Offsets, sweeps, and Minkowski operations (M-ops) are easy to define in the existential (representation-free) mathematics of point sets, but computing ‘values’ for offset, swept, and M-summed entities is thought to be difficult by many. This article argues that such computations may be easy if (1) they are cast in specific application contexts, and (2) relevant mathematical definitions are discretized and implemented directly. The argument is based on 10 years of research on a range of motional, process-modeling, and visualization problems that involved offsetting, sweeping, and M-ops; the solution paradigm common to all was direct approximation of mathematical definitions, using ray representations and parallel computation as primary media. This article presents no new results; it merely summarizes a body of well documented research that illustrates an approach to problem solving, whose primary tenets are: compute only what you need to solve the problem at hand, and do that as directly as possible.

Solids defined by Boolean combinations of solid primitives may be represented in constructive solid geometry (CSG) as binary trees. Most CSG-based algorithms (e.g., for boundary evaluation, graphic shading, interference detection) do various forms of set-membership classification by traversing the tree associated with the solid. These algorithms usually generate intermediate results that do not contribute to the final result, and hence may be regarded as redundant and a source of inefficiency. To reduce such inefficiencies, we associate with each primitive A in a tree S an active zone Z that represents the region of space where changes to A affect the solid represented by S , and we use a representation of Z instead of S for set-membership classification. In the paper we develop a mathematical theory of active zones, prove that they correspond to the intersection of certain nodes of the original trees, and show how they lead to efficient new algorithms for boundary evaluation, for detecting and eliminating redundant nodes in CSG trees, for interference (null-set) detection, and for graphic shading.

This paper introduces a language called MPL for representing machining process plans, and an experimental MPL translator called XMPL. MPL may be regarded as either an output language for automatic process planning programs, or as a high-level manual programming language for machining centers. This paper summarizes the concepts underlying the language and the facilities supported by the current processor. A typical machining plan (or program) in MPL is a sequence of setup and machining statements. Setup statements specify mainly positioning operations through stock and fixture feature-matching relations. Machining statements specify removal operations on features of the part. XMPL translates MPL programs into NC part programs and rigid motions for setup. The MPL/XMPL system requires a solid modeller (currently PADL-2) as a central utility processor, and the system's "machining versatility" is set mainly by the modeller's geometric coverage.

A machining simulator seeks to display graphically the effects on the workpiece (and associated fixtures) of the cutter motions prescribed in an NC program. Simulators enable NC programmers and machine operators to detect visually potential collisions and gross programming errors. A machining verifier seeks to determine automatically, without recourse to human judgement, whether an NC program will produce a specified part without undesirable side effects (collisions, cutter breakage, etc.). Simulators and verifiers both require solid modelling facilities, but simulators need only fast display generators for Boolean combinations whereas verifiers require more varied and powerful facilities. This paper summarizes the issues underlying simulation and verification while describing a new simulator that is being converted into a verifier.

Solid modeling plays a key role in electromechanical CAD/CAM, three-dimensional computer graphics, computer vision, robotics, and other disciplines and activities that deal with spatial phenomena. Almost all contemporary solid modeling systems support Boolean operations akin to set intersection, union, and difference on solids. Boundary representations (face/edge/vertex structures) for solids defined through Boolean operations are generated in these modelers by using so-called boundary evaluation and boundary merging procedures. These are the most complex and delicate software modules in a solid modeler. This paper describes boundary evaluation algorithms used by the PADL solid modeling systems developed at the University of Rochester, and discusses other known approaches in terms of concepts that emerged from the PADL work, notably set membership classification and neighborhood manipulation.

