Useful geometric properties of the generalized cone
Rao, K.
Medioni, G.
Dept. of Electr. Eng. & Comput. Sci., Univ. of Southern California, Los Angeles, 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): 276-281
Meeting Date: 06/05/1988 - 06/09/1988
Location: Ann Arbor, MI, USA
ISBN: 0-8186-0862-5
References Cited: 22
INSPEC Accession Number: 3248005
Digital Object Identifier: 10.1109/CVPR.1988.196248
Current Version Published: 2002-08-06
Abstract
The authors present results on geometric properties of the
generalized cone, in an effort to utilize it for a shape description
system. They first derive the relationship between the generalized cone
description and the surface description given by differential geometry.
Then they derive expressions for the Gaussian and mean curvatures of a
generalized cone, in general, and obtain expressions for some special
cases like the torus, the solid of revolution etc. They study the
planarity property of the contour generators of a generalized cone, in
particular, one with a planar axis. They find that homogeneous
generalized cones with planar axes and circular cross sections or
constant-size cross sections have planar contour generators in an
orthographic side view. An example of such a generalized cone is the
torus. However, the contour generators are not planar in a general view.
They also study symmetry properties of some generalized cones and find,
in particular, that in orthographic projection the contour of the solid
of revolution is symmetric about the projection of its axis from any
point of view
Index
Terms
Available to subscribers and IEEE members.
References
Available to subscribers and IEEE members.
Citing Documents
Available to subscribers and IEEE members.
Cart
