Grid Edge ConceptGrid EntitiesGrid Element ConceptGrid Vertex Concept

Grid Vertex Concept


A Grid Vertex represents the mathematical concept of a vertex -- a 0-dimensional entity in a Grid .

Refinement of

Grid Element


V is a type which is a model of grid vertex
v is an object of type V
g is an object of type V::grid_type
h is an object of type V::vertex_handle
ci is an object of type V::CellIterator

Associated types

NOTE: The types and expression involving Incidence Iterators are given below for the case of cell-on-vertex 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 vertex 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 V::vertex_handle type of the corresponding Vertex Handle
Optional part (as example)
cell-on-vertex iterator V::CellIterator type of the corr. CellOnVertexIterator

Valid Expressions


Expression Type requirements return type
handle v.handle()   V::vertex_handle
Optional part (as example)
cell-on-vertex iteration start v.FirstCell()   V::CellIterator
number of incident cells v.NumOfCells()   int

Expression semantics


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

Complexity guarantees

All operations are amortized constant timeX.


Vertex classes of complex2d (see Vertex2D), complex3d, cartesian2d, cartesian3d, or triang2d.

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

Grid   Grid Element Handle   Vertex Handle  Grid Element   Grid Cell   Sequence Iterator   Incidence Iterator  

Guntram Berti

Grid Edge ConceptGrid EntitiesGrid Element ConceptGrid Vertex Concept