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Shape smoothing using double offsets

It has been observed for a long time that the operation consisting of offsetting a solid by a quantity r and then offsetting its complement by d < r produces, in some cases, a new solid with the same topology but with a smooth boundary. While this fact has been widely used in Computer Aided Geometric Design or in the field of image processing, we provide here for the first time a tight and robust condition that guarantees the smoothness of the new solid and gives a lower bound on its reach (distance to the medial axis). This condition is based on the general properties of the distance function to a compact set and relies on the recently introduced critical function and μ-reach.