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 [AT] imag.fr>
COPYRIGHT
Copyright (C) 2000-2018 Pierre Saramito <Pierre.Saramito [AT] 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.