Algorithms.hh 14.8 KB
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/*===========================================================================*\
 *                                                                           *
 *                              OpenFlipper                                  *
 *      Copyright (C) 2001-2009 by Computer Graphics Group, RWTH Aachen      *
 *                           www.openflipper.org                             *
 *                                                                           *
 *---------------------------------------------------------------------------*
 *  This file is part of OpenFlipper.                                        *
 *                                                                           *
 *  OpenFlipper is free software: 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 with the              *
 *  following exceptions:                                                    *
 *                                                                           *
 *  If other files instantiate templates or use macros                       *
 *  or inline functions from this file, or you compile this file and         *
 *  link it with other files to produce an executable, this file does        *
 *  not by itself cause the resulting executable to be covered by the        *
 *  GNU Lesser General Public License. This exception does not however       *
 *  invalidate any other reasons why the executable file might be            *
 *  covered by the GNU Lesser General Public License.                        *
 *                                                                           *
 *  OpenFlipper 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 Lesser General Public License for more details.                      *
 *                                                                           *
 *  You should have received a copy of the GNU LesserGeneral Public          *
 *  License along with OpenFlipper. If not,                                  *
 *  see <http://www.gnu.org/licenses/>.                                      *
 *                                                                           *
\*===========================================================================*/

/*===========================================================================*\
 *                                                                           *
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 *   $Revision$                                                       *
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 *   $Author$                                                      *
 *   $Date$                   *
 *                                                                           *
\*===========================================================================*/
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#ifndef GEO_ALGORITHMS_HH
#define GEO_ALGORITHMS_HH


//== INCLUDES =================================================================

#include <float.h>
#include "../Math/VectorT.hh"


namespace ACG {
namespace Geometry {


//== 3D STUFF =================================================================

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/// return circumcenter of tetrahedron (_v0,_v1,_v2,_v3)
template<typename Scalar>
bool
circumCenter( const VectorT<Scalar,3>&  _v0,
	      const VectorT<Scalar,3>&  _v1,
	      const VectorT<Scalar,3>&  _v2,
	      const VectorT<Scalar,3>&  _v3,
	      VectorT<Scalar,3>&        _result );


/// return squared radius of circumcircle of tetrahedron (_v0,_v1,_v2,_v3)
template<typename Scalar>
Scalar
circumRadiusSquared( const VectorT<Scalar,3>&  _v0,
		     const VectorT<Scalar,3>&  _v1,
		     const VectorT<Scalar,3>&  _v2,
		     const VectorT<Scalar,3>&  _v3 )
{
  VectorT<Scalar,3> cc;
  return circumCenter(_v0, _v1, _v2, _v3, cc) ? (cc-_v0).sqrnorm() : FLT_MAX;
}


/// return radius of circumcircle of tetrahedron (_v0,_v1,_v2,_v3)
template<typename Scalar>
Scalar
circumRadius( const VectorT<Scalar,3>&  _v0,
	      const VectorT<Scalar,3>&  _v1,
	      const VectorT<Scalar,3>&  _v2,
	      const VectorT<Scalar,3>&  _v3 )
{
  return sqrt(circumRadiusSquared(_v0, _v1, _v2, _v3));
}


/// find a vector that's perpendicular to _v
template <typename Scalar>
VectorT<Scalar,3>
perpendicular( const VectorT<Scalar,3>&  _v );


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//== 2D STUFF =================================================================
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/// orientation of point _p w.r.t. line through _v0,_v1 in 2D
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template<typename Scalar>
Scalar
pointLineOrientation( const VectorT<Scalar,2>&  _p,
		      const VectorT<Scalar,2>&  _v0,
		      const VectorT<Scalar,2>&  _v1 )
{
  VectorT<Scalar,2> d1(_p-_v0), d2(_v1-_v0);
  return (d1[0]*d2[1]-d1[1]*d2[0]);
}


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/// are 3 vertices in counterclockwise order? in 2D
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template<typename Scalar>
bool
isCCW( const VectorT<Scalar,2>&  _v0,
       const VectorT<Scalar,2>&  _v1,
       const VectorT<Scalar,2>&  _v2 )
{
  return ( pointLineOrientation(_v0, _v1, _v2) < Scalar(0.0) );
}


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/// are 3 vertices in clockwise order? in 2D
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template<typename Scalar>
bool
isCW( const VectorT<Scalar,2>&  _v0,
      const VectorT<Scalar,2>&  _v1,
      const VectorT<Scalar,2>&  _v2 )
{
  return ( pointLineOrientation(_v0, _v1, _v2) > Scalar(0.0) );
}


/// intersect two line segments (_v0,_v1) and (_v2,_v3)
template<typename Scalar>
bool
lineIntersection( const VectorT<Scalar,2>&  _v0,
		  const VectorT<Scalar,2>&  _v1,
		  const VectorT<Scalar,2>&  _v2,
		  const VectorT<Scalar,2>&  _v3,
		  Scalar& _t1,
		  Scalar& _t2 );


