The power of geometric duality
BIT - Ellis Horwood series in artificial intelligence
Constructing arrangements of lines and hyperplanes with applications
SIAM Journal on Computing
Topologically sweeping an arrangement
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
On the sum of squares of cell complexities in hyperplane arrangements
Journal of Combinatorial Theory Series A
Pseudo-triangulations: theory and applications
Proceedings of the twelfth annual symposium on Computational geometry
Vertex-edge pseudo-visibility graphs: characterization and recognition
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Fast and accurate hierarchical radiosity using global visibility
ACM Transactions on Graphics (TOG)
Kinetic collision detection for simple polygons
Proceedings of the sixteenth annual symposium on Computational geometry
Using the Visibility Complex for Radiosity Computation
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
A combinatorial approach to planar non-colliding robot arm motion planning
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Straightening polygonal arcs and convexifying polygonal cycles
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
The predicates for the Voronoi diagram of ellipses
Proceedings of the twenty-second annual symposium on Computational geometry
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We present a new and simpler method to implement in constant amortized time the flip operation of the so-called &ldqo;Greedy Flip Algorithm”, an optimal algorithm to compute the visibility complex of a collection of pairwise disjoint bounded convex sets of constant complexity. The method relies on a “sum of squares” like theorem for visibility complexes stated and proved in this paper. (The sum of squares theorem for an arrangement of lines states that the average value of the square of the number of vertices of a face of the arrangement is a $O(1)$.)