<title>Complexity of computing nice viewpoints of objects in space</title>

Abstract

ABSTRACT A polyhedral object in 3-dimensional space is often well represented by a set of points and line segments that act asits features. By a nice viewpoint of an object we mean a projective view in which all (or most) of the features of theobject, relevant for some task, are clearly visible. Such a view is often called a non-degenerate view or projection. Inthis paper we are concerned with computing non-degenerate orthogonal and perspective projections of sets of pointsand line segments (objects) in 3-dimensional space. We outline the areas in which such problems arize, discuss recentresearch on the computational complexity of these problems, illustrate the fundamental ideas used in the design ofalgorithms for computing non-degenerate projections, and provide pointers to the literature where the results can befound.Keywords: Data visualization, nice viewpoints, knot theory, computer vision, graph drawing, computer graphics,degeneracies, general position, orthogonal projections, perspective projections, robustness of algorithms, computa-tional geometry.