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//===========================================================================
/** @name Distance Functions ( N-Dimensional )
* @{ */
//===========================================================================     

/// distance from point _p to line (_v0,_v1)
template<class Vec>
typename Vec::value_type
distPointLine( const Vec& _p,
               const Vec& _v0,
               const Vec& _v1,
               Vec*       _min_v=0 )
{ return sqrt(distPointLineSquared(_p, _v0, _v1, _min_v)); }


/// squared distance from point _p to line (_v0,_v1)
template<class Vec>
typename Vec::value_type
distPointLineSquared( const Vec& _p,
                      const Vec& _v0,
                      const Vec& _v1,
                      Vec*       _min_v=0);

/// distance from point _p to triangle (_v0, _v1, _v2)
template <class Vec>
typename Vec::value_type
distPointTriangle( const Vec& _p,
                   const Vec& _v0,
                   const Vec& _v1,
                   const Vec& _v2,
                   Vec& _nearestPoint )
{ return sqrt(distPointTriangleSquared(_p, _v0, _v1, _v2, _nearestPoint)); }


/// squared distance from point _p to triangle (_v0, _v1, _v2)
template <class Vec>
typename Vec::value_type
distPointTriangleSquared( const Vec& _p,
                          const Vec& _v0,
                          const Vec& _v1,
                          const Vec& _v2,
                          Vec& _nearestPoint );
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/** \brief Checks the distance from a point to a plane
*
*
* @param _porigin Planes origin
* @param _pnormal Plane normal ( has to be normalized!)
* @param _point   point to test
* @return         distance
*/
template < typename VectorT , typename ValueT >
inline
ValueT 
distPointPlane(const VectorT& _porigin, 
               const VectorT& _pnormal, 
               const VectorT&  _point);                          
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/** @} */   
          
//===========================================================================
/** @name Distance Functions ( 3-Dimensional )
* @{ */
//===========================================================================                             
                          
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/// squared distance of lines (_v00, _v01) and (_v10, _v11)
template<typename Scalar>
Scalar
distLineLineSquared( const VectorT<Scalar,3>& _v00,
                     const VectorT<Scalar,3>& _v01,
                     const VectorT<Scalar,3>& _v10,
                     const VectorT<Scalar,3>& _v11,
                     VectorT<Scalar,3>*       _min_v0=0,
                     VectorT<Scalar,3>*       _min_v1=0,
                     bool                          _fastApprox=false );


/// distance of lines (_v00, _v01) and (_v10, _v11)
template<typename Scalar>
Scalar
distLineLine( const VectorT<Scalar,3>& _v00,
              const VectorT<Scalar,3>& _v01,
              const VectorT<Scalar,3>& _v10,
              const VectorT<Scalar,3>& _v11,
              VectorT<Scalar,3>*       _min_v0=0,
              VectorT<Scalar,3>*       _min_v1=0 )
{
  return sqrt(distLineLineSquared(_v00, _v01, _v10, _v11,
                                  _min_v0, _min_v1));
}

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/** @} */   
   
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//===========================================================================
/** @name Projection Functions ( N-Dimensional )
* @{ */
//===========================================================================      


/**
project one point to an edge. If its projection is not on the edge itself, the start or the endpoint is returned
@param _start beginning of edge
@param _end   end of the edge
@param _point point to be projected
*/
template < typename VectorT >
VectorT projectToEdge(const VectorT& _start , 
                      const VectorT& _end , 
                      const VectorT& _point );
                      
                      
/** \brief projects a point to a plane
* @param _porigin Planes origin
* @param _pnormal Plane normal ( has to be normalized! )
* @param _point   point to project
* @return         projected point
*/
template < typename VectorT >
inline
VectorT
projectToPlane(const VectorT& _porigin, 
               const VectorT& _pnormal, 
               const VectorT&  _point);                      
              
/** @} */           

//===========================================================================
/** @name Triangle Functions (2D Only!!)
* @{ */
//===========================================================================   

/** \brief return circumcenter of triangle (_v0,_v1,_v2)
*
*/

/// barycentric coord of _p w.r.t. (_u,_v,_w) in 2D
template<typename Scalar>
bool
baryCoord( const VectorT<Scalar,2>&  _p,
           const VectorT<Scalar,2>&  _u,
           const VectorT<Scalar,2>&  _v,
           const VectorT<Scalar,2>&  _w,
           VectorT<Scalar,3>&        _result );
           

