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 visual 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.