casting algorithms because the latter must perform analytic geometry calculations (e.g. intersecting rays with axis-aligned boxes). The new scanline-order algorithm simply streams through the volume and the image in storage order. We describe variants of the algorithm for both parallel and perspective

Abstract: Suppose that we have several polytopes in Rd and we can translate them without rotation. Here we consider the intersection maximization problem, which asks the positions of the polytopes which maximizes the volume of their intersection. In this paper, we address this problem, and show

research directions in the field. A cross a wide variety of fields, data are being collected and accumulated at a dramatic pace. There is an urgent need for a new generation of computational theories and tools to assist humans in extracting useful information (knowledge) from the rapidly growing volumes

volume than bounding rectangles with high-dimensional data and that this reduces search efficiency. To overcome this drawback, we propose a new index structure called the SR-tree (Sphere/Rectangle-tree) which integrates bounding spheres and bounding rectangles. A region of the SR-tree is specified

and of the environment. Our algorithms have been implemented and tested. We provide experimental evidence showing that our approach yields substantially faster collision detection than previous methods. Index Terms—Collision detection, intersection searching, bounding volume hierarchies, discrete orientation polytopes

similar 3D objects. For visualization, 3D shapes are often represented as a surface, in particular polygonal meshes, for example in VRML format. Often these models contain holes, intersecting polygons, are not manifold, and do not enclose a volume unambiguously. On the contrary, 3D volume models

We show that the set of colored Jones polynomials and the set of generalized Alexander polynomials defined by Akutsu, Deguchi and Ohtsuki intersect non-trivially. Moreover it is shown that the intersection is (at least includes) the set of Kashaev’s quantum dilogarithm invariants for links

We determine the minimum volume (sum of cardinalities) of an intersecting family of subsets of an n-set, given the size of the family, by solving a simple linear program. From this we obtain a lower bound on the average size of the sets in an intersecting family. This answers a question of G. O. H

for intersection culling: hierarchical bounding volumes 1, 2, 3, 4 and space partitioning...

to provide the practitioner with a guide for selecting intersection trfilc control based on peak hour intersection volumes. With the release of the 1994 Highway Capaci ~ Manual (HCM)l and the revisions to Chapter 10 on unsignalized intersections, the ability to directly compare intersection