Article Free Access Share on Solid modeling(Panel Session) Authors: David Gossard MIT MITView Profile , Richard Riesenfeld University of Utah University of UtahView Profile , Herbert Voelcker University of Rochester University of RochesterView Profile , Tony Woo University of Michigan University of MichiganView Profile , Chairman: Ronald N. Goldman Control Data Corporation Control Data CorporationView Profile Authors Info & Claims SIGGRAPH '83: Proceedings of the 10th annual conference on Computer graphics and interactive techniquesJuly 1983 Pages 163–165https://doi.org/10.1145/800059.801146Published:01 July 1983Publication History 0citation349DownloadsMetricsTotal Citations0Total Downloads349Last 12 Months3Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

Colleges and universities are not meeting industry needs for graduates trained in the use or implementation of computer-aided design and manufacturing systems since few schools have experience in teaching CAD/CAM. Furthermore, many Bachelor's-level graduates are going directly into industry, rather than pursuing graduate degrees, thereby compounding this problem. Members of this panel represent both schools and industry and together attempt to outline approaches to developing more extensive CAD/CAM emphasis in education, including- the role colleges and universities can or should play in addressing industry needs in this area- user- and implementor-oriented CAD/CAM education- CAD/CAM education as an integral part of university engineering curricula- problems encountered in organizing and implementing CAD/CAM curriculum- universities' relationships with industry.It is our hope that panelists' experiences will help guide schools in structuring CAD/CAM programs to best insure that the United States remain at the forefront of technology and compete industrially world-wide.Frank PuhlVictor LangerDonald P. GreenbergMark S. ShepardHerb VoelckerUniversities' Relationships With IndustryFrank PuhlAmerican industry needs engineers who have been brought up with the realization that computers are intimately involved in all aspects of design, analysis, and manufacturing. Industry, of course, needs engineers who are already trained in fundamental CAD/CAM principles and in solving real world problems using computers, as well as those who have been taught to be productivity- and cost-conscious.To help meet these needs, we must now provide answers to several significant questions:What part should industry play in encouraging and sponsoring research and education in CAD/CAM?How can we resolve conflicts between industries' “trade secrets” and universities' “open research”?How can industry and educational institutions work together to increase U.S. productivity so as to regain our competitive edge?Lockheed Corporation and CADAM, Inc. are addressing these issues by supporting selected schools, installing CADAM systems, and providing fellowships for education and research at upperclass and graduate levels. In addition, we are involved in various joint research projects with universities, and we look optimistically toward continuing these projects.CADD CAM User EducationCADD CAM User EducationVictor LangerGeneral Electric Medical Systems Division in Milwaukee experienced a severe shortage of CADD CAM operators and encouraged MATC to develop a training program which started in 1980. A three-year NSF- CAUSE grant and a partial donation of a Computervision CADDS 3 (now CADD 4 Designer V six-station) system resulted in a program for upgrading employed designers and for two-year associate degree full-time students. The program enrolls 200 students per semester, with 70% continuing education students and 30% full-time students. Before students can effectively apply CADD CAM education, they must have drafting and design experience or at least a year of engineering training, plus ability to use spatial relationships and a course in descriptive geometry. With this background, students learn to create geometry for a 2-D drawing database and gain sufficient experience in the first course to be as productive as employees with six months' full-time experience. In the final semester or in the second advanced course, students create 3-D geometry and apply analytical computer capabilities for design, specializing for uses in mechanical, electrical, structural, architectural, and graphics arts applications. The defined geometry is also used in CAM for generating numerical control machining and flame-cutting paths, and for robotic control.Each course has been evaluated, follow-up studies have been completed, and an advisory committee has guided development. Employees have verified success and ease in transferring geometric skills to many different CADD CAM systems in the market. Beginning in the Fall of 1982, Apple microcomputers will be used to teach all 2-D computer graphics skills previously taught on the Computervision system, and CADD CAM education is now becoming available on an economical basis to all users.Some Problems in CAD EducationDonald GreenbergIt is imperative that universities educating the next generation of engineers introduce computer-aided design courses into their curricula. There are many obstacles in accomplishing this within a university structure. This presentation describes the facilities and operation at Cornell University and discusses the potential benefits and difficulties.CAD/CAM Education in an Engineering CurriculumMark S. ShepardToday there is a large industrial demand for engineering graduates that understand CAD/CAM techniques and computer graphics. Therefore, many colleges and universities already have or are planning to introduce computer graphics and CAD/CAM concepts into their curriculum. The major questions to be addressed in integrating these techniques into the curriculum include type and amount of hardware, development and maintenance of software and method of introduction into the curriculum.In 1977, RPI's school of engineering established the Center for Interactive Computer Graphics which is charged with integrating interactive computer graphics into the entire undergraduate engineering curriculum and providing a facility for graduate instruction and research. With heavy industrial support, the Center has also developed a research program in computer graphics and CAD/CAM. This presentation will discuss RPI's overall approach to integrating interactive computer graphics into the engineering curriculum.A Postgraduate Program in “Programmable Automation”Ari RequichaHerb Voelcker“Programmable Automation” designates the emerging body of knowledge surrounding CAD/CAM and industrial robotics. Graduate study in the field is aimed at (1) understanding the informational aspects of design and production in the discrete goods industries, and (2) developing new technologies for producing goods automatically with programmable, general-purpose tools. Some of the knowledge and techniques used in Programmable Automation are drawn from established fields (computer science, material science, control theory, ...), but the distinctive character of Programmable Automation is set mainly by the pervasive roles played by geometry and computation.A postgraduate program in Programmable Automation is being launched at the University of Rochester to train MS/level systems engineers for industry, and Ph.D-level researchers and teachers. The program's evolution reflects a “trickle-down” philosophy of education, wherein major new fields enter engineering education through on-going research; research begets seminars, seminars sometimes evolve into graduate courses, and graduate courses sometimes spawn undergraduate courses. (Put differently, the process starts with mature minds grappling with poorly understood concepts and ends with immature minds assimilating tightly codified concepts.)The Rochester program is sited in Electrical Engineering and draws heavily on the staff and facilities of the Production Automation Project; it also has strong links with Mechanical Engineering and Computer Science. The initial curriculum is based on two core courses in computational geometry, a graphics lab, and a systems seminar; these are supplemented with established courses in computer science, digital systems, finite-element analysis, control theory, and so forth. An NC Systems course and lab will be introduced a year hence. Plans for linking the program with Rochester's VLSI program, and for launching robotics research and teaching, are still in an embryonic stage.

PADL (Part and Assembly Description Language) is a language for defining solid objects via constructive solid geometry, i.e. as (regularized) set-theoretical compositions of primitive solid “building blocks”. The current processor for Version 1.0 of the language accepts PADL statements either in batch or in keyboard-interactive mode and produces line drawings of objects on CRT's and plotting devices. A variety of drawing styles is available: dimensioned orthographics, perspectives, section views, interference drawings, etc.

Two algorithms are proposed for recovering signals subjected to bandpass clipping and related types of nonlinear transformations. Both are based on contraction mapping principles and both seem to work experimentally, but neither has been validated formally. The conditions on signal determinism suggested by the algorithms have interesting practical implications.

Band-limited (BL) random-real-zero (RRZ) signals are a class of stationary stochastic processes whose zero crossings are the randomly perturbed zeros of a sinusoid. They are the only nontrivial examples known to date of band-limited signals whose correlation function and power spectrum can be computed exactly from a probabilistic description of their zeros. Such signals have optimal correlation characteristics, in the sense that their correlation function exhibits the maximum peak to sidelobe ratio attainable under a fixed bandwidth constraint.

Most engineers accept that an angle-modulated signal can be demodulated given only its zero crossings. Unfortunately, proofs of this fact tend to be either quite complicated and devoid of physical insight or to incorporate a significant amount of intuition. The treatment in this paper is cast in terms of sampling theory and trigonometric interpolation. Under this viewpoint, the effects of devices such as digital frequency dividers and pulse-count discriminators are quite easy to understand, and the enhanced noise immunity associated with bandwidth expansion can be interpreted in terms of diversity reception.