1.2 Terminology

Most technical names are self-explanatory and care has been taken to use well defined and precise expressions. In order to avoid any confusion a few terms require further comments and are given in Table 1.1.

Table 1.1: A short glossary of important terms.

location	a space defined by a set of coordinates
vertex	a zero-dimensional part of a higher dimensional entity, e.g. part of a geometry, a polygon, or polyhedron
n-simplex	(n+1) affinely independent vertices
point	a zero-simplex
edge	a one-simplex
triangle	a two-simplex
tetrahedron	a three-simplex
node	not a point, but part of a tree data structure
facet	a two-dimensional entity, e.g. a polygon
face	the verb as in ``facing a direction''
non-planar	curved, but mostly used as short form for piecewise-planar
topology	the connectivity of a set of points where adjacency is given by the edges regardless of the location of the points
boundary	(n-1)-dimensional topology in $R^{n}$
grid	n-dimensional structured topology in $R^{n}$, numerical grid
mesh	n-dimensional unstructured topology in $R^{n}$
surface mesh	(n-1)-dimensional unstructured topology in $R^{n}$
triangulation	a simplicial complex [118] where the highest order element is a 2-simplex in $R^{n}$
tetrahedralization	a simplicial complex where the highest order element is a 3-simplex in $R^{n}$
Triangulation	special triangulation or tetrahedralization as for example in ``Delaunay Triangulation'' or ``Steiner Triangulation'', independent of the order of the simplices
boundary consistent	incorporating the boundary, as opposed to intersecting or overlapping
boundary-fitted	nicely aligned with the boundary and not just boundary consistent
boundary conforming	This term is avoided because it is sometimes used in different ways throughout literature, e.g. as boundary consistent or as boundary-fitted.