vcglib/vcg/space/triangle3.h

/****************************************************************************
* VCGLib                                                            o o     *
* Visual and Computer Graphics Library                            o     o   *
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* Copyright(C) 2004-2016                                           \/)\/    *
* Visual Computing Lab                                            /\/|      *
* ISTI - Italian National Research Council                           |      *
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* This program is distributed in the hope that it will be useful,           *
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* GNU General Public License (http://www.gnu.org/licenses/gpl.txt)          *
* for more details.                                                         *
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#ifndef __VCG_TRIANGLE3
#define __VCG_TRIANGLE3

#include <vcg/space/box3.h>
#include <vcg/space/point2.h>
#include <vcg/space/point3.h>
#include <vcg/space/plane3.h>
#include <vcg/space/segment3.h>
#include <vcg/space/triangle2.h>

namespace vcg {

/** \addtogroup space */
/*@{*/
/**
        Templated class for storing a generic triangle in a 3D space.
    Note the relation with the Face class of TriMesh complex, both classes provide the P(i) access functions to their points and therefore they share the algorithms on it (e.g. area, normal etc...)
 */
template <class ScalarTriangleType> class Triangle3
{
public:
  typedef ScalarTriangleType ScalarType;
    typedef Point3< ScalarType > CoordType;
    /// The bounding box type
    typedef Box3<ScalarType> BoxType;

/*********************************************
    blah
    blah
**/
    Triangle3(){}
    Triangle3(const CoordType & c0,const CoordType & c1,const CoordType & c2){_v[0]=c0;_v[1]=c1;_v[2]=c2;}
protected:
    /// Vector of vertex pointer incident in the face
    Point3<ScalarType> _v[3];
public:

  /// Shortcut per accedere ai punti delle facce
  inline CoordType & P( const int j ) { return _v[j];}
  inline CoordType & P0( const int j ) { return _v[j];}
  inline CoordType & P1( const int j ) { return _v[(j+1)%3];}
  inline CoordType & P2( const int j ) { return _v[(j+2)%3];}
  inline const CoordType &  P( const int j ) const { return _v[j];}
  inline const CoordType & cP( const int j ) const { return _v[j];}
  inline const CoordType &  P0( const int j ) const { return _v[j];}
  inline const CoordType &  P1( const int j ) const { return _v[(j+1)%3];}
  inline const CoordType &  P2( const int j ) const { return _v[(j+2)%3];}
  inline const CoordType & cP0( const int j ) const { return _v[j];}
  inline const CoordType & cP1( const int j ) const { return _v[(j+1)%3];}
  inline const CoordType & cP2( const int j ) const { return _v[(j+2)%3];}

  inline int VN() const { return 3;}
}; //end Class

/********************** Normal **********************/

/// Returns the normal to the plane passing through p0,p1,p2
template<class TriangleType>
typename TriangleType::CoordType TriangleNormal(const TriangleType &t)
{
  return (( t.cP(1) - t.cP(0)) ^ (t.cP(2) - t.cP(0)));
}
/// Returns the normal to the plane passing through p0,p1,p2
template<class TriangleType>
typename TriangleType::CoordType NormalizedTriangleNormal(const TriangleType &t)
{
  return (( t.cP(1) - t.cP(0)) ^ (t.cP(2) - t.cP(0))).Normalize();
}
template<class Point3Type>
Point3Type Normal( Point3Type const &p0, Point3Type const & p1,  Point3Type const & p2)
{
  return (( p1 - p0) ^ (p2 - p0));
}

/********************** Interpolation **********************/

// The function to computing barycentric coords of a point inside a triangle.
// it requires the knowledge of what is the direction that is more orthogonal to the face plane.
//  ScalarType nx = math::Abs((*fi).cN()[0]);
//  ScalarType ny = math::Abs((*fi).cN()[1]);
//  ScalarType nz = math::Abs((*fi).cN()[2]);
//  if(nx>ny && nx>nz) { axis = 0; }
//  else if(ny>nz)     { axis = 1 }
//  else               { axis = 2 }
//  InterpolationParameters(*fp,axis,Point,L);
//
// This normal direction is used to project the triangle in 2D and solve the problem in 2D where it is simpler and often well defined.

