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We consider the problem of separating a set of polygons by a sequence of translations (one such collision-free translation motion for each polygon). If all translations are performed in a common direction the separability problem so obtained has been referred to as the uni-directional separability problem; for different translation directions, the more general multi-directional separability problem arises. The class of such separability problems has been studied previously and arises e.g. in computer graphics and robotics. Existing solutions to the uni-directional problem typically assume the objects to have a certain predetermined shape (e.g., rectangular or convex objects), or to have a direction of separation already available. Here we show how to compute all directions of unidirectional separability for sets of arbitrary simple polygons. The problem of determining whether a set of polygons is multi-directionally separable had been posed by G.T. Toussaint. Here we present an algorithm for solving this problem which, in addition to detecting whether or not the given set is multidirectionally separable, also provides an ordering in which to separate the polygons. In case that the entire set is not multi-directionally separable, the algorithm will find the largest separable subset. [ABSTRACT FROM AUTHOR]

This paper presents a definition of 'optical clusters' which is derived from the concept of optical resolution. The clustering problem (induced by this definition) is transformed such that the application of well known Computational Geometry methods yields efficient solutions. One result (which can be extended to different classes of objects and metrices) is the following: Given a set S of N disjoint line segments in E. [ABSTRACT FROM AUTHOR]