Some mathematical tools for a modeler's workbench

This article is a retrospective look at a modeling effort involving the generation of a computer model from informal drawings and a plastic model of a helicopter. When the exercise was taken on at the suggestion of a sponsor at the US Army Ballistic Research Laboratory (BRL) in Aberdeen, Maryland, we accepted the task as a means of examining a significant class of objects in which lofting was the predominant, characterizing modeling technique. During the course of this modeling effort, we were able to gain some insights into the kinds of computeraided geometric design tools that would be appropriate to support this kind of work. It is our expectation that from the results of a project like this we will see ways to develop a set of mathematical software tools in a "workbench environment" - tools that will make subsequent efforts to model related objects a much more straightforward process. The Alpha_I System, which is an experimental spline-based solid modeler used to generate the models discussed in this article, is being developed in the Computer Science Department at the University of Utah. Alpha_1 is intended to become part of an interactive environment that will eventually provide the designer with the kind of workbench necessary to carry out a large variety of tasks beyond specialized lofting projects.