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COMPUTATIONAL TOPOLOGY FOR RECONSTRUCTION OF SURFACES
 

Summary: COMPUTATIONAL TOPOLOGY FOR
RECONSTRUCTION OF SURFACES
WITH BOUNDARY, PART I:
APPLICATIONS
K. ABE, J. BISCEGLIO, T. J. PETERS,
A. C. RUSSELL, D. R. FERGUSON, T. SAKKALIS
Abstract. This paper presents computational topology techniques for reconstruc-
tion of surfaces with boundary, where all manifolds considered are assumed to be
embedded in R3
. The focus here is upon examples and applications, with the
theoretical basis being presented in a companion paper. As a step towards these
results, we consider any C2
compact 2-manifold M with boundary and then we
define and construct its envelope E(M), such that E(M) has no boundary. Then
E(M) can be used to approximate M, even though E(M) need not be C2
. This
construction supports extensions of many previous results on surface reconstruc-
tion, where the assumption of an empty boundary of M had been crucial. Note,
also that the original surface M need not be orientable, again extending previously
known techniques. Our prototype code is discussed and examples are shown to

  

Source: Abe, Kinetsu - Department of Mathematics, University of Connecticut

 

Collections: Mathematics