[2][1]=dirZ[1];
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Trans[2][2]=dirZ[2];
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/////then find the inverse
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return (Trans);
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}
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template <class S>
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Matrix33<S> Inverse(const Matrix33<S>&m)
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{
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Eigen::Matrix3d mm,mmi;
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m.ToEigenMatrix(mm);
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mmi=mm.inverse();
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Matrix33<S> res;
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res.FromEigenMatrix(mmi);
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return res;
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}
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///given 2 vector centered into origin calculate the rotation matrix from first to the second
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template <class S>
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Matrix33<S> RotationMatrix(vcg::Point3<S> v0,vcg::Point3<S> v1,bool normalized=true)
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{
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typedef typename vcg::Point3<S> CoordType;
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Matrix33<S> rotM;
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const S epsilon=0.00001;
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if (!normalized)
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{
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v0.Normalize();
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v1.Normalize();
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}
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S dot=(v0*v1);
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///control if there is no rotation
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if (dot>((S)1-epsilon))
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{
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rotM.SetIdentity();
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return rotM;
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}
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///find the axis of rotation
|
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CoordType axis;
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|
axis=v0^v1;
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axis.Normalize();
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|
|
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///construct rotation matrix
|
|
S u=axis.X();
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|
S v=axis.Y();
|
|
S w=axis.Z();
|
|
S phi=acos(dot);
|
|
S rcos = cos(phi);
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|
S rsin = sin(phi);
|
|
|
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rotM[0][0] = rcos + u*u*(1-rcos);
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rotM[1][0] = w * rsin + v*u*(1-rcos);
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|
rotM[2][0] = -v * rsin + w*u*(1-rcos);
|
|
rotM[0][1] = -w * rsin + u*v*(1-rcos);
|
|
rotM[1][1] = rcos + v*v*(1-rcos);
|
|
rotM[2][1] = u * rsin + w*v*(1-rcos);
|
|
rotM[0][2] = v * rsin + u*w*(1-rcos);
|
|
rotM[1][2] = -u * rsin + v*w*(1-rcos);
|
|
rotM[2][2] = rcos + w*w*(1-rcos);
|
|
|
|
return rotM;
|
|
}
|
|
|
|
///return the rotation matrix along axis
|
|
template <class S>
|
|
Matrix33<S> RotationMatrix(const vcg::Point3<S> &axis,
|
|
const float &angleRad)
|
|
{
|
|
vcg::Matrix44<S> matr44;
|
|
vcg::Matrix33<S> matr33;
|
|
matr44.SetRotate(angleRad,axis);
|
|
for (int i=0;i<3;i++)
|
|
for (int j=0;j<3;j++)
|
|
matr33[i][j]=matr44[i][j];
|
|
return matr33;
|
|
}
|
|
|
|
/// return a random rotation matrix, from the paper:
|
|
/// Fast Random Rotation Matrices, James Arvo
|
|
/// Graphics Gems III pp. 117-120
|
|
template <class S>
|
|
Matrix33<S> RandomRotation(){
|
|
S x1,x2,x3;
|
|
Matrix33<S> R,H,M,vv;
|
|
Point3<S> v;
|
|
R.SetIdentity();
|
|
H.SetIdentity();
|
|
x1 = rand()/S(RAND_MAX);
|
|
x2 = rand()/S(RAND_MAX);
|
|
x3 = rand()/S(RAND_MAX);
|
|
|
|
R[0][0] = cos(S(2)*M_PI*x1);
|
|
R[0][1] = sin(S(2)*M_PI*x1);
|
|
R[1][0] = - R[0][1];
|
|
R[1][1] = R[0][0];
|
|
|
|
v[0] = cos(2.0 * M_PI * x2)*sqrt(x3);
|
|
v[1] = sin(2.0 * M_PI * x2)*sqrt(x3);
|
|
v[2] = sqrt(1-x3);
|
|
|
|
vv.OuterProduct(v,v);
|
|
H -= vv*S(2);
|
|
M = H*R*S(-1);
|
|
return M;
|
|
}
|
|
|
|
///
|
|
typedef Matrix33<short> Matrix33s;
|
|
typedef Matrix33<int> Matrix33i;
|
|
typedef Matrix33<float> Matrix33f;
|
|
typedef Matrix33<double> Matrix33d;
|
|
|
|
} // end of namespace
|
|
|
|
#endif
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