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point(2rheolef) rheolef point(2rheolef)

NAME

point - d-dimensional physical point or vector (rheolef-7.2)

DESCRIPTION

The point 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 d-1, e.g. x[0], x[1] and x[2].

The default constructor set all components to zero:


point x;


and this default could be overridden:


point x (1, 2, 3.14);


or alternatively:


point x = {1, 2, 3.14};


The standard linear algebra for vectors is supported by the point class.

IMPLEMENTATION

This documentation has been generated from file fem/geo_element/point.h

The point class is simply an alias to the point_basic class

typedef point_basic<Float> point;


The point_basic class is a template class with the floating type as parameter:

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;

};

These linear and nonlinear functions are completed by some usual functions:

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);

AUTHOR

Pierre Saramito <Pierre.Saramito@imag.fr>

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.

Thu Jul 14 2022 Version 7.2