We investigate whether polyhedral models suffice for accurate silhouette computation. Therefore, we set up a theoretical framework, a mathematical foundation, to compare various algorithms computing silhouettes on spatial and topological accuracy. Within this carefully constructed environment, we can argue on a formal basis why some silhouette-computing algorithms are better than others. In doing so, we distinguish image space algorithms and object space algorithms. We show that only object space algorithms that respect topology are accurate enough for general applications.