An Electronic topological picturebook

Abstract

An electronic topological picturebook is envisaged as a computerized version of A Topological Picturehook by George K. Francis, .Springer-Verlag, New York (1987). Francis’ book is full of complicated topological figures, mostly drawn manually. The main goal of the thesis is to automate the production of such illustrations and to obtain publication-quality hardcopy using assorted techniques of computer graphics. To that end, sweeping is discussed as a major surface modeling tool. Some interactive methods are given to produce interesting topological surfaces. The program Tb (which stands for ‘Topologybook’) is described and various pictures generated by this software are presented. Tl· is a free-form surface modeler and produces topological shapes with little effort. Central to the implementation of Tb is a paradigm of solid modeling in which computation of a shape is regarded as sweeping with some parametric variations, viz. shape = sweep + control.