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We propose a novel framework for computing the medial axis transform of 3Dshapes while preserving their medial features via restricted power diagram(RPD). Medial features, including external features such as the sharp edges andcorners of the input mesh surface and internal features such as the seams andjunctions of medial axis, are important shape descriptors both topologicallyand geometrically. However, existing medial axis approximation methods fail tocapture and preserve them due to the fundamentally under-sampling in thevicinity of medial features, and the difficulty to build their correctconnections. In this paper we use the RPD of medial spheres and its affiliatedstructures to help solve these challenges. The dual structure of RPD providesthe connectivity of medial spheres. The surface restricted power cell (RPC) ofeach medial sphere provides the tangential surface regions that these sphereshave contact with. The connected components (CC) of surface RPC give us theclassification of each sphere, to be on a medial sheet, a seam, or a junction.They allow us to detect insufficient sphere sampling around medial features anddevelop necessary conditions to preserve them. Using this RPD-based framework,we are able to construct high quality medial meshes with features preserved.Compared with existing sampling-based or voxel-based methods, our method is thefirst one that can preserve not only external features but also internalfeatures of medial axes.

Computing Medial Axis Transform with Feature Preservation via Restricted Power Diagram