Geometric and other primitives

Collaboration diagram for Geometric and other primitives:

Namespaces
namespace	TensorAccessors

Classes
struct	GeometryInfo< 0 >
struct	GeometryInfo< dim >
class	Point< dim, Number >
class	SymmetricTensor< rank_, dim, Number >
class	Tensor< 0, dim, Number >
class	Tensor< rank_, dim, Number >
class	ReferenceCell

Detailed Description

This group contains a number of classes that act as geometric primitives or primitives for other mathematical objects. For example, the Tensor <rank,dim> class provides tensors of rank rank in dim space dimensions. Likewise, the SymmetricTensor offers symmetric tensors.

Geometrically, the Point class is the foundation of all geometric descriptions in the deal.II library. It denotes a geometric point in dim dimensional space. One can view a point as a vector the with dim coordinates that connects the origin with that particular point; as such, the Point class is derived from tensors of rank 1 (i.e. vectors), but in contrast to arbitrary tensors points have the special connotation of points in space, and therefore have some additional properties.

In deal.II, meshes are built from line segments, quadrilaterals, or hexahedra (depending on the space dimension). The GeometryInfo class is used to describe properties of these basic objects in unit space (i.e. for the unit line, unit square, and unit cube). It offers static data members denoting the number of vertices per cell, lines per face, or where which vertex is located. This abstraction allows to write applications mostly independently of the actual space dimension: loops over all vertices would simply run from zero to GeometryInfo<dim>::vertices_per_cell instead of from 0 to 4 (in 2d) or 0 to 8 (in 3d). In this way, the program will be correct in 2d as well as 3d, and one can run a program in a different space dimension simply by recompilation instead of having to change a significant portion of the code. These dimension-independent programming techniques are extensively discussed in the first few tutorial programs and are used throughout deal.II.