Geometric modeling for computer aided design

The primary goal of this grant has been the design and implementation of software to be used in the conceptual design of aerospace vehicles particularly focused on the elements of geometric design, graphical user interfaces, and the interaction of the multitude of software typically used in this engineering environment. This has resulted in the development of several analysis packages and design studies. These include two major software systems currently used in the conceptual level design of aerospace vehicles. These tools are SMART, the Solid Modeling Aerospace Research Tool, and EASIE, the Environment for Software Integration and Execution. Additional software tools were designed and implemented to address the needs of the engineer working in the conceptual design environment. SMART provides conceptual designers with a rapid prototyping capability and several engineering analysis capabilities. In addition, SMART has a carefully engineered user interface that makes it easy to learn and use. Finally, a number of specialty characteristics have been built into SMART which allow it to be used efficiently as a front end geometry processor for other analysis packages. EASIE provides a set of interactive utilities that simplify the task of building and executing computer aided design systems consisting of diverse, stand-alone, analysis codes. Resulting in a streamlining of the exchange of data between programs reducing errors and improving the efficiency. EASIE provides both a methodology and a collection of software tools to ease the task of coordinating engineering design and analysis codes

A constant time parallel algorithm for the triangularization of a sparse matrix using CD-PARBS

An algorithm for the triangularization of a matrix whose graph is a directed acyclic graph, popularly known as dag, is presented. One of the algorithms for obtaining this special form has been given by Sargent and Westerberg. Their approach is practically good but sequential in nature and cannot be parallelised easily. In this work we present a parallel algorithm which is based on the observation that, if we find the transitive closure matrix of a directed acyclic graph, count the number of entries in each row, sort them in the ascending order of their values and rank them accordingly, we get a lower triangular matrix. We show that all these operations can be done using 3-d CD- PARBS(Complete Directed PARBS) in constant time. The same approach can be used for the block cases, producing the same relabelling as produced by Tarjan’s algorithm, in constant time. To the best of our knowledge, it is the first approach to solve such problems using directed PARBS

Efficient parallel processing with optical interconnections

With the advances in VLSI technology, it is now possible to build chips which can each contain thousands of processors. The efficiency of such chips in executing parallel algorithms heavily depends on the interconnection topology of the processors. It is not possible to build a fully interconnected network of processors with constant fan-in/fan-out using electrical interconnections. Free space optics is a remedy to this limitation. Qualities exclusive to the optical medium are its ability to be directed for propagation in free space and the property that optical channels can cross in space without any interference. In this thesis, we present an electro-optical interconnected architecture named Optical Reconfigurable Mesh (ORM). It is based on an existing optical model of computation. There are two layers in the architecture. The processing layer is a reconfigurable mesh and the deflecting layer contains optical devices to deflect light beams. ORM provides three types of communication mechanisms. The first is for arbitrary planar connections among sets of locally connected processors using the reconfigurable mesh. The second is for arbitrary connections among N of the processors using the electrical buses on the processing layer and N2 fixed passive deflecting units on the deflection layer. The third is for arbitrary connections among any of the N2 processors using the N2 mechanically reconfigurable deflectors in the deflection layer. The third type of communication mechanisms is significantly slower than the other two. Therefore, it is desirable to avoid reconfiguring this type of communication during the execution of the algorithms. Instead, the optical reconfiguration can be done before the execution of each algorithm begins. Determining a right configuration that would be suitable for the entire configuration of a task execution is studied in this thesis. The basic data movements for each of the mechanisms are studied. Finally, to show the power of ORM, we use all three types of communication mechanisms in the first O(logN) time algorithm for finding the convex hulls of all figures in an N x N binary image presented in this thesis

A fast parallel algorithm for special linear systems of equations using processor arrays with reconfigurable bus systems

