COMPUTATIONAL TOPOLOGY FOR RECONSTRUCTION OF SURFACES WITH BOUNDARY , PART I : APPLICATIONS

This paper presents computational topology techniques for reconstruction of surfaces with boundary, where all manifolds considered are assumed to be embedded in R. The focus here is upon examples and applications, with the theoretical basis being presented in a companion paper. We consider any C compact 2-manifold M with boundary and define and construct its ρ-envelope Eρ(M), such that Eρ(M) has no boundary. Then Eρ(M) can be used to approximate M , even though Eρ(M) need not be C. This approach extends many previous results on surface reconstruction, where the assumption of an empty boundary of M had been crucial. Note, also that the original surface M need not be orientable for the definition and construction of Eρ(M). This leads to our approximations of some non-orientable manifolds, such as the Möbius strip, again extending previously known techniques. Our prototype code is discussed and examples are shown to demonstrate the effectiveness of this approach, with specific demonstration of reconstruction improvements along a boundary where refined normal approximations have been crucial.

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