Three-dimensional strong convexity and visibility

Eugene Fink; Derick Wood

doi:10.1117/12.216441

11 August 1995 Three-dimensional strong convexity and visibility

Eugene Fink, Derick Wood

Proceedings Volume 2573, Vision Geometry IV; (1995) https://doi.org/10.1117/12.216441
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

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.

Citation Download Citation

Eugene Fink and Derick Wood "Three-dimensional strong convexity and visibility", Proc. SPIE 2573, Vision Geometry IV, (11 August 1995); https://doi.org/10.1117/12.216441

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