Two-Dimensional Visibility Charts for Continuous Curves

This paper considers computation of visibility for twodimensional shapes whose boundaries are C1 continuous curves. We assume we are given a one-parameter family of candidate viewpoints, which may be interior or exterior to the object, and at finite or infinite locations. We consider how to compute whether the whole boundary of the shape is visible from some finite set of viewpoints taken from this family, and if so, how to compute a minimal set of such viewpoints. The viewpoint families we can handle include (i) the set of viewing directions from infinity, (ii) viewpoints on a circle located outside the object (for inspection from a turntable), and (iii) viewpoints located on the walls of the shape itself. We compute a structure called a visibility chart, which simultaneously encodes the visible part of the shape’s boundary from every view in the family. Using such a visibility chart, finding a minimal set of viewpoints reduces to the set-covering problem over the reals. Pract...

• Type: Conference
• Year: 2005
• Where: SMI
• Authors: Gershon Elber, Robert Sayegh, Gill Barequet, Ralph R. Martin
• Keywords: SMI 2005, Viewpoints, Visibility, Visibility Chart