Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
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
Advanced database indexing
Computational Geometry: Theory and Applications
Efficient Collision Detection Using Bounding Volume Hierarchies of k-DOPs
IEEE Transactions on Visualization and Computer Graphics
On R-trees with low query complexity
Computational Geometry: Theory and Applications
Spatial Data Structures: Concepts and Design Choices
Algorithmic Foundations of Geographic Information Systems, this book originated from the CISM Advanced School on the Algorithmic Foundations of Geographic Information Systems
Proceedings of the Sixth International Conference on Data Engineering
Rapid Collision Detection by Dynamically Aligned DOP-Trees
VRAIS '98 Proceedings of the Virtual Reality Annual International Symposium
Balanced aspect ratio trees
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Rotated-Box Trees: A Lightweight c-Oriented Bounding-Volume Hierarchy
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
| Hi-index | 0.00 |
A c-dop is a c-oriented convex polytope, that is, a convex polytope whose facets have orientations that come from a fixed set of c (undirected) orientations. In this paper we study dop-trees-bounding-volume hierarchies that use c-dops as bounding volumes-in the plane. We prove that for any set S of n disjoint c-dops in the plane, one can construct a dop-tree such that all kdops in S that intersect any given query c-dop can be retrieved in O(n^1^/^2^+^@e+k) time in the worst case, when c and @e are constant. This is optimal up to the factor O(n^@e). The same query time can be achieved when the c-dops do not intersect too heavily, that is, when any point in the plane is contained in only a constant number of c-dops. When the c-dops in S may intersect arbitrarily, the worst-case query time becomes O(n^1^-^1^/^c+k), which is optimal.