 
Summary: COMPUTATIONAL TOPOLOGY FOR
RECONSTRUCTION OF SURFACES
WITH BOUNDARY, PART II:
MATHEMATICAL FOUNDATIONS
K. Abe 1
, J. Bisceglio 2
, D. R. Ferguson 3
,
T. J. Peters 4
, A. C. Russell 5
, T. Sakkalis6
Abstract. This paper presents new mathematical foundations for topologically
correct surface reconstruction techniques that are applicable to 2manifolds with
boundary, where provable techniques previously had been limited to surfaces with
out boundary. This is done by an intermediate construction of the envelope (as
defined herein) of the original surface. For any C2
manifold it is then shown that
its envelope is C1,1
and this envelope can be reconstructed with topological guaran
tees. The proof is then completed by defining functions which permit the mapping
