Reference documentation for deal.II version Git b90157c 20181117 13:29:28 0500

#include <deal.II/base/point.h>
Public Member Functions  
Point ()  
Point (const Tensor< 1, dim, Number > &)  
Point (const Number x)  
Point (const Number x, const Number y)  
Point (const Number x, const Number y, const Number z)  
Number  operator() (const unsigned int index) const 
Number &  operator() (const unsigned int index) 
Point< dim, Number >  operator+ (const Tensor< 1, dim, Number > &) const 
Tensor< 1, dim, Number >  operator (const Point< dim, Number > &) const 
Point< dim, Number >  operator (const Tensor< 1, dim, Number > &) const 
Point< dim, Number >  operator () const 
template<typename OtherNumber >  
Point< dim, typename ProductType< Number, typename EnableIfScalar< OtherNumber >::type >::type >  operator/ (const OtherNumber) const 
Number  operator* (const Tensor< 1, dim, Number > &p) const 
numbers::NumberTraits< Number >::real_type  square () const 
numbers::NumberTraits< Number >::real_type  distance (const Point< dim, Number > &p) const 
numbers::NumberTraits< Number >::real_type  distance_square (const Point< dim, Number > &p) const 
template<class Archive >  
void  serialize (Archive &ar, const unsigned int version) 
Public Member Functions inherited from Tensor< 1, dim, Number >  
Tensor ()  
Tensor (const array_type &initializer)  
Tensor (const Tensor< rank_, dim, OtherNumber > &initializer)  
Tensor (const Tensor< 1, dim, Tensor< rank_1, dim, OtherNumber >> &initializer)  
operator Tensor< 1, dim, Tensor< rank_1, dim, OtherNumber >> () const  
value_type &  operator[] (const unsigned int i) 
const value_type &  operator[] (const unsigned int i) const 
const Number &  operator[] (const TableIndices< rank_ > &indices) const 
Number &  operator[] (const TableIndices< rank_ > &indices) 
Number *  begin_raw () 
const Number *  begin_raw () const 
Number *  end_raw () 
const Number *  end_raw () const 
Tensor &  operator= (const Tensor< rank_, dim, OtherNumber > &rhs) 
Tensor &  operator= (const Number &d) 
bool  operator== (const Tensor< rank_, dim, OtherNumber > &) const 
bool  operator!= (const Tensor< rank_, dim, OtherNumber > &) const 
Tensor &  operator+= (const Tensor< rank_, dim, OtherNumber > &) 
Tensor &  operator= (const Tensor< rank_, dim, OtherNumber > &) 
Tensor &  operator*= (const OtherNumber &factor) 
Tensor &  operator/= (const OtherNumber &factor) 
Tensor  operator () const 
void  clear () 
numbers::NumberTraits< Number >::real_type  norm () const 
numbers::NumberTraits< Number >::real_type  norm_square () const 
void  unroll (Vector< OtherNumber > &result) const 
void  serialize (Archive &ar, const unsigned int version) 
Static Public Member Functions  
static Point< dim, Number >  unit_vector (const unsigned int i) 
Static Public Member Functions inherited from Tensor< 1, dim, Number >  
static unsigned int  component_to_unrolled_index (const TableIndices< rank_ > &indices) 
static TableIndices< rank_ >  unrolled_to_component_indices (const unsigned int i) 
static std::size_t  memory_consumption () 
Related Functions  
(Note that these are not member functions.)  
template<typename OtherNumber >  
Point< dim, typename ProductType< Number, typename EnableIfScalar< OtherNumber >::type >::type >  operator* (const OtherNumber) const 
template<int dim, typename Number >  
std::ostream &  operator<< (std::ostream &out, const Point< dim, Number > &p) 
template<int dim, typename Number >  
std::istream &  operator>> (std::istream &in, Point< dim, Number > &p) 
Additional Inherited Members  
Public Types inherited from Tensor< 1, dim, Number >  
using  value_type = typename Tensor< rank_1, dim, Number >::tensor_type 
using  array_type = typename Tensor< rank_1, dim, Number >::array_type[(dim!=0)?dim:1] 
using  tensor_type = Tensor< rank_, dim, Number > 
Static Public Attributes inherited from Tensor< 1, dim, Number >  
static const unsigned int  dimension 
static const unsigned int  rank 
static const unsigned int  n_independent_components 
A class that represents a point in a Cartesian space of dimension dim
.
Objects of this class are used to represent points (i.e., vectors anchored at the origin) of a vector space equipped with a Cartesian coordinate system. They are, among other uses, passed to functions that operate on points in spaces of a priori fixed dimension: rather than using functions like double f(const double x)
and double f(const double x, const double y)
, you can use double f(const Point<dim> &p)
instead as it allows writing dimension independent code.
deal.II specifically uses Point objects as indicating points that are represented by Cartesian coordinates, i.e., where a point in dim
space dimensions is characterized by signed distances along the axes of a coordinate system spanned by dim
mutually orthogonal unit vectors (called the "coordinate axes"). This choice of representing a vector makes addition and scaling of vectors particularly simple: one only has to add or multiply each coordinate value. On the other hand, adding or scaling vectors is not nearly as simple when a vector is represented in other kinds of coordinate systems (e.g., spherical coordinate systems).
Point<dim>
and what is a Tensor<1,dim>
?The Point class is derived from Tensor<1,dim> and consequently shares the latter's member functions and other attributes. In fact, it has relatively few additional functions itself (the most notable exception being the distance() function to compute the Euclidean distance between two points in space), and these two classes can therefore often be used interchangeably.
Nonetheless, there are semantic differences that make us use these classes in different and welldefined contexts. Within deal.II, we use the Point
class to denote points in space, i.e., for vectors (rank1 tensors) that are anchored at the origin. On the other hand, vectors that are anchored elsewhere (and consequently do not represent points in the common usage of the word) are represented by objects of type Tensor<1,dim>. In particular, this is the case for direction vectors, normal vectors, gradients, and the differences between two points (i.e., what you get when you subtract one point from another): all of these are represented by Tensor<1,dim> objects rather than Point<dim>.
Furthermore, the Point class is only used where the coordinates of an object can be thought to possess the dimension of a length. An object that represents the weight, height, and cost of an object is neither a point nor a tensor (because it lacks the transformation properties under rotation of the coordinate system) and should consequently not be represented by either of these classes. Use an array of size 3 in this case, or the std::array
class. Alternatively, as in the case of vectorvalued functions, you can use objects of type Vector or std::vector
.
dim  An integer that denotes the dimension of the space in which a point lies. This of course equals the number of coordinates that identify a point. 
Number  The data type in which the coordinates values are to be stored. This will, in almost all cases, simply be the default double , but there are cases where one may want to store coordinates in a different (and always scalar) type. An example would be an interval type that can store the value of a coordinate as well as its uncertainty. Another example would be a type that allows for Automatic Differentiation (see, for example, the Sacado type used in step33) and thereby can generate analytic (spatial) derivatives of a function when passed a Point object whose coordinates are stored in such a type. 
Standard constructor. Creates an object that corresponds to the origin, i.e., all coordinates are set to zero.

