Characterizing envelopes of moving rotational cones and applications in  CNC machining

Skopenkov, Mikhail; Bo, Pengbo; Bartoň, Michael; Pottmann, Helmut

dc.contributor.author	Skopenkov, Mikhail
dc.contributor.author	Bo, Pengbo
dc.contributor.author	Bartoň, Michael
dc.contributor.author	Pottmann, Helmut
dc.date.accessioned	2020-10-20T12:10:06Z
dc.date.available	2020-01-14T13:02:43Z
dc.date.available	2020-10-20T12:10:06Z
dc.date.issued	2020-10-16
dc.identifier.citation	Skopenkov, M., Bo, P., Bartoň, M., & Pottmann, H. (2020). Characterizing envelopes of moving rotational cones and applications in CNC machining. Computer Aided Geometric Design, 83, 101944. doi:10.1016/j.cagd.2020.101944
dc.identifier.doi	10.1016/j.cagd.2020.101944
dc.identifier.uri	http://hdl.handle.net/10754/661034
dc.description.abstract	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.
dc.description.sponsorship	Three of the four coauthors are grateful to King Abdullah University of Science and Technology, where they met altogether and started this project. The authors are also grateful to R. Bryant, S. Ivanov, and A. Skopenkov for useful discussions. The first author has been supported within the framework of the Academic Fund Program at the National Research University Higher School of Economics (HSE) in 2018-2019 (grant N18-01-0023) and by the Russian Academic Excellence Project “5-100”. The second author has been partially supported by the National Natural Science Foundation of China (61672187) and the Shandong Provincial Key R&D Program (2018GGX103038). The third author has been partially supported by Spanish Ministry of Science, Innovation and Universities: Ram´on y Cajal with reference RYC-2017-22649 and the European Unions Horizon 2020 research and innovation programme under agreement No. 862025.
dc.publisher	Elsevier BV
dc.relation.url	https://www.sciencedirect.com/science/article/pii/S016783962030131X
dc.rights	Archived with thanks to arXiv
dc.title	Characterizing envelopes of moving rotational cones and applications in CNC machining
dc.type	Article
dc.contributor.department	Applied Mathematics and Computational Science Program
dc.contributor.department	Visual Computing Center (VCC)
dc.contributor.department	Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.eprint.version	Post-print
dc.contributor.institution	National Research University Higher School of Economics, Faculty of Mathematics, Usacheva 6, Moscow 119048, Russia
dc.contributor.institution	Institute for Information Transmