Computational geometry: an introduction
Computational geometry: an introduction
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
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
Realistic input models for geometric algorithms
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Practical techniques for constructing binary space partitions for orthogonal rectangles
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Surface Approximation and Geometric Partitions
SIAM Journal on Computing
Balanced aspect ratio trees: combining the advantages of k-d trees and octrees
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Binary Space Partitions for Fat Rectangles
SIAM Journal on Computing
Computational Geometry: Theory and Applications
Box-trees for collision checking in industrial installations
Proceedings of the eighteenth annual symposium on Computational geometry
Binary Space Partitions for Line Segments with a Limited Number of Directions
SIAM Journal on Computing
New Results on Binary Space Partitions in the Plane (Extended Abstract)
SWAT '94 Proceedings of the 4th 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
Balanced aspect ratio trees
Guarding scenes against invasive hypercubes
Computational Geometry: Theory and Applications
Vertical ray shooting for fat objects
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Vertical ray shooting and computing depth orders for fat objects
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Ray shooting and intersection searching amidst fat convex polyhedra in 3-space
Proceedings of the twenty-second annual symposium on Computational geometry
Ray shooting and intersection searching amidst fat convex polyhedra in 3-space
Computational Geometry: Theory and Applications
Computing the visibility map of fat objects
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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We show how any BSP tree ${\mathcal T}_P$ for the endpoints of a set of n disjoint segments in the plane can be used to obtain a BSP tree of size $O(n.depth({\mathcal T}_P))$ for the segments themselves, such that the range-searching efficiency remains almost the same. We apply this technique to obtain a BSP tree of size O(n log n) such that ε-approximate range searching queries with any constant-complexity convex query range can be answered in O(minε0{1/ε+kε}log n) time, where kε is the number of segments intersecting the ε-extended range. The same result can be obtained for disjoint constant-complexity curves, if we allow the BSP to use splitting curves along the given curves. We also describe how to construct a linear-size BSP tree for low-density scenes consisting of n objects in ${\mathbb R}^{d}$ such that ε-approximate range searching with any constant-complexity convex query range can be done in $O(log n + {\rm min}_{\epsilon 0}{\{1/\epsilon^{(d-1)}+k_{\epsilon}\}})$ time.