Computing an exact spherical visibility map for meshed polyhedra

Authors:
Min Liu;Karthik Ramani
Affiliations:
Purdue University, West Lafayette, Indiana;Purdue University, West Lafayette, Indiana
Venue:
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Year:
2007

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Abstract

This paper considers computation of the exact visibility range (or the spherical visibility map) for a closed polyhedron whose boundary is represented as a triangle mesh. For each facet on the mesh, we calculate the set of view directions from which all the points on the facet can be seen from the exterior. The projection of those visible directions onto the unit sphere forms the visibility map for the facet. We show that the exact visibility map is a spherical arrangement of closed 0-cells, 1-cells, and 2-cells embedded on the surface of the unit sphere. Based on a provable method for calculating the potential occlusion regions of a facet, a vector visibility algorithm is developed for computing the exact solution of the spherical visibility map for a facet. Examples are given to illustrate our algorithm.