Binary space partitions for fat rectangles

The authors consider the practical problem of constructing binary space partitions (BSPs) for a set S of n orthogonal, nonintersecting, two-dimensional rectangles in R/sup 3/ such that the aspect ratio of each rectangle in S is at most /spl alpha/, for some constant a /spl alpha//spl ges/1. They present an n2/sup O(/spl radic/logn)/-time algorithm to build a binary space partition of size n2/sup O(/spl radic/logn)/ for S. They also show that if m of the n rectangles in S have aspect ratios greater than /spl alpha/, they can contact a BSP of size n/spl radic/m2/sup O(/spl radic/logn)/ for S in n/spl radic/2/sup O(/spl radic/logn)/ time. The constants of proportionality in the big-oh terms are linear in log /spl alpha/. They extend these results to cases in which the input contains non-orthogonal or intersecting objects.

[1]  Susan E. Dorward.  A survey of object-space hidden surface removal , 1994, Int. J. Comput. Geom. Appl..

[2]  Seth Teller,et al.  Visibility Computations in Densely Occluded Polyhedral Environments , 1992 .

[3]  Edwin Earl Catmull,et al.  A subdivision algorithm for computer display of curved surfaces. , 1974 .

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

[5]  Henry Fuchs,et al.  Near real-time shaded display of rigid objects , 1983, SIGGRAPH.

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

[7]  John M. Airey,et al.  Increasing update rates in the building walkthrough system with automatic model-space subdivision and potentially visible set calculations , 1990 .

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

[9]  Joseph S. B. Mitchell,et al.  On maximum flows in polyhedral domains , 1988, SCG '88.

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

[11]  Bernard Chazelle,et al.  Convex Partitions of Polyhedra: A Lower Bound and Worst-Case Optimal Algorithm , 1984, SIAM J. Comput..

[12]  Bruce F. Naylor.  SCULPT: an interactive solid modeling tool , 1990 .

[13]  A. T. Campbell.  Modeling global diffuse illumination for image synthesis , 1992 .

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

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

[16]  R. Schmacher,et al.  Study for Applying Computer-Generated Images to Visual Simulation: (510842009-001) , 1969 .

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

[18]  Mark de Berg,et al.  Linear Size Binary Space Partitions for Fat Objects , 1995, ESA.

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

[20]  J. Vitter,et al.  The Object Complexity Modelfor Hidden-Surface , 1995 .

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

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

[23]  Steven K. Feiner,et al.  Computer graphics: principles and practice (2nd ed.) , 1990 .

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