Fast rendering of irregular grids
Proceedings of the 1996 symposium on Volume visualization
Paul Erdös (1913-996): his influence on the theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Space-time tradeoffs for emptiness queries (extended abstract)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
A general framework for assembly planning: the motion space approach
Proceedings of the fourteenth annual symposium on Computational geometry
Cutting cylces of rods in space
Proceedings of the fourteenth annual symposium on Computational geometry
An exact interactive time visibility ordering algorithm for polyhedral cell complexes
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Efficient generation of k-directional assembly sequences
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Online point location in planar arrangements and its applications
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Schematization of road networks
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Dense point sets have sparse Delaunay triangulations: or "…but not too nasty"
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
The Lazy Sweep Ray Casting Algorithm for Rendering Irregular Grids
IEEE Transactions on Visualization and Computer Graphics
A High Accuracy Volume Renderer for Unstructured Data
IEEE Transactions on Visualization and Computer Graphics
Proceedings of the 2005 symposium on Interactive 3D graphics and games
Vertical ray shooting and computing depth orders for fat objects
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Cutting cycles of rods in space: hardness and approximation
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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A depth order on a set of line segments in 3-space is an order such that line segment $a$ comes before line segment $a'$ in the order when $a$ lies below $a'$ or, in other words, when there is a vertical ray that first intersects $a'$ and then intersects $a$. Efficient algorithms for the computation and verification of depth orders of sets of $n$ line segments in 3-space are presented. The algorithms run in time $O(n^{4/3+\varepsilon})$, for any fixed $\varepsilon 0$. If all line segments are axis-parallel or, more generally, have only a constant number of different orientations, then the sorting algorithm runs in $O(n\log^3 n)$ time and the verification takes $O(n\log^2 n)$ time. The algorithms can be generalized to handle triangles and other polygons instead of line segments. They are based on a general framework for computing and verifying linear orders extending implicitly defined binary relations.