Straight homogeneous generalized cylinders: differential geometryand uniqueness results
Ponce, J.
Dept. of Comput. Sci., Stanford Univ., CA;
This paper appears in: Computer Vision and Pattern Recognition, 1988. Proceedings CVPR '88., Computer Society Conference on
Publication Date: 5-9 Jun 1988
On page(s): 327-334
Meeting Date: 06/05/1988 - 06/09/1988
Location: Ann Arbor, MI, USA
ISBN: 0-8186-0862-5
References Cited: 17
INSPEC Accession Number: 3248008
Digital Object Identifier: 10.1109/CVPR.1988.196256
Current Version Published: 2002-08-06
Abstract
The author studies the differential geometry of straight
homogeneous generalized cylinders (SHGCs). He derives a necessary and
sufficient condition that an SHGC must verify to parameterize a regular
surface, computes the Gaussian curvature of a regular SHGC, and proves
that the parabolic lines of an SHGC are either meridians or parallels.
Using these results, he addresses the following problem: under which
conditions can a given surface have several descriptions by SHGCs? He
proves several results. In particular, he proves that two SHGCs with the
same cross-section plane and axis direction are necessarily deduced from
each other through inverse scalings of their cross-sections and sweeping
rule curve. He extends Shafer's pivot and slant theorems. Finally, he
proves that a surface with at least two parabolic lines has at most
three different SHGC descriptions, and that a surface with at least four
parabolic lines has at most a unique SHGC description
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