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Point sets are the standard output of many 3D scanning systems and depth cameras. Presenting the set of points as is, might "hide" the prominent features of the object from which the points are sampled. Our goal is to reduce the number of points in a point set, for improving the visual comprehension from a given viewpoint. This is done by controlling the density of the reduced point set, so as to create bright regions (low density) and dark regions (high density), producing an effect of shading. This data reduction is achieved by leveraging a limitation of a solution to the classical problem of determining visibility from a viewpoint. In addition, we introduce a new dual problem, for determining visibility of a point from infinity, and show how a limitation of its solution can be leveraged in a similar way.