Worst-case optimal algorithms for constructing visibility polygons with holes
SCG '86 Proceedings of the second annual symposium on Computational geometry
Worst-case optimal hidden-surface removal
ACM Transactions on Graphics (TOG)
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
Visibility, occlusion, and the aspect graph
International Journal of Computer Vision
Efficiently Computing and Representing Aspect Graphs of Polyhedral Objects
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computing the antipenumbra of an area light source
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Fast object-precision shadow generation for area light sources using BSP trees
I3D '92 Proceedings of the 1992 symposium on Interactive 3D graphics
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Visibility with a moving point of view
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Three-dimensional weak visibility: complexity and applications
Theoretical Computer Science
On the complexity of computing the measure of ∪[ai,bi]
Communications of the ACM
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Computational Line Geometry
IEEE Computer Graphics and Applications
Transversals to Line Segments in Three-Dimensional Space
Discrete & Computational Geometry
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Let T be a set of n triangles in three-dimensional space, let s be a line segment, and let t be a triangle, both disjoint from T. We consider the subdivision of T based on (in)visibility from s; this is the visibility map of the segment s with respect to T. The visibility map of the triangle t is defined analogously. We look at two different notions of visibility: strong (complete) visibility, and weak (partial) visibility. The trivial @W(n^2) lower bound for the combinatorial complexity of the strong visibility map of both s and t is almost tight: we prove an O(n^2@a(n)) upper bound for both structures, where @a(n) is the extremely slowly increasing inverse Ackermann function. Furthermore, we prove that the weak visibility map of s has complexity @Q(n^5), and the weak visibility map of t has complexity @Q(n^7). If T is a polyhedral terrain, the complexity of the weak visibility map is @W(n^4) and O(n^5), both for a segment and a triangle. We also present efficient algorithms to compute all discussed structures.