Volumes.h

//===========================================================================
// GoTools - SINTEF Geometry Tools version 1.1
//
// GoTools module: CORE
//
// Copyright (C) 2000-2007 SINTEF ICT, Applied Mathematics, Norway.
//
// This program is free software; you can redistribute it and/or          
// modify it under the terms of the GNU General Public License            
// as published by the Free Software Foundation version 2 of the License. 
//
// This program is distributed in the hope that it will be useful,        
// but WITHOUT ANY WARRANTY; without even the implied warranty of         
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the          
// GNU General Public License for more details.                           
//
// You should have received a copy of the GNU General Public License      
// along with this program; if not, write to the Free Software            
// Foundation, Inc.,                                                      
// 59 Temple Place - Suite 330,                                           
// Boston, MA  02111-1307, USA.                                           
//
// Contact information: E-mail: tor.dokken@sintef.no                      
// SINTEF ICT, Department of Applied Mathematics,                         
// P.O. Box 124 Blindern,                                                 
// 0314 Oslo, Norway.                                                     
//
// Other licenses are also available for this software, notably licenses
// for:
// - Building commercial software.                                        
// - Building software whose source code you wish to keep private.        
//===========================================================================
#ifndef _VOLUMES_H
#define _VOLUMES_H

#include "Factorial.h"
#include "Array.h"
#include <vector>


namespace Go {



template< typename T >
inline T determinantOf(const Array<T, 2>* a) 
{
    return a[0][0] * a[1][1] - a[1][0] * a[0][1];
};


template<typename T>
inline T determinantOf(const Array<T, 3>* a) 
{
    return 
        a[0][0] * (a[1][1] * a[2][2] - a[2][1] * a[1][2]) -
        a[0][1] * (a[1][0] * a[2][2] - a[2][0] * a[1][2]) +
        a[0][2] * (a[1][0] * a[2][1] - a[2][0] * a[1][1]);
};


template<typename T, int Dim>
inline T simplex_volume(const Array<T, Dim>* a)
{
    Array<T, Dim> tmp[Dim];
    for (int i = 0; i < Dim; ++i) {
        tmp[i] = a[i] - a[i+1];
    }
    return determinantOf(tmp) * InverseFactorial<double, Dim>::val();
    // determinant / factorial
}


template <typename T>
inline T area(const Array<T, 2>* c)
{ return simplex_volume(c); }


template < typename T >
inline T area(const Array<T, 3>* c)
{
    // Using the one-half cross product rule
    Array<T, 3> d0 = c[1] - c[0];
    Array<T, 3> d1 = c[2] - c[0];
    Array<T, 3> crossprod = d0.cross(d1);
    return 0.5 * crossprod.length();
}


template <typename T>
inline T volume(const Array<T, 3>* c)
{ return simplex_volume(c); }


template <typename T>
T signed_area(const Array<T, 3>* c, const Array<T, 3>& normal)
{
    // Using the one-half cross product rule
    Array<T, 3> d0 = c[1] - c[0];
    Array<T, 3> d1 = c[2] - c[0];
    Array<T, 3> crossprod = d0.cross(d1);
    if (crossprod*normal > 0) {
        return 0.5 * crossprod.length();
    } else {
        return -0.5 * crossprod.length();
    }
}


} // namespace Go


#endif // _VOLUMES_H

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