Grids and Grid RangesGrid-With-Boundary ConceptArchetypedGrid Concept

ArchetypedGrid Concept


An ArchetypedGrid is a grid which associates an archetype with each cell. An archetype is a combinatorial model of a cell, or, more precisely, of the boundary of a cell. Thus, the archetype A of a cell C of dimension d is a grid of dimension d-1. The cells of A correspond to the facets of C.

The rationale for having archetypes stems from the fact that in general, it is not enough to know the vertices of a cell to determine its topology. We must also know how the vertices form the facets of the cell. In general, the archetype will again be a model of ArchetypedGrid, so that we can apply the concept recursively.

For an example of how to use archetypes, consider the problem of copying grids from one representation (source) into a different one (target). Consider the case of quadrilateral cells, where the vertices of a cell are ordered in a binary way in the source representation (for example, row-major numbering in a Cartesian grid), and cyclically in the target representation. If we don't care about this different numbering, twisted cells will result. In order to avoid this, we must somehow know about the different orderings. We can of course implement ad hoc copy procedures for each pair of grid representations, but this is against the "generic spirit".

Incompatible vertex-ordering may result in self-intersecting cells
A binary ordering (left), an incompatible cyclic ordering (middle), and the effect of direct copying (right)

A better way is to make this ordering explicit and amenable to algorithmic treatment. This is what archetypes are for. Before starting the actual copying of the grid, we try to match the archetypes of the source grid to that of the target grid by calculating isomorphisms between source and target archetypes. These isomorphisms will define a permutation of the vertex ordering of the source cells, such that an isomorphic copy of the source grid results.

Refinement of

Cell-Vertex Input Grid Range


G is a type which is a model of ArchetypedGrid
g is an object of type G
A is an object of type G::archetype_type
a is an object of type G::archetype_handle
ai is an object of type G::archetype_iterator
C is an object of type G::Cell c is an object of type G::cell_handle

Associated types


Expression Description
archetype type G::archetype_type The type of cell archetypes,

model of Grid and of Cell-Vertex Input Grid Range of dimension G::dimension()-1

archetype handle G::archetype_handle unique handle for an archetype within the grid G
archetype iterator G::archetype_iterator iterator over all archetypes of a grid

Valid Expressions


Expression Type requirements return type
Archetype association g.Archetypeof(C)   archetype_type const&
Archetype association g.archetype_of(c)   archetype_handle
Archetype iteration start g.BeginArchetype()   archetype_iterator
Archetype iteration past-the-end g.EndArchetype()   archetype_iterator
Archetype count g.NumOfArchetypes()   unsigned
Handle to archetype g.Archetype(a)   archetype_type const&
iterator to handle g.handle(ai)   archetype_handle

Expression semantics


Expression Precondition Semantics Postcondition


&(g.Archetype(archetype_of(C))) == &(g.ArchetypeOf(C))
std::distance(g.BeginArchetype(), g.EndArchetype()) == g.NumOfArchetypes()
&(*ai) == &(g.Archetype(g.handle(ai)))



    See also

    Guntram Berti

    Grids and Grid RangesGrid-With-Boundary ConceptArchetypedGrid Concept