Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm
SIAM Journal on Computing
Set operations on polyhedra using binary space partitioning trees
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Near real-time shadow generation using BSP trees
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
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
Efficient binary space partitions for hidden-surface removal and solid modeling
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
Merging BSP trees yields polyhedral set operations
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Visibility preprocessing for interactive walkthroughs
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Optimal binary space partitions for orthogonal objects
Journal of Algorithms
Points, spheres, and separators: a unified geometric approach to graph partitioning
Points, spheres, and separators: a unified geometric approach to graph partitioning
Fast object-precision shadow generation for area light sources using BSP trees
I3D '92 Proceedings of the 1992 symposium on Interactive 3D graphics
Efficient processing of spatial joins using R-trees
SIGMOD '93 Proceedings of the 1993 ACM SIGMOD international conference on Management of data
Impulse-based dynamic simulation
WAFR Proceedings of the workshop on Algorithmic foundations of robotics
Efficient collision detection for moving polyhedra
Proceedings of the eleventh annual symposium on Computational geometry
A Delaunay based numerical method for three dimensions: generation, formulation, and partition
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Approximating polyhedra with spheres for time-critical collision detection
ACM Transactions on Graphics (TOG)
OBBTree: a hierarchical structure for rapid interference detection
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Range searching and point location among fat objects
Journal of Algorithms
Range searching in low-density environments
Information Processing Letters
Consistent solid and boundary representations from arbitrary polygonal data
Proceedings of the 1997 symposium on Interactive 3D graphics
Realistic input models for geometric algorithms
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Tetrahedral mesh generation by Delaunay refinement
Proceedings of the fourteenth annual symposium on Computational geometry
Collision detection in aspect and scale bounded polyhedra
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Analysis of a bounding box heuristic for object intersection
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Fast software for box intersections
Proceedings of the sixteenth annual symposium on Computational geometry
Generating well-shaped Delaunay meshed in 3D
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Nice point sets can have nasty Delaunay triangulations
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Collision detection for deforming necklaces
Proceedings of the eighteenth annual symposium on Computational geometry
Efficient maintenance and self-collision testing for Kinematic Chains
Proceedings of the eighteenth annual symposium on Computational geometry
Box-trees for collision checking in industrial installations
Proceedings of the eighteenth annual symposium on Computational geometry
R-trees: a dynamic index structure for spatial searching
SIGMOD '84 Proceedings of the 1984 ACM SIGMOD international conference on Management of data
Efficient Collision Detection Using Bounding Volume Hierarchies of k-DOPs
IEEE Transactions on Visualization and Computer Graphics
SWAT '98 Proceedings of the 6th Scandinavian Workshop on Algorithm Theory
On visible surface generation by a priori tree structures
SIGGRAPH '80 Proceedings of the 7th annual conference on Computer graphics and interactive techniques
An empirical comparison of techniques for updating Delaunay triangulations
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Collision detection for deforming necklaces
Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometry—SoCG2002
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We introduce a new realistic input model for geometric graphs and nonconvex polyhedra. A geometric graph G is local if (1) the longest edge at every vertex v is only a constant factor longer than the distance from v to its Euclidean nearest neighbor and (2) the lengths of the longest and shortest edges differ by at most a polynomial factor. A polyhedron is local if all its faces are simplices and its edges form a local geometric graph. We show that any boolean combination of any two local polyhedra in IRd, each with n vertices, can be computed in O(n log n) time, using a standard hierarchy of axis-aligned bounding boxes. Using results of de Berg, we also show that any local polyhedron in IRd has a binary space partition tree of size O(n logd-1 n). Finally, we describe efficient algorithms for computing Minkowski sums of local polyhedra in two and three dimensions.