template<class TriangleType, class ScalarType>
bool InterpolationParameters(const TriangleType t, const int Axis, const Point3<ScalarType> & P,  Point3<ScalarType> & L)
{
    typedef Point2<ScalarType> P2;
    if(Axis==0) return InterpolationParameters2( P2(t.cP(0)[1],t.cP(0)[2]), P2(t.cP(1)[1],t.cP(1)[2]), P2(t.cP(2)[1],t.cP(2)[2]), P2(P[1],P[2]), L);
    if(Axis==1) return InterpolationParameters2( P2(t.cP(0)[0],t.cP(0)[2]), P2(t.cP(1)[0],t.cP(1)[2]), P2(t.cP(2)[0],t.cP(2)[2]), P2(P[0],P[2]), L);
    if(Axis==2) return InterpolationParameters2( P2(t.cP(0)[0],t.cP(0)[1]), P2(t.cP(1)[0],t.cP(1)[1]), P2(t.cP(2)[0],t.cP(2)[1]), P2(P[0],P[1]), L);
    return false;
}
/// Handy Wrapper of the above one that uses the passed normal N to choose the right orientation
template<class TriangleType, class ScalarType>
bool InterpolationParameters(const TriangleType t, const Point3<ScalarType> & N, const Point3<ScalarType> & P,  Point3<ScalarType> & L)
{
  if(fabs(N[0])>fabs(N[1]))
    {
    if(fabs(N[0])>fabs(N[2]))
            return InterpolationParameters(t,0,P,L); /* 0 > 1 ? 2 */
        else
            return InterpolationParameters(t,2,P,L); /* 2 > 1 ? 2 */
        }
    else
    {
    if(fabs(N[1])>fabs(N[2]))
            return InterpolationParameters(t,1,P,L); /* 1 > 0 ? 2 */
        else
            return InterpolationParameters(t,2,P,L); /* 2 > 1 ? 2 */
    }
}

// Function that computes the barycentric coords of a 2D triangle.
template<class ScalarType>
bool InterpolationParameters2(const Point2<ScalarType> &V1,
                                                       const Point2<ScalarType> &V2,
                                                         const Point2<ScalarType> &V3,
                                                         const Point2<ScalarType> &P, Point3<ScalarType> &L)
{
    vcg::Triangle2<ScalarType> t2=vcg::Triangle2<ScalarType>(V1,V2,V3);
    return (t2.InterpolationParameters(P,L.X(),L.Y(),L.Z() ));
}

/// Handy Wrapper of the above one that calculate the normal on the triangle
template<class TriangleType, class ScalarType>
bool InterpolationParameters(const TriangleType t, const Point3<ScalarType> & P,  Point3<ScalarType> & L)
{
  vcg::Point3<ScalarType> N=vcg::TriangleNormal<TriangleType>(t);
  return (InterpolationParameters<TriangleType,ScalarType>(t,N,P,L));
}


/********************** Quality **********************/

/// Compute a shape quality measure of the triangle composed by points p0,p1,p2
/// It Returns 2*AreaTri/(MaxEdge^2),
/// the range is range [0.0, 0.866]
/// e.g. Equilateral triangle sqrt(3)/2, halfsquare: 1/2, ... up to a line that has zero quality.
template<class P3ScalarType>
P3ScalarType Quality( Point3<P3ScalarType> const &p0, Point3<P3ScalarType> const & p1,  Point3<P3ScalarType> const & p2)
{
    Point3<P3ScalarType> d10=p1-p0;
    Point3<P3ScalarType> d20=p2-p0;
    Point3<P3ScalarType> d12=p1-p2;
    Point3<P3ScalarType> x = d10^d20;

    P3ScalarType a = Norm( x );
    if(a==0) return 0; // Area zero triangles have surely quality==0;
    P3ScalarType b = SquaredNorm( d10 );
  if(b==0) return 0; // Again: area zero triangles have surely quality==0;
    P3ScalarType t = b;
    t = SquaredNorm( d20 ); if ( b<t ) b = t;
    t = SquaredNorm( d12 ); if ( b<t ) b = t;
    return a/b;
}


