Agarwal, P. K., Murali, T. M., and Vitter, J. S. Practical techniques for constructing binary space partitions for orthogonal rectangles. In Proceedings of the Thirteenth Annual Symposium on Computational Geometry, June 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... a collection arbitrary polyhedra and to perform set operations on the polyhedra [194, 122, 124, 125, 123] Dynamic changes to BSP trees were studied in [197, 38] Recently, Naylor introduced an algorithm for converting discrete images to 2D BSP trees [177] Other work on BSP trees can be found in [119, 68, 1, 93, 116, 22, 51, 121, 127, 196]. The hierarchical z buffer algorithm introduced by Greene [80] uses a discrete z pyramid to represent the occlusion map. It exploits spatial coherence by processing the object (spatial) hierarchy through the z pyramid. Although it is a very promising approach if using hardware resources, the ....

P. Agarwal, T. Murali, and J. Vitter. Practical techniques for constructing binary space partitions for orthogonal rectangles. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 382--384, 1997.

....objects without extremely skinny and long 2 parts) Their algorithm creates BSP trees of n2 O( p log n) size for scene of n fat rectangles and of n p m2 O( p log n) size for scene of (n Gamma m) fat rectangles. The running time is linear to output BSP tree size. In the next paper [2] they compared implementation of this algorithm with other BSP algorithms. It was shown that their algorithm is really applicable in practice. Mark de Berg et al. have extensively studied the problem of BSP in the plane [8] They showed existence of a linear size BSP for sets of line segments ....

Pankaj K. Agarwal, T. Murali, and J. Vitter. Practical techniques for constructing binary space partitions for orthogonal rectangles. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 382384, 1997. 25

....intuitive objects without extremely skinny and long 2 parts) Their algorithm creates BSP trees of n2 O( # log n) size for scene of n fat rectangles and of n # m2 O( # log n) size for scene of (n m) fat rectangles. The running time is linear to output BSP tree size. In the next paper [2] they compared implementation of this algorithm with other BSP algorithms. It was shown that their algorithm is really applicable in practice. Mark de Berg et al. have extensively studied the problem of BSP in the plane [8] They showed existence of a linear size BSP for sets of line segments ....

Pankaj K. Agarwal, T. Murali, and J. Vitter. Practical techniques for constructing binary space partitions for orthogonal rectangles. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 382--384, 1997. 25

....objects without extremely skinny and long parts) Their algorithm creates BSP trees of n2 O( p log n) size for scene of n fat rectangles and of n p m2 O( p log n) size for scene of (n Gamma m) fat rectangles. The running time is linear to output BSP tree size. In the next paper [Agarw97] they compared implementation of this algorithm with other BSP algorithms. It was shown that theirs algorithm is really suitable in practice. Mark de Berg et al. have extensively studied the problem of BSP in the plane [Berg94] They showed existence of a linear size BSP for sets of line segments ....

Pankaj K. Agarwal, T. Murali, and J. Vitter. Practical techniques for constructing binary space partitions for orthogonal rectangles. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 382384, 1997.

....are intuitive objects without extremely skinny and long parts) Their algorithm creates BSP trees of n2 O( # log n) size for scene of n fat rectangles and of n # m2 O( # log n) size for scene of (n m) fat rectangles. The running time is linear to output BSP tree size. In the next paper [Agarw97] they compared implementation of this algorithm with other BSP algorithms. It was shown that theirs algorithm is really suitable in practice. Mark de Berg et al. have extensively studied the problem of BSP in the plane [Berg94] They showed existence of a linear size BSP for sets of line segments ....

Pankaj K. Agarwal, T. Murali, and J. Vitter. Practical techniques for constructing binary space partitions for orthogonal rectangles. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 382--384, 1997.

....v and each portion will be stored in the corresponding subtree. There is no special rule for selecting the cutting hyperplanes for a BSP tree. However, the choice of cutting hyperplanes affects the size and maximum depth of the BSP tree and the number of object fragments that arise. Several works [1, 2, 4, 14, 15] have been devoted to the problem of selecting the cutting hyperplanes so as to minimize the complexity of the resulting BSP tree. For example, if there is a facet of an object lying on a hyperplane which does not intersect the interior of any other objects of this node, then this is a good ....

Pankaj K. Agarwal, T. Murali, and J. Vitter. Practical techniques for constructing binary space partitions for orthogonal rectangles. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 382--384, 1997.

....the construction of a BSP tree and its resulting properties is the criterion for positioning the splitting plane. The construction of BSP trees for ray tracing was studied by Kaplan [15] and improved by MacDonald and Booth [17] There are recent publications in computational geometry (e.g. [1]) that show a persistent research interest in BSP trees. We adopted the subdivision method of MacDonald and Booth, which is described in the next section in detail. Statistical Optimization of a BSP Tree The time needed for construction of a BSP tree is typically insignificant compared with the ....

P. Agarwal, T. Murali, and J. Vitter. Practical techniques for constructing binary space partitions for orthogonal rectangles. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 382--384, 1997.

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Agarwal, P. K., Murali, T. M., and Vitter, J. S. Practical techniques for constructing binary space partitions for orthogonal rectangles. In Proceedings of the Thirteenth Annual Symposium on Computational Geometry, June 1997.

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