A segment-tree based kinetic BSP

We present anew technique to maintain a BSP for a set of n moving disj oint segments in the plane. Our kinetic BSP uses O(n log n) storage and it undergoes O(n 2 ) changes in the worst case, assuming that the endpoints of the segments move along bounded-degree algebraically dened trajecto- ries. The response time (the time needed to update the BSP when it undergoes a change) is O(log 2 n). A random- ized variant achieves O(log n) expected response time, while the worst-case response time remains O(log 2 n). The new BSP is based on a simple technique for main- taining a 1-d segment tree on a set of intervals on the real line with moving endpoints. The response time of the ki- netic segment treeisO(log n) intheworst case, and O(1) expected.

[1]  P. Agarwal,et al.  Kinetic binary space partitions for triangles , 1998 .

[2]  Franco P. Preparata,et al.  A New Approach to Planar Point Location , 1981, SIAM J. Comput..

[3]  Mark de Berg,et al.  Linear Size Binary Space Partitions for Uncluttered Scenes , 2000, Algorithmica.

[4]  T. M. Murali,et al.  Consistent solid and boundary representations from arbitrary polygonal data , 1997, SI3D.

[5]  Alade O. Tokuta.  Motion planning using binary space partitioning , 1991, Proceedings IROS '91:IEEE/RSJ International Workshop on Intelligent Robots and Systems '91.

[6]  Carlo H. Séquin,et al.  Visibility preprocessing for interactive walkthroughs , 1991, SIGGRAPH.

[7]  L. Guibas,et al.  Kinetic vertical decomposition trees , 1999 .

[8]  Enric Torres,et al.  Optimization of the Binary Space Partition Algorithm (BSP) for the Visualization of Dynamic Scenes , 1990, Eurographics.

[9]  P. Agarwal,et al.  Lower Bounds for Kinetic Planar Subdivisions , 2000 .

[10]  John Amanatides,et al.  Merging BSP trees yields polyhedral set operations , 1990, SIGGRAPH.

[11]  Leonidas J. Guibas,et al.  Cylindrical static and kinetic binary space partitions , 2000, Comput. Geom..

[12]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[13]  V. Leitáo,et al.  Computer Graphics: Principles and Practice , 1995 .

[14]  M. Carter.  Computer graphics: Principles and practice , 1997 .

[15]  Leonidas J. Guibas,et al.  Kinetic binary space partitions for intersecting segments and disjoint triangles , 1998, SODA '98.

[16]  F. Frances Yao,et al.  Efficient binary space partitions for hidden-surface removal and solid modeling , 1990, Discret. Comput. Geom..

[17]  Leonidas J. Guibas,et al.  Data structures for mobile data , 1997, SODA '97.

[18]  Leonidas J. Guibas,et al.  A dichromatic framework for balanced trees , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).

[19]  Henry Fuchs,et al.  On visible surface generation by a priori tree structures , 1980, SIGGRAPH '80.

[20]  Mark de Berg,et al.  New Results on Binary Space Partitions in the Plane , 1997, Comput. Geom..

[21]  F. Frances Yao,et al.  Optimal binary space partitions for orthogonal objects , 1990, SODA '90.

[22]  Bruce F. Naylor,et al.  Constructing good partitioning trees , 1993 .

[23]  Steven K. Feiner,et al.  Fast object-precision shadow generation for area light sources using BSP trees , 1992, I3D '92.

[24]  Bruce F. Naylor,et al.  Set operations on polyhedra using binary space partitioning trees , 1987, SIGGRAPH.

[25]  Bruce F. Naylor,et al.  Interactive solid geometry via partitioning trees , 1992 .

[26]  Steven K. Feiner,et al.  Near real-time shadow generation using BSP trees , 1989, SIGGRAPH '89.