Constructing Binary Space Partitions for Orthogonal Rectabgles in Practice
نویسندگان
چکیده
In this paper, we develop a simple technique for constructing a Binary Space Partition (BSP) for a set of orthogonal rectangles in R 3. Our algorithm has the novel feature that it tunes its performance to the geometric properties of the rectangles, e.g., their aspect ratios. We have implemented our algorithm and tested its performance on real data sets. We have also systematically compared the performance of our algorithm with that of other techniques presented in the literature. Our studies show that our algorithm constructs BSPs of near-linear size and small height in practice, has fast running times, and answers queries eeciently. It is a method of choice for constructing BSPs for orthogonal rectangles.
منابع مشابه
Binary Space Partitions for Fat Rectangles
We consider the practical problem of constructing binary space partitions (BSPs) for a set S of n orthogonal, nonintersecting, two-dimensional rectangles in IR3 such that the aspect ratio of each rectangle in S is at most , for some constant 1. We present an n2O(plogn )-time algorithm to build a binary space partition of size n2O(plogn ) for S. We also show that if m of the n rectangles in S ha...
متن کاملSliced space - filling designs
We propose an approach to constructing a new type of design, a sliced space-filling design, intended for computer experiments with qualitative and quantitative factors. The approach starts with constructing a Latin hypercube design based on a special orthogonal array for the quantitative factors and then partitions the design into groups corresponding to different level combinations of the qual...
متن کاملLinear Binary Space Partitions and the Hierarchy of Object Classes
We consider the problem of constructing binary space partitions for the set P of d-dimensional objects in d-dimensional space. There are several classes of objects defined for such settings that support the design of effective algorithms. We extend the existing de Berg hierarchy of classes [4] by defining new classes based on old ones and we show the desirability of such an extension. Moreover ...
متن کاملFixed point theory in generalized orthogonal metric space
In this paper, among the other things, we prove the existence and uniqueness theorem of fixed point for mappings on a generalized orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point of Cauchy problem for the first order differential equation.
متن کاملLinear BSP Trees for Sets of Hyperrectangles with Low Directional Density
We consider the problem of constructing of binary space partitions (BSP) for a set S of n hyperrectangles in arbitrary dimensional space. If the set S fulfills the low directional density condition defined in this paper then the resultant BSP has O(n) size and it can be constructed in O(n log n) time in R. The low directional density condition defines a new class of objects which we are able to...
متن کامل