/// is point _p in triangle (_v0,_v1,_v2) in 2D
template<typename Scalar>
bool
isInTriangle( const VectorT<Scalar,2>&  _p,
              const VectorT<Scalar,2>&  _u,
              const VectorT<Scalar,2>&  _v,
              const VectorT<Scalar,2>&  _w )
{
  VectorT<Scalar,3> bary;
  if (baryCoord(_p, _u, _v, _w, bary)) 
    return ((bary[0]>0.0) && (bary[1]>0.0) && (bary[2]>0.0));
  else {
    std::cerr << "point in triangle error\n";
    return false;
  }
}

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template<typename Scalar>
bool
circumCenter( const VectorT<Scalar,2>&  _v0,
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              const VectorT<Scalar,2>&  _v1,
              const VectorT<Scalar,2>&  _v2,
              VectorT<Scalar,2>&        _result );
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/** @} */   
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//===========================================================================
/** @name Triangle Functions 3-Dimensional
* @{ */
//===========================================================================  
 
/** barycentric coord of _p w.r.t. (_u,_v,_w) in 3D
    _p has to lie in plane (_u,_v,_w) **/
template<typename Scalar>
bool
baryCoord( const VectorT<Scalar,3>&  _p,
           const VectorT<Scalar,3>&  _u,
           const VectorT<Scalar,3>&  _v,
           const VectorT<Scalar,3>&  _w,
           VectorT<Scalar,3>&        _result );


/// construct min. enclosing sphere
template<typename Scalar>
bool
minSphere(const VectorT<Scalar,3>&  _v0,
          const VectorT<Scalar,3>&  _v1,
          const VectorT<Scalar,3>&  _v2,
          VectorT<Scalar,3>&        _center,
          Scalar&                   _radius);


/// return squared radius of min. enclosing circle of triangle (_v0,_v1,_v2)
template<typename Scalar>
Scalar
minRadiusSquared( const VectorT<Scalar,3>&  _v0,
                  const VectorT<Scalar,3>&  _v1,
                  const VectorT<Scalar,3>&  _v2 );

  
/// return radius of min. enclosing circle of triangle (_v0,_v1,_v2)
template<typename Scalar>
Scalar
minRadius( const VectorT<Scalar,3>&  _v0,
           const VectorT<Scalar,3>&  _v1,
           const VectorT<Scalar,3>&  _v2 )
{
  return sqrt(minRadiusSquared(_v0, _v1, _v2));
}


/// return circumcenter of triangle (_v0,_v1,_v2)
template<typename Scalar>
bool
circumCenter( const VectorT<Scalar,3>&  _v0,
              const VectorT<Scalar,3>&  _v1,
              const VectorT<Scalar,3>&  _v2,
              VectorT<Scalar,3>&        _result );


/// return squared radius of circumcircle of triangle (_v0,_v1,_v2)
template<typename Scalar>
Scalar
circumRadiusSquared( const VectorT<Scalar,3>&  _v0,
                     const VectorT<Scalar,3>&  _v1,
                     const VectorT<Scalar,3>&  _v2 );


/// return radius of circumcircle of triangle (_v0,_v1,_v2)
template<typename Scalar>
Scalar
circumRadius( const VectorT<Scalar,3>&  _v0,
              const VectorT<Scalar,3>&  _v1,
              const VectorT<Scalar,3>&  _v2 )
{
  return sqrt(circumRadiusSquared(_v0, _v1, _v2));
}

/** @} */   
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//===========================================================================
/** @name Triangle Functions N-Dimensional
* @{ */
//===========================================================================   
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/** \brief return area of triangle (_v0, _v1, _v2)
*
*/
template <class Vec>
typename Vec::value_type
triangleArea( const Vec& _v0,
              const Vec& _v1,
              const Vec& _v2 )
{
  return sqrt(triangleAreaSquared(_v0,_v1,_v2));
}
  

/** \brief return squared area of triangle (_v0, _v1, _v2)
*
*/
template <class Vec>
typename Vec::value_type
triangleAreaSquared( const Vec& _v0,
                     const Vec& _v1,
                     const Vec& _v2 );



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/** \brief return aspect ratio of triangle
*
*/
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template <typename Scalar, int N>
Scalar
aspectRatio( const VectorT<Scalar, N>& _v0,
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             const VectorT<Scalar, N>& _v1,
             const VectorT<Scalar, N>& _v2 );
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/** \brief return roundness of triangle: 1=equilateral, 0=colinear
*
*/
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template <typename Scalar, int N>
Scalar
roundness( const VectorT<Scalar, N>& _v0,
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           const VectorT<Scalar, N>& _v1,
           const VectorT<Scalar, N>& _v2 );
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/** @} */              
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//=============================================================================
} // namespace Geometry
} // namespace ACG
//=============================================================================
#if defined(INCLUDE_TEMPLATES) && !defined(GEO_ALGORITHMS_C)
#define GEO_ALGORITHMS_TEMPLATES
#include "Algorithms.cc"
#endif
//=============================================================================
#endif // GEO_ALGORITHMS_HH defined
//=============================================================================