/// Return the _q of the face, the return value is in [0,sqrt(3)/2] = [0 - 0.866.. ]
template<class TriangleType>
typename TriangleType::ScalarType QualityFace(const TriangleType &t)
{
  return Quality(t.cP(0), t.cP(1), t.cP(2));
}
/// Compute a shape quality measure of the triangle composed by points p0,p1,p2
/// It Returns inradius/circumradius
/// the range is range [0, 1]
/// e.g. Equilateral triangle 1, halfsquare: 0.81, ... up to a line that has zero quality.
template<class P3ScalarType>
P3ScalarType QualityRadii(Point3<P3ScalarType> const &p0,
                                                    Point3<P3ScalarType> const &p1,
                                                    Point3<P3ScalarType> const &p2) {

    P3ScalarType a=(p1-p0).Norm();
    P3ScalarType b=(p2-p0).Norm();
    P3ScalarType c=(p1-p2).Norm();

    P3ScalarType sum = (a + b + c)*0.5;
    P3ScalarType area2 =  sum*(a+b-sum)*(a+c-sum)*(b+c-sum);
    if(area2 <= 0) return 0;
    //circumradius: (a*b*c)/(4*sqrt(area2))
    //inradius: (a*b*c)/(4*circumradius*sum) => sqrt(area2)/sum;
    return (8*area2)/(a*b*c*sum);
}

/// Compute a shape quality measure of the triangle composed by points p0,p1,p2
/// It Returns mean ratio 2sqrt(a, b)/(a+b) where a+b are the eigenvalues of the M^tM of the
/// transformation matrix into a regular simplex
/// the range is range [0, 1]
template<class P3ScalarType>
P3ScalarType QualityMeanRatio(Point3<P3ScalarType> const &p0,
                                                    Point3<P3ScalarType> const &p1,
                                                    Point3<P3ScalarType> const &p2) {

    P3ScalarType a=(p1-p0).Norm();
    P3ScalarType b=(p2-p0).Norm();
    P3ScalarType c=(p1-p2).Norm();
    P3ScalarType sum = (a + b + c)*0.5; //semiperimeter
    P3ScalarType area2 =  sum*(a+b-sum)*(a+c-sum)*(b+c-sum);
    if(area2 <= 0) return 0;
    return (4.0*sqrt(3.0)*sqrt(area2))/(a*a + b*b + c*c);
}



/// Return the Double of area of the triangle
// NOTE the old Area function has been removed to intentionally
// cause compiling error that will help people to check their code...
// A some  people used Area assuming that it returns the double and some not.
// So please check your codes!!!
// And please DO NOT Insert any Area named function here!

template<class TriangleType>
typename TriangleType::ScalarType DoubleArea(const TriangleType &t)
{
    return Norm( (t.cP(1) - t.cP(0)) ^ (t.cP(2) - t.cP(0)) );
}

template<class TriangleType>
typename TriangleType::ScalarType CosWedge(const TriangleType &t, int k)
{
  typename TriangleType::CoordType
    e0 = t.cP((k+1)%3) - t.cP(k),
    e1 = t.cP((k+2)%3) - t.cP(k);
  return (e0*e1)/(e0.Norm()*e1.Norm());
}

template<class TriangleType>
Point3<typename TriangleType::ScalarType> Barycenter(const TriangleType &t)
{
    return ((t.cP(0)+t.cP(1)+t.cP(2))/(typename TriangleType::ScalarType) 3.0);
}

template<class TriangleType>
typename TriangleType::ScalarType Perimeter(const TriangleType &t)
{
  return Distance(t.cP(0),t.cP(1))+
         Distance(t.cP(1),t.cP(2))+
         Distance(t.cP(2),t.cP(0));
}

template<class TriangleType>
Point3<typename TriangleType::ScalarType> Circumcenter(const TriangleType &t)
{
   typename TriangleType::ScalarType a2 = (t.cP(1) - t.cP(2)).SquaredNorm();
   typename TriangleType::ScalarType b2 = (t.cP(2) - t.cP(0)).SquaredNorm();
   typename TriangleType::ScalarType c2 = (t.cP(0) - t.cP(1)).SquaredNorm();
   Point3<typename TriangleType::ScalarType>c = t.cP(0)*a2*(-a2 + b2 + c2) +
                                                t.cP(1)*b2*( a2 - b2 + c2) +
                                                t.cP(2)*c2*( a2 + b2 - c2);
   c /= 2*(a2*b2 + a2*c2 + b2*c2) - a2*a2 - b2*b2 - c2*c2;
   return c;
}


}	 // end namespace


#endif