The Complexity of Computing Nice Viewpoints of Objects in Space

A polyhedral object in 3-dimensional space is often well represented by a set of points and line segments that act as its features. By a nice viewpoint of an object we mean a projective view in which all (or most) of the features of the object, relevant for some task, are clearly visible. Such a view is often called a non-degenerate view or projection. In this paper we are concerned with computing non-degenerate orthogonal and perspective projections of sets of points and line segments (objects) in 3-dimensional space. We outline the areas in which such problems arize, discuss recent research on the computational complexity of these problems, illustrate the fundamental ideas used in the design of algorithms for computing non-degenerate projections, and provide pointers to the literature where the results can be found.