Impl

Classes
class	Dune::Fem::PointGeometry
	generic geometry modelling a single point More...
class	Dune::Fem::PyramidGeometry< BaseGeometry >
	generic geometry modelling a pyramid over a base geometry More...
class	Dune::Fem::ProductGeometry< FirstGeometry, SecondGeometry >
	generic geometry modelling the product of two base geometries More...

Detailed Description

Generic geometries are a way of constructing new geometries out of existing ones. This allows for code depending on the geometry to be written generically. For example, the LagrangeBaseFunction is written in this generic way. Therefore, you could create a LagrangeBaseFunction for a 7 dimensional simplex (and no new code is needed).

Generic geometries are created out of simpler ones by the following rules:

• A point (denoted by \(p\)) is a 0-dimensional generic geometry (PointGeometry). Its reference element is the origin of the coordinate system.
• Let \(g\) be a \(d\)-dimensional generic geometry. Then the pyramid over \(g\) (denoted by \(g^\cdot\)) with the reference geometry

  \[ g^\cdot = \bigl\lbrace (s x,s) \in {R}^{d+1} \bigm\vert s \in [0,1], x \in g \bigr\rbrace \]

  is also a generic geometry (PyramidGeometry).
• Let \(g_1\), \(g_2\) be generic geometries. The their product \(g_1 \times g_2\) (with the obvious reference geometry) is also a generic geometry (ProductGeometry).

Consider the following examples of generic geometries:

• the line \(p^\cdot\),
• the tetrahedron \(p^{\cdot\cdot\cdot}\),
• the cube (3-dimensioal) \(p^\cdot \times p^\cdot \times p^\cdot\),
• the prism \(p^{\cdot\cdot} \times p^\cdot\),
• the 4-sided pyramid \((p^\cdot \times p^\cdot)^\cdot\).

Note

All reference geometries defined in dune-grid can be expressed as generic geometries.