quads.hpp

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// Copyright (c) 2012-2019 University of Lyon and CNRS (France).
// All rights reserved.
//
// This file is part of MEPP2; you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 3 of
// the License, or (at your option) any later version.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
#pragma once
 
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/properties.hpp>
#include "FEVV/Wrappings/Geometry_traits.h"
 
#include "FEVV/Operators/Geometry/AngleOperations.hpp"
// For are_collinear() and MACH_EPS_DOUBLE :
#include "FEVV/Tools/Math/MatrixOperations.hpp"
 
namespace FEVV {
namespace Operators {
namespace Geometry {
template< typename GeometryTraits >
inline typename GeometryTraits::Point
quad_barycenter(const typename GeometryTraits::Point &a,
                const typename GeometryTraits::Point &b,
                const typename GeometryTraits::Point &c,
                const typename GeometryTraits::Point &d,        
                const GeometryTraits &gt)
{
  typedef typename GeometryTraits::Point Point;
 
  return Point((a[0] + b[0] + c[0] + d[0]) / 4,
               (a[1] + b[1] + c[1] + d[1]) / 4,
               (a[2] + b[2] + c[2] + d[2]) / 4);
}
template< typename GeometryTraits >
inline double
quad_perimeter(const typename GeometryTraits::Point &a,
               const typename GeometryTraits::Point &b,
               const typename GeometryTraits::Point &c,
               const typename GeometryTraits::Point &d,        
               const GeometryTraits &gt)
{
  typedef typename GeometryTraits::Vector Vector;
 
  Vector ab(b - a), bc(c - b), cd(d - c), da(a - d);
 
  return (gt.length(ab) + gt.length(bc) + gt.length(cd)) + gt.length(da));
}
 
template< typename GeometryTraits >
inline double
quad_area(const typename GeometryTraits::Point &a,
          const typename GeometryTraits::Point &b,
          const typename GeometryTraits::Point &c,
          const typename GeometryTraits::Point &d,      
          const GeometryTraits &gt)
{
  typedef typename GeometryTraits::Vector Vector;
 
  Vector n1 = triangle_normal_unnormalized< GeometryTraits >(a, b, c, gt);
  Vector n2 = triangle_normal_unnormalized< GeometryTraits >(c, d, a, gt);
  return (gt.length(n1) + gt.length(n2)) * 0.5;
}
 
} // namespace Geometry
} // namespace Operators
} // namespace FEVV