Computational differential topology

Document Type

Conference Proceeding

Publication Date

1-1-2007

Abstract

Some of the more differential aspects of the nascent field of computational topology are introduced and treated in considerable depth. Relevant categories based upon stratified geometric objects are proposed, and fundamental problems are identified and discussed in the context of both differential topology and computer science. New results on the triangulation of objects in the computational differential categories are proven, and evaluated from the perspective of effective computability (algorithmic solvability). In addition, the elements of innovative, effectively computable approaches for analyzing and obtaining computer generated representations of geometric objects based upon singularity/stratification theory and obstruction theory are formulated. New methods for characterizing complicated intersection sets are proven using differential analysis and homology theory. Also included are brief descriptions of several implementation aspects of some of the approaches described, as well as applications of the results in such areas as virtual sculpting, virtual surgery, modeling of heterogeneous biomaterials, and high speed visualizations. © Universidad Politécnica de Valencia.

Identifier

34248564597 (Scopus)

Publication Title

Applied General Topology

External Full Text Location

https://doi.org/10.4995/agt.2007.1909

e-ISSN

19894147

ISSN

15769402

First Page

35

Last Page

92

Issue

1

Volume

8

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