Characterizing envelopes of moving rotational cones and applications in CNC machining

Mikhail Skopenkov, Pengbo Bo, Michael Bartoň, Helmut Pottmann

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Motivated by applications in CNC machining, we provide a characterization of surfaces which are enveloped by a one-parametric family of congruent rotational cones. As limit cases, we also address developable surfaces and ruled surfaces. The characterizations are higher order nonlinear PDEs generalizing the ones by Gauss and Monge for developable surfaces and ruled surfaces, respectively. The derivation includes results on local approximations of a surface by cones of revolution, which are expressed by contact order in the space of planes. These results are themselves of interest in geometric computing, for example in cutter selection and positioning for flank CNC machining.
Original languageEnglish (US)
Pages (from-to)101944
JournalComputer Aided Geometric Design
StatePublished - Oct 20 2020


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