Abstract
Geometric manipulation of 3D objects can benefit from analogies among similar shapes and parts. However, analogies that are easily found by humans are difficult to detect and maintain in algorithms that manipulate 3D meshes. One of the reasons for this is that such analogies are perceived between 3D volumetric parts of the objects whereas models defined by mesh surfaces are boundary representations of the object. The shape-diameter function (SDF) maps volumetric information of the shape onto the boundary mesh and provides a link between the two. This function is related to the medial axis transform, measuring the local diameter of the object at points on its boundary. The SDF remains largely oblivious to pose changes of the same object and maintains similar values in analogue parts of different objects. By using the SDF attribute of an object we are able to find similarities between object parts, even when the topology or structure of the objects are different.
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