Abstract
In this paper we study the ray-shooting problem for three special classes of polyhedral objects in space: axis-parallel polyhedra, curtains (unbounded polygons with three edges, two of which are parallel to the z-axis and extend downward to minus infinity), and fat horizontal triangles (triangles parallel to the xy-plane whose angles are greater than some given constant). For all three problems structures are presented using O(n2+e{open}) preprocessing, for any fixed e{open} > 0, with O(log n) query time. We also study the general ray-shooting problem in an arbitrary set of triangles. Here we present a structure that uses On4+e{open}) preprocessing and has a query time of O(log n). We use the ray-shooting structure for curtains to obtain an algorithm for computing the view of a set of nonintersecting prolyhedra. For any e{open} > 0, we can obtain an algorithm with running time {Mathematical expression}, where n is the total number of vertices of the polyhedra and k is the size of the output. This is the first output-sensitive algorithm for this problem that does not need a depth order on the faces of the polyhedra.
Original language | English |
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Pages (from-to) | 30-53 |
Number of pages | 24 |
Journal | Algorithmica |
Volume | 12 |
Issue number | 1 |
DOIs | |
State | Published - Jul 1994 |
Keywords
- Computational geometry
- Hidden surface removal
- Multilevel data structures
- Output-sensitive
- Ray shooting