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Proceedings Paper

Three-dimensional strong convexity and visibility
Author(s): Eugene Fink; Derick Wood
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Paper Abstract

We define the notions of strong convexity and strong visibility. These notions generalize standard convexity and visibility, as well as several types of nontraditional convexity, such as iso-oriented rectangles and C-oriented polygons. We explore the properties of strong convexity and strong visibility in two and three dimensions. In particular, we establish analogs of the following properties of standard convex sets: (1) Every two points of a convex set are visible to each other. (2) The intersection of convex sets is a convex set. (3) For every point in the boundary of a convex set, there exists a supporting plane through this point. (4) A closed convex set in three dimensions is the intersection of all halfspaces that contain it.

Paper Details

Date Published: 11 August 1995
PDF: 12 pages
Proc. SPIE 2573, Vision Geometry IV, (11 August 1995); doi: 10.1117/12.216441
Show Author Affiliations
Eugene Fink, Carnegie Mellon Univ. (United States)
Derick Wood, Hong Kong Univ. of Science and Technology (Hong Kong)

Published in SPIE Proceedings Vol. 2573:
Vision Geometry IV
Robert A. Melter; Angela Y. Wu; Fred L. Bookstein; William D. K. Green, Editor(s)

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