ISSN:
1432-0541
Keywords:
Key words. Computational geometry, Complete visibility, Penumbra.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract. Given a set P of polygons in three-dimensional space, two points p and q are said to be visible from each other with respect to P if the line segment joining them does not intersect any polygon in P . A point p is said to be completely visible from an area source S if p is visible from every point in S . The completely visible region CV(S, P) from S with respect to P is defined as the set of all points in three-dimensional space that are completely visible from S . We present two algorithms for computing CV(S, P) for P with a total of n vertices and a convex polygonal source S with m vertices. Our first result is a divide-and-conquer algorithm which runs in O(m 2 n 2 α(mn)) time and space, where α(mn) is the inverse of Ackermann's function. We next give an incremental algorithm for computing CV(S,P) in O(m 2 n+mn 2 α(n)) time and O(mn+n 2 ) space. We also prove that CV(S,P) consists of Θ(mn+n 2 ) surface elements such as vertices, edges, and faces.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/PL00009193
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