Classifying
Edges and Faces as Manifold or Non-Manifold Elements in 4D Orthogonal
Pseudo-Polytopes
Ricardo Pérez
Aguila
Antonio Aguilera
Ramírez
Centro de Investigación en
Tecnologías de Información y Automatización (CENTIA)
Universidad de las Américas – Puebla
(UDLAP)
Ex-Hacienda Santa Catarina
Mártir. Phone: +52 (222) 229-2664
México 72820, Cholula, Puebla.
|
|
|
|
||
|
|
|
|
Keywords: Computational geometry, Geometric interrogations and
reasoning, Geometric and topological representations.
This article
presents our experimental results for classifying edges and faces as manifold
or non-manifold elements in 4D Orthogonal Pseudo-Polytopes (4D-OPP's). For
faces in 4D-OPP's we propose a condition to classify them as manifold or non-manifold.
For the edges' analysis in 4D-OPP's we have developed two approaches: 1) The
analogy between incident (manifold and non-manifold) edges to a vertex in 3D
Orthogonal Pseudo-Polyhedra (3D-OPP's) with incident
(manifold and non-manifold)
faces to a edge in 4D-OPP's; and 2) The extension of the concept of "cones
of faces" (which is applied for classifying a vertex in 3D-OPP's as
manifold or non-manifold) to "hypercones of volumes" for classifying
an edge as manifold or non-manifold in 4D-OPP's. Both approaches have provided
the same results, which present that there are eight types of edges in
4D-OPP's. Finally, the generalizations for classifying the n-3 and the n-2
dimensional boundary elements for n-dimensional Orthogonal Pseudo-Polytopes as manifold
or non-manifold elements is also presented.