explicit 
Convert a tensor to a point.
Constructor for one dimensional points. This function is only implemented for dim==1
since the usage is considered unsafe for points with dim!=1
as it would leave some components of the point coordinates uninitialized.
Point< dim, Number >::Point  (  const Number  x, 
const Number  y  
) 
Constructor for two dimensional points. This function is only implemented for dim==2
since the usage is considered unsafe for points with dim!=2
as it would leave some components of the point coordinates uninitialized (if dim>2) or would not use some arguments (if dim<2).
Point< dim, Number >::Point  (  const Number  x, 
const Number  y,  
const Number  z  
) 
Constructor for three dimensional points. This function is only implemented for dim==3
since the usage is considered unsafe for points with dim!=3
as it would leave some components of the point coordinates uninitialized (if dim>3) or would not use some arguments (if dim<3).

static 
Return a unit vector in coordinate direction i
, i.e., a vector that is zero in all coordinates except for a single 1 in the i
th coordinate.
Number Point< dim, Number >::operator()  (  const unsigned int  index  )  const 
Read access to the index
th coordinate.
Number& Point< dim, Number >::operator()  (  const unsigned int  index  ) 
Read and write access to the index
th coordinate.
Point<dim, Number> Point< dim, Number >::operator+  (  const Tensor< 1, dim, Number > &  )  const 
Add an offset given as Tensor<1,dim,Number> to a point.
Tensor<1, dim, Number> Point< dim, Number >::operator  (  const Point< dim, Number > &  )  const 
Subtract two points, i.e., obtain the vector that connects the two. As discussed in the documentation of this class, subtracting two points results in a vector anchored at one of the two points (rather than at the origin) and, consequently, the result is returned as a Tensor<1,dim> rather than as a Point<dim>.
Point<dim, Number> Point< dim, Number >::operator  (  )  const 
The opposite vector.
Point<dim, typename ProductType<Number, typename EnableIfScalar<OtherNumber>::type>::type> Point< dim, Number >::operator/  (  const OtherNumber  )  const 
Divide the current point by a factor.
Number Point< dim, Number >::operator*  (  const Tensor< 1, dim, Number > &  p  )  const 
Return the scalar product of the vectors representing two points.
numbers::NumberTraits<Number>::real_type Point< dim, Number >::square  (  )  const 
Return the scalar product of this point vector with itself, i.e. the square, or the square of the norm. In case of a complex number type it is equivalent to the contraction of this point vector with a complex conjugate of itself.
numbers::NumberTraits<Number>::real_type Point< dim, Number >::distance  (  const Point< dim, Number > &  p  )  const 
Return the Euclidean distance of this
point to the point p
, i.e. the l_2
norm of the difference between the vectors representing the two points.
numbers::NumberTraits<Number>::real_type Point< dim, Number >::distance_square  (  const Point< dim, Number > &  p  )  const 
Return the squared Euclidean distance of this
point to the point p
.
void Point< dim, Number >::serialize  (  Archive &  ar, 
const unsigned int  version  
) 
Read or write the data of this object to or from a stream for the purpose of serialization

related 
Multiply the current point by a factor.

related 

related 