.\"
.de Id
..
.de Sp
.if n .sp
.if t .sp 0.4
..
.TH point 2rheolef "rheolef-6.7" "rheolef-6.7" "rheolef-6.7"
.\" label: /*Class:point
.SH NAME
\fBpoint\fP - vertex of a mesh
.\" skip: @clindex point
.\" skip: @clindex geo
.SH DESCRIPTION

Defines geometrical vertex as an array of coordinates.
This array is also used as a vector of the three dimensional
physical space.
.\" END
.SH IMPLEMENTATION
.\" begin_example
.Sp
.nf
template <class T>
class point_basic {
    public:

// typedefs:

        typedef size_t size_type;
        typedef T      element_type;
        typedef T      scalar_type;
        typedef T      float_type;

// allocators:

        explicit point_basic () { _x[0] = T();  _x[1] = T();  _x[2] = T(); }

        explicit point_basic (
                const T& x0,
                const T& x1 = 0,
                const T& x2 = 0)
                        { _x[0] = x0; _x[1] = x1; _x[2] = x2; }

        template <class T1>
        point_basic<T>(const point_basic<T1>& p)
                { _x[0] = p._x[0]; _x[1] = p._x[1]; _x[2] = p._x[2]; }

        template <class T1>
        point_basic<T>& operator = (const point_basic<T1>& p)
                { _x[0] = p._x[0]; _x[1] = p._x[1]; _x[2] = p._x[2]; return *this; }

#ifdef _RHEOLEF_HAVE_STD_INITIALIZER_LIST
        point_basic (const std::initializer_list<T>& il);
#endif // _RHEOLEF_HAVE_STD_INITIALIZER_LIST

// accessors:

        T& operator[](int i_coord)              { return _x[i_coord%3]; }
        const T&  operator[](int i_coord) const { return _x[i_coord%3]; }
        T& operator()(int i_coord)              { return _x[i_coord%3]; }
        const T&  operator()(int i_coord) const { return _x[i_coord%3]; }

        // interface for CGAL library inter-operability:
        const T& x() const { return _x[0]; }
        const T& y() const { return _x[1]; }
        const T& z() const { return _x[2]; }
        T& x(){ return _x[0]; }
        T& y(){ return _x[1]; }
        T& z(){ return _x[2]; }

// inputs/outputs:

        std::istream& get (std::istream& s, int d = 3)
        {
            switch (d) {
            case 0 : _x[0] = _x[1] = _x[2] = 0; return s;
            case 1 : _x[1] = _x[2] = 0; return s >> _x[0];
            case 2 : _x[2] = 0; return s >> _x[0] >> _x[1];
            default: return s >> _x[0] >> _x[1] >> _x[2];
            }
        }
        // output
        std::ostream& put (std::ostream& s, int d = 3) const;

// algebra:

        bool operator== (const point_basic<T>& v) const
                { return _x[0] == v[0] && _x[1] == v[1] && _x[2] == v[2]; }

        bool operator!= (const point_basic<T>& v) const
                { return !operator==(v); }

        point_basic<T>& operator+= (const point_basic<T>& v)
                { _x[0] += v[0]; _x[1] += v[1]; _x[2] += v[2]; return *this; }

        point_basic<T>& operator-= (const point_basic<T>& v)
                { _x[0] -= v[0]; _x[1] -= v[1]; _x[2] -= v[2]; return *this; }

        point_basic<T>& operator*= (const T& a)
                { _x[0] *= a; _x[1] *= a; _x[2] *= a; return *this; }

        point_basic<T>& operator/= (const T& a)
                { _x[0] /= a; _x[1] /= a; _x[2] /= a; return *this; }

        point_basic<T> operator+ (const point_basic<T>& v) const
                { return point_basic<T> (_x[0]+v[0], _x[1]+v[1], _x[2]+v[2]); }

        point_basic<T> operator- () const
                { return point_basic<T> (-_x[0], -_x[1], -_x[2]); }

        point_basic<T> operator- (const point_basic<T>& v) const
                { return point_basic<T> (_x[0]-v[0], _x[1]-v[1], _x[2]-v[2]); }

        template <class U>
        typename
        std::enable_if<
          details::is_rheolef_arithmetic<U>::value
         ,point_basic<T>
        >::type
        operator* (const U& a) const
                { return point_basic<T> (_x[0]*a, _x[1]*a, _x[2]*a); }
        point_basic<T> operator/ (const T& a) const
                { return operator* (T(1)/T(a)); }
        point_basic<T> operator/ (point_basic<T> v) const
                { return point_basic<T> (_x[0]/v[0], _x[1]/v[1], _x[2]/v[2]); }

// data:
// protected:
        T _x[3];
// internal:
        static T _my_abs(const T& x) { return (x > T(0)) ? x : -x; }
};
typedef point_basic<Float> point;

// algebra:
template <class T, class U>
inline
typename
std::enable_if<
  details::is_rheolef_arithmetic<U>::value
 ,point_basic<T>
>::type
operator* (const U& a, const point_basic<T>& u)
{
  return point_basic<T> (a*u[0], a*u[1], a*u[2]);
}
template<class T>
inline
point_basic<T>
vect (const point_basic<T>& v, const point_basic<T>& w)
{
  return point_basic<T> (
        v[1]*w[2]-v[2]*w[1],
        v[2]*w[0]-v[0]*w[2],
        v[0]*w[1]-v[1]*w[0]);
}
// metrics:
template<class T>
inline
T dot (const point_basic<T>& x, const point_basic<T>& y)
{
  return x[0]*y[0]+x[1]*y[1]+x[2]*y[2];
}
template<class T>
inline
T norm2 (const point_basic<T>& x)
{
  return dot(x,x);
}
template<class T>
inline
T norm (const point_basic<T>& x)
{
  return sqrt(norm2(x));
}
template<class T>
inline
T dist2 (const point_basic<T>& x,  const point_basic<T>& y)
{
  return norm2(x-y);
}
template<class T>
inline
T dist (const point_basic<T>& x,  const point_basic<T>& y)
{
  return norm(x-y);
}
template<class T>
inline
T dist_infty (const point_basic<T>& x,  const point_basic<T>& y)
{
  return max(point_basic<T>::_my_abs(x[0]-y[0]),
         max(point_basic<T>::_my_abs(x[1]-y[1]),
             point_basic<T>::_my_abs(x[2]-y[2])));
}
template <class T>
T vect2d (const point_basic<T>& v, const point_basic<T>& w);

template <class T>
T mixt (const point_basic<T>& u, const point_basic<T>& v, const point_basic<T>& w);

// robust(exact) floating point predicates: return the sign of the value as (0, > 0, < 0)
// formally: orient2d(a,b,x) = vect2d(a-x,b-x)
template <class T>
int
sign_orient2d (
  const point_basic<T>& a,
  const point_basic<T>& b,
  const point_basic<T>& c);

template <class T>
int
sign_orient3d (
  const point_basic<T>& a,
  const point_basic<T>& b,
  const point_basic<T>& c,
  const point_basic<T>& d);

// compute also the value:
template <class T>
T orient2d(
  const point_basic<T>& a,
  const point_basic<T>& b,
  const point_basic<T>& c);

// formally: orient3d(a,b,c,x) = mixt3d(a-x,b-x,c-x)
template <class T>
T orient3d(
  const point_basic<T>& a,
  const point_basic<T>& b,
  const point_basic<T>& c,
  const point_basic<T>& d);

template <class T>
std::string ptos (const point_basic<T>& x, int d = 3);

// ccomparators: lexicographic order
template<class T, size_t d>
bool
lexicographically_less (const point_basic<T>& a, const point_basic<T>& b)
{
  for (typename point_basic<T>::size_type i = 0; i < d; i++) {
    if (a[i] < b[i]) return true;
    if (a[i] > b[i]) return false;
  }
  return false; // equality
}
.Sp
.fi
.\" end_example