Parallel boxing in B-spline intersection

A modified formulation of oriented boxing called oriented slab boxing is presented. It almost doubles the speed of the oriented boxing component in B-spline intersection. The method used to accelerate B-spline intersection includes algorithmic improvements and parallelization of the algorithm at different levels of granularity to find an optimum solution on a network of parallel processors. The software testbed is linked to a B-spline-based library, which is a prototype of what may be used in an actual engineering design environment. A parallel implementation of the algorithm on a network of three processors achieves an additional twofold improvement in speed     

The Feasibility of a VLSI Chip for Ray Tracing Bicublic Patches

In this article we explore the possibility of a VLSI chip for ray tracing bicubic patches in Bezier form. The purpose of the chip is to calculate the intersection point of a ray with the bicubic patch to a specified level of accuracy, returning parameter values (u,v) specifying the location of the intersection on the patch, and a parameter value, t, which specifies the location of the intersection on the ray. The intersection is calculated by succesively subdividing the patch and computing the intersection of the ray with a bounding box of each subpatch until the bounding volume meets theaccuracy requirement. There are two operating modes: another in which all intersections are found. This algorithm (and the chip) correctly handle the difficult cases of the ray tangentially intersecting a planar patch and intersections of the ray at a silhouette edge of the patch. Estimates indicate that such a chip could be implemented in 2-micron NMOS (N-type metal oxide semiconductor) and could computer patch-ray intersections at the rate of one every 15 microseconds for patces that are prescaled and specified to a 12-bit fixed point for each of the x, y, and z components. A version capable of handling 24-bit patches could compute patch/ray intersections at the rate of one every 140 section point could be performed with the addition of nine scalar subtractions and six scalar multiplies. Images drawn using a software version of the algorithm are presented and discussed.     

New primal and dual matching heuristics

We describe a new heuristic for constructing a minimum-cost perfect matching designed for problems on complete graphs whose cost functions satisfy the triangle inequality (e.g., Euclidean problems). The running time for ann node problem is O(n logn) after a minimum-cost spanning tree is constructed. We also describe a procedure which, added to Kruskal's algorithm, produces a lower bound on the size of any perfect matching. This bound is based on a dual problem which has the following geometric interpretation for Euclidean problems: Pack nonoverlapping disks centered at the nodes and moats surrounding odd sets of nodes so as to maximize the sum of the disk radii and moat widths.This research was supported in part by the Natural Sciences and Engineering Research Council of Canada.