.TH "point" 2rheolef "Version 7.2" "rheolef" \" -*- nroff -*-
.ad l
.nh
.SH NAME
point \- d-dimensional physical point or vector (rheolef-7\&.2)
.SH "DESCRIPTION"
.PP
The \fCpoint\fP defines a vertex or vector in the physical d-dimensional space, d=1,2,3\&. It is represented as an array of coordinates\&. The coordinate index starts at zero and finishes at \fCd-1\fP, e\&.g\&. \fCx[0]\fP, \fCx[1]\fP and \fCx[2]\fP\&.
.PP
The default constructor set all components to zero: 
.PP
.nf
    point x;

.fi
.PP
 and this default could be overridden: 
.PP
.nf
    point x (1, 2, 3\&.14);

.fi
.PP
 or alternatively: 
.PP
.nf
    point x = {1, 2, 3\&.14};

.fi
.PP
 The standard linear algebra for vectors is supported by the \fCpoint\fP class\&.
.SH "IMPLEMENTATION"
.PP
This documentation has been generated from file fem/geo_element/point\&.h
.PP
The \fCpoint\fP class is simply an alias to the \fC\fBpoint_basic\fP\fP class
.PP
.PP
.nf
typedef point_basic<Float> point;
.fi
.PP
.PP
The \fC\fBpoint_basic\fP\fP class is a template class with the floating type as parameter:
.PP
.PP
.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();
  explicit point_basic (const T& x0, const T& x1 = 0, const T& x2 = 0);
        
  template <class T1>
  point_basic<T>(const point_basic<T1>& p);

  template <class T1>
  point_basic<T>& operator= (const point_basic<T1>& p);

  point_basic (const std::initializer_list<T>& il);

// accessors:

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

// algebra:

  bool operator== (const point_basic<T>& v) const;
  bool operator!= (const point_basic<T>& v) const;
  point_basic<T> operator+ (const point_basic<T>& v) const;
  point_basic<T> operator\- (const point_basic<T>& v) const;
  point_basic<T> operator\- () const;
  point_basic<T>& operator+= (const point_basic<T>& v);
  point_basic<T>& operator\-= (const point_basic<T>& v);
  point_basic<T>& operator*= (const T& a);
  point_basic<T>& operator/= (const T& a);

  template <class U>
  typename
  std::enable_if<
    details::is_rheolef_arithmetic<U>::value
    ,point_basic<T>
  >::type
  operator* (const U& a) const;
  point_basic<T> operator/ (const T& a) const;
  point_basic<T> operator/ (point_basic<T> v) const;

// i/o:

  std::istream& get (std::istream& s, int d = 3);
  std::ostream& put (std::ostream& s, int d = 3) const;
.fi
.PP
 
.PP
.nf
};

.fi
.PP
 
.PP
\fB\fP
.RS 4

.RE
.PP
These linear and nonlinear functions are completed by some usual functions:
.PP
.PP
.nf
template<class T>
std::istream& operator >> (std::istream& s, point_basic<T>& p);

template<class T>
std::ostream& operator << (std::ostream& s, const point_basic<T>& p);

template <class T, class U>
typename
std::enable_if<
  details::is_rheolef_arithmetic<U>::value
 ,point_basic<T>
>::type
operator* (const U& a, const point_basic<T>& u);

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

// metrics:
template<class T>
T dot (const point_basic<T>& x, const point_basic<T>& y);

template<class T>
T norm2 (const point_basic<T>& x);

template<class T>
T norm (const point_basic<T>& x);

template<class T>
T dist2 (const point_basic<T>& x,  const point_basic<T>& y);

template<class T>
T dist (const point_basic<T>& x,  const point_basic<T>& y);

template<class T>
T dist_infty (const point_basic<T>& x,  const point_basic<T>& y);

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);
.fi
.PP
 
.SH AUTHOR
Pierre  Saramito  <Pierre.Saramito@imag.fr>
.SH COPYRIGHT
Copyright   (C)  2000-2018  Pierre  Saramito  <Pierre.Saramito@imag.fr>
GPLv3+: GNU GPL version 3 or later  <http://gnu.org/licenses/gpl.html>.
This  is  free  software:  you  are free to change and redistribute it.
There is NO WARRANTY, to the extent permitted by law.