The problem of efficiently creating images of mathematical objects and animations of geometric algorithms is the focus of Professor Dobkin's research. The issues range from problems of pure combinatorial mathematics to problems of implementation in hardware and software.
The ultimate aim of the research is to create a system which computer scientists and mathematicians can use to illustrate their ideas, in informal discourse and in publications. To this end, it is necessary that an interactive system be efficient and that output images be elegant.
There are several concerns in setting up such a system. First, it is necessary to create realistic three-dimensional images of the objects being considered and to provide tools for modeling scenes from such images. Next, realistic displays of single or multiple views of the scenes must be produced. Finally, once a realistic image or set of images has been created, there is the issue of animating the actual images.