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This paper considers computation of visibility for two dimensional shapes whose boundaries are C1 continuous curves. We assumewe are given a one-parameter family of candidate viewpoints, whichmay be interior or exterior to the object, and at finite or infinite locations.We consider how to compute whether the whole boundary of theshape is visible from some finite set of viewpoints taken from this family, and if so, how to compute a minimal set of such viewpoints.The viewpoint families we can handle include (i) the set of viewingdirections from infinity, (ii) viewpoints on a circle located outside theobject (for inspection from a turntable), and (iii) viewpoints locatedon the walls of the shape itself. We compute a structure called a visibility chart, which simultaneously encodes the visible part of the shape驴s boundary from every view inthe family. Using such a visibility chart, finding a minimal set ofviewpoints reduces to the set-covering problem over the reals.Practical algorithms are obtained by a discrete sampling of thevisibility chart. For exterior visibility problems, a reasonable approach is to compute an almost-optimal solution (in terms of number of viewpoints), which can be done in almost-linear time. For interior visibility problems, or when a more correct solution is required, we solve the general set-covering problem, guaranteeing an optimal solution but taking exponential time. In either case, conservative solutions are obtained, ensuring that no part of the curve remains invisible from some viewpoint. Examples are given to illustrate our algorithm.