The computer-aided solution to algorithmic problems is
becoming more and more important in various
application domains. This is in particular true for
computational geometry. For example, geometric
problems naturally arise in image processing,
computer graphics, and all kinds of computer-aided
design, just to mention a few. Even more, the
general tendency towards the application of visiual
aids in virtually all fields of science, technology,
and business raises many new, unexpected geometric
challenges.
A sound mathematical treatment of these problems and
a systematic computational study on the resulting
algorithms are desirable. However, in practice,
there are often obstacles to such an attempt. In
this paper, we will systematically discuss our
experiences with a few obstacles that occurred in
four of our projects and significantly influenced
our reasoning on algorithms in each of them.