A parallel algorithm using Processor Arrays with Reconfigurable Bus Systems has been designed to solve dense Symmetric Positive Definite (SPD) systems of equations Ax = b. The key content of this report is the parallelisation of the algorithm by Delosme & Ipson [8]. In order to design a parallel algorithm for PARBS, many procedures involved in [8] are handled in a slightly different way. The parallel time and processor’s complexity of each step of the algorithm is calculated. The parallel time complexity is O(n) using 2n × 2n × 5n number of Processing Elements

Visibility-Related Problems on Parallel Computational Models

Visibility-related problems find applications in seemingly unrelated and diverse fields such as computer graphics, scene analysis, robotics and VLSI design. While there are common threads running through these problems, most existing solutions do not exploit these commonalities. With this in mind, this thesis identifies these common threads and provides a unified approach to solve these problems and develops solutions that can be viewed as template algorithms for an abstract computational model. A template algorithm provides an architecture independent solution for a problem, from which solutions can be generated for diverse computational models. In particular, the template algorithms presented in this work lead to optimal solutions to various visibility-related problems on fine-grain mesh connected computers such as meshes with multiple broadcasting and reconfigurable meshes, and also on coarse-grain multicomputers. Visibility-related problems studied in this thesis can be broadly classified into Object Visibility and Triangulation problems. To demonstrate the practical relevance of these algorithms, two of the fundamental template algorithms identified as powerful tools in almost every algorithm designed in this work were implemented on an IBM-SP2. The code was developed in the C language, using MPI, and can easily be ported to many commercially available parallel computers

GPU-based proximity query processing on unstructured triangular mesh model

This paper presents a novel proximity query (PQ) approach capable to detect the collision and calculate the minimal Euclidean distance between two non-convex objects in 3D, namely the robot and the environment. Such approaches are often considered as computationally demanding problems, but are of importance to many applications such as online simulation of haptic feedback and robot collision-free trajectory. Our approach enables to preserve the representation of unstructured environment in the form of triangular meshes. The proposed PQ algorithm is computationally parallel so that it can be effectively implemented on graphics processing units (GPUs). A GPU-based computation scheme is also developed and customized, which shows >200 times faster than an optimized CPU with single core. Comprehensive validation is also conducted on two simulated scenarios in order to demonstrate the practical values of its potential application in image-guided surgical robotics and humanoid robotic control.published_or_final_versio

Time-Optimal Algorithms on Meshes With Multiple Broadcasting

The mesh-connected computer architecture has emerged as a natural choice for solving a large number of computational tasks in image processing, computational geometry, and computer vision. However, due to its large communication diameter, the mesh tends to be slow when it comes to handling data transfer operations over long distances. In an attempt to overcome this problem, mesh-connected computers have recently been augmented by the addition of various types of bus systems. One such system known as the mesh with multiple broadcasting involves enhancing the mesh architecture by the addition of row and column buses. The mesh with multiple broadcasting has proven to be feasible to implement in VLSI, and is used in the DAP family of computers. In recent years, efficient algorithms to solve a number of computational problems on meshes with multiple broadcasting have been proposed in the literature. The problems considered in this thesis are semigroup computations, sorting, multiple search, various convexity-related problems, and some tree problems. Based on the size of the input data for the problem under consideration, existing results can be broadly classified into sparse and dense. Specifically, for a given √n x √n mesh with multiple broadcasting, we refer to problems involving $m \in O(\sqrt{n}$) items as sparse, while the case £ O(n) will be referred to as dense. Finally, the case corresponding to 2 ≤ m ≤ n is be termed general. The motivation behind the current work is twofold. First, time-optimal solutions are proposed for the problems listed above. Secondly, an attempt is made to remove the artificial limitation of problems studied to sparse and dense cases. To establish the time-optimality of the algorithms presented in this work, we use some existing lower bound techniques along with new ones that we develop. We solve the semigroup computation problem for the general case and present a novel lower bound argument. We solve the multiple search problem in the general case and present some surprising applications to computational geometry. In the case of sorting, the general case is defined to be slightly different. For the specified range of the size of input, we present a time and VLSI-optimal algorithm. We also present time lower bound results and matching algorithms for a number of convexity related and tree problems in the sparse case