Geodesic
3D circular shapes and curve skeletons
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2012), pp. 90-99

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The medial axis of a planar shape is the set of points having at least two closest points on the shape boundary. This notion is widely used in computer science. In this paper we propose a mathematical model enabling us to define the notion of a curve skeleton as a 3D generalization of the 2D medial axis. We propose a criterion for comparing various particular methods for the construction of curve skeletons.
Keywords: medial axis, curve skeleton, fat curve. 
@article{IVM_2012_4_a9,
     author = {D. V. Khromov},
     title = {3D circular shapes and curve skeletons},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {90--99},
     publisher = {mathdoc},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_4_a9/}
}
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D. V. Khromov. 3D circular shapes and curve skeletons. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2012), pp. 90-99. http://geodesic.mathdoc.fr/item/IVM_2012_4_a9/