Three dimensional (3D) graphics applications is an important workload running on today’s computer system. A cost-effective graphics solution is to use a general processor for 3D geometry processing and a specialized hardware for rasterization. 3D geometry processing is an inherently parallel task. Therefore, many CPU vendors add SIMD (Single Instruction Multiple Data) instruction extensions to ...

The analysis of high-dimensional data offers a great challenge to the analyst because the human intuition about geometry of high dimensions fails. We have found that a combination of three basic techniques proves to be extraordinarily effective for visualizing large, high-dimensional data sets. Two important methods for visualizing high-dimensional data involve the parallel coordinate system an...

ParLeda is a software library that provides the basic primitives needed for parallel implementation of computational geometry applications. It can also be used in implementing a parallel application that uses geometric data structures. The parallel model that we use is based on a new heterogeneous parallel model named HBSP which is based on BSP and is introduced here. ParLeda uses two main libr...

In this paper, a parallel algorithm for the Steiner tree problem is presented. The algorithm is based on the well-known multi-start paradigm the GRASP and the well-known proximity structures from computational geometry. The main contribution of this paper is the O(n log n+log n log( n log n )) parallel algorithm for computing Steiner tree on the Euclidean plane. The parallel algorithm used prox...

Two teams — Computational Environment, and Computational Mathematics and Geometry — address research in the Computer Science Group. The target of our Computational Environment team is to provide the broad computational infrastructure necessary to support complex, large-scale simulations in general, and for rocket simulation in particular. Areas of research include parallel programming environme...

We describe a novel high aspect ratio radiofrequency linear ion trap geometry that is amenable to modern microfabrication techniques. The ion trap electrode structure consists of a pair of stacked conducting cantilevers resulting in confining fields that take the form of fringe fields from parallel plate capacitors. The confining potentials are modeled both analytically and numerically. This io...

This paper studies the kinematic geometry of general 3-RPR planar parallel robots with actuated base joints. These robots, while largely overlooked, have simple direct kinematics and large singularity-free workspace. Furthermore, their kinematic geometry is the same as that of a newly developed parallel robot with SCARA-type motions. Starting from the direct and inverse kinematic model, the exp...

Two teams, Computational Mathematics and Geometry, and Computational Environment, address research in Computer Science. Work in computational mathematics and geometry focuses on the areas of linear solvers, mesh generation and refinement, and interpolation between diverse discretizations. The target of our computational environment program is to provide the broad computational infrastructure ne...