The power of geometric duality
BIT - Ellis Horwood series in artificial intelligence
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
New techniques for computing order statistics in Euclidean space (extended abstract)
SCG '85 Proceedings of the first annual symposium on Computational geometry
An efficient algorithm for finding the CSG representation of a simple polygon
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
On visible surface generation by a priori tree structures
SIGGRAPH '80 Proceedings of the 7th annual conference on Computer graphics and interactive techniques
Generalized sweep methods for parallel computational geometry
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Merging BSP trees yields polyhedral set operations
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Hidden surface removal with respect to a moving view point
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Efficient hidden surface removal for objects with small union size
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Visibility-ordering meshed polyhedra
ACM Transactions on Graphics (TOG)
Shadow volume BSP trees for computation of shadows in dynamic scenes
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
Optimal binary space partitions for orthogonal objects
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Visibility with a moving point of view
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
A note on binary plane partitions
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
A new BSP tree framework incorporating dynamic LoD models
VRST '00 Proceedings of the ACM symposium on Virtual reality software and technology
Graph Drawing
A comparison of sampling strategies for computing general sweeps
Computer-Aided Design
Depth-presorted triangle lists
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
| Hi-index | 0.00 |
We consider schemes for recursively dividing a set of geometric objects by hyperplanes until all objects are separated. Such a binary partition is naturally considered as a binary tree where each internal node corresponds to a division and the leaves correspond to the resulting fragments of objects. The goal is to choose the hyperplanes properly so that the size of the binary partition, i.e., the number of resulting fragments of the objects, is minimized. We construct binary partitions of size &Ogr;(n log n) for n edges in the plane, and of size &Ogr;(n) if the edges are orthogonal. In three dimensions, we obtain binary partitions of size &Ogr;(n2) for n planar facets, and prove a lower bound of &OHgr;(n3/2). Two applications of efficient binary partitions are given. The first is an &Ogr;(n2)-sized data structure for implementing a hidden-surface removal scheme of Fuchs, Kedem and Naylor [5]. The second application is in solid modelling: given a polyhedron described by its n faces, we show how to generate an &Ogr;(n2)-sized CSG (constructive-solid-geometry) formula whose literals correspond to half-spaces supporting the faces of the polyhedron (see Peterson [9] and Dobkin et al. [3]). The best previous results for both of these problems were &Ogr;(n3).