Contents

We will discuss three problems:

1.

Boolean operations on polygons with circular arcs.

2.

Arrangements of ellipsoids

3.

Boolean operations on polyhedra with curved faces and edges

For each problem we will collect and present the methods needed to solve the problem. Observe that this way of presenting the material differs from the usual order. Usually, one presents a method and then the problems that can be solved with it. We start with three natural problems and then present the methods required to solve the problems.

The methods stem from different areas: computational geometry, data structures, numerical analysis, computer algebra, and software design. It is conceivable that you know some of the material already.

There are loose ends. We are not claiming that we know the ultimate solutions to the problems above. We know some solutions and it will become clear from the presentation that there is plenty of room for improvements and further work. In fact, we believe that the charm of course lies in the fact that there are many loose ends. We hope that you pick them up in Fopras, Diplomarbeiten and PhD-projects.

See also the Course Announcement for this course.