Cellular Lines
by
Keith Unsworth
Lincoln University
Coauthors: Panama Geer (Rensselaer Polytechnic Institute), Harry McLaughlin (Rensselaer Polytechnic Institute)

Users of Computer Aided Design software typically construct a mathematical model of a physical object and then render the model on a computer screen. An object's preconceived form is used as a basis for the object's model. The users' geometry toolbox includes powerful mathematical constructs (e.g. splines) and construction procedures (e.g. subdivision).

We question whether this is the most appropriate and most natural way of constructing geometric objects, such as curves and surfaces. In exploring alternative approaches, we could learn from biology and study what is in nature's toolbox. Is it possible to model nature's geometry without first constructing models of the type referred to above?

We suggest that this may be possible using cell sets in 2D and 3D cellular arrays without using continuum-based constructs. As a first step in this exploration, we introduce a cell set which may be recognised as a line, and which can be constructed without having to rely on Euclidean constructs. We call these cellular lines.

Date received: February 13, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caie-23.