Visibility problems for polyhedral terrains
Journal of Symbolic Computation
Sharp upper and lower bounds on the length of general Davenport-Schinzel Sequences
Journal of Combinatorial Theory Series A
Lines in space-combinators, algorithms and applications
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Combinatorial complexity bounds for arrangements of curves and spheres
Discrete & Computational Geometry - Special issue on the complexity of arrangements
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
On the two-dimensional davenport-schinzel problem
Journal of Symbolic Computation
On lines missing polyhedral sets in 3-space
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
A Singly-Expenential Stratification Scheme for Real Semi-Algebraic Varieties and Its Applications
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Almost tight upper bounds for the single cell and zone problems in three dimensions
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Computing envelopes in four dimensions with applications
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Voronoi diagrams of lines in 3-space under polyhedral convex distance functions
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Oriented convex polyhedra for collision detection in 3D computer animation
Proceedings of the 4th international conference on Computer graphics and interactive techniques in Australasia and Southeast Asia
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We consider the problem of bounding the complexity of the lowerenvelope of n surface patches in3-space, all algebraic of constant maximum degree, and bounded byalgebraic arcs of constant maximum degree, with the additional propertythat the interiors of any triple of these surfaces intersect in at mosttwo points. We show that the number of vertices on the lower envelope ofn such surface patches isOn2˙2clogn for some constantc depending on the shape and degreeof the surface patches. We apply this result to obtain an upper bound onthe combinatorial complexity of the “lower envelope” of thespace of all rays in 3-space that lieabove a given polyhedral terrain Kwith n edges. This envelope consistsof all rays that touch the terrain (but otherwise lie above it). We showthat the combinatorial complexity of this ray-envelope isOn2˙2clogn for some constantc; in particular, there are at mostthat many rays that pass above the terrain and touch it in 4 edges. Thisbound, combined with the analysis of de Berg et al. [2], gives an upperbound (which is almost tight in the worst case) on the number oftopologically-different orthographic views of such a terrain.