Grid Facet ConceptGrid EntitiesGrid Vertex ConceptGrid Edge Concept

Grid Edge Concept


A Grid Edge represents the mathematical concept of an edge -- a 1-dimensional entity in a Grid.

Refinement of

Grid Element


E is a type which is a model of Grid Edge
e is an object of type E
V is a shorthand for the E::Vertex type
v is an object of type V
g is an object of type E::grid_type
h is an object of type E::edge_handle

Associated types

NOTE: The types and expression involving Incidence Iterators are given below for the case of cell-on-edge iteration. Analogous types and expressions can be defined for the other element types, like edge, facet, or cell. The tables are to be understood in the following sense:
If a edge defines the incidence iterator over cells, then the requirements under Optional part apply. Analogous requirements take effect if `cell' is replaced by another element type.


Expression Description
handle type E::edge_handle type of the corresponding Edge Handle
vertex type E::Vertex Vertex type of the edge, short for E::grid_type::Vertex.
Optional part (as example)
cell-on-edge iterator E::CellIterator type of the corr. CellOnEdgeIterator

Valid Expressions


Expression Type requirements return type
handle e.handle()   E::edge_handle
first vertex v = e.V1()   Vertex
second vertex v = e.V2()   Vertex
Optional part (as example)
cell-on-edge iteration start e.FirstCell()   E::CellIterator
number of incident cells E.NumOfCells()   int

Expression semantics


Expression Precondition Semantics Postcondition
handle h = e.handle(); e is valid shorthand for h = e.TheGrid(). handle(e) e == e.TheGrid(). edge(h)
Optional part (as example)
cell-on-edge iteration start ci = e.FirstCell() e is valid let ci point to the first cell incident to e ci.TheEdge() == ci.TheAnchor() == e and ci.TheGrid() == e.TheGrid()
number of incident cells n = e.NumOfCells() e is valid n is the number of cells that are incident to e  

Complexity guarantees

All operations are amortized constant timeX.


Complex2D::Edge defined in edge2d.h

  1. Amortization is understood to involve calling the operations for all edges of a grid.
See also

Grid   Grid Element Handle   Edge Handle  Grid Element   Grid Cell   Sequence Iterator   Incidence Iterator  

Guntram Berti

Grid Facet ConceptGrid EntitiesGrid Vertex ConceptGrid Edge Concept