Applying half edge collapse to a set of n tetrahedra
covering a domain, another set of m tetrahedra
, m < n, covering the same domain is obtained.
In particular, material zeolites provide diverse periodic networks of corner-linked regular tetrahedra
, with striking geometric and topological structure.
Clay minerals have a layered structure at the nanoscale, and each layer consists of some combinations of two layer types with silicon tetrahedra
and aluminum octahedra as basic units [1, 2].
[Cs.sub.2][Nb.sub.4][O.sub.11] is the one that coexisted with Nb[O.sub.6] octahedra and Nb[O.sub.4] tetrahedra
in the structure [12,18].
Delaunay tessellation was applied to the three-dimensional (3D) atomic coordinates of each protein chain, whereby atoms were treated as vertices to generate a convex hull encompassing thousands of space-filling, nonoverlapping, irregular tetrahedra
If T contains t tetrahedra
, we can make a one-to-one correspondence of normal surfaces and 7t-tuples which satisfy a system of linear equations, called matching equations.
Their topics include results and examples, geometric motifs, hypergraph regularity theory, and packing tetrahedra
. ([umlaut] Ringgold, Inc., Portland, OR)
The technique extrudes layers of high-aspect ratio, right-angle-included tetrahedra
outward from a surface mesh.
The set of C-alpha points associated with a protein structure are used as vertices to create hundreds of nonoverlapping, space filling, irregular tetrahedra
that collectively form a convex hull, referred to as a Delaunay tessellation in the computational geometry literature , which we generate with the Qhull software package .
Size of tetrahedra
depends just on the spatial distribution and density of input points.
Most of the chapters in the book concern a different approach to constructing isosurfaces: marching cubes, dual contouring, interpolation, patch construction, and meshes based on tetrahedra
; multiresolution meshes and those making use of combined cubic, pyramidal, polyhedral elements are also covered.
The Li vacancy was shown to stabilize a hole at the "bridging" oxygen (common vertex of two BO4 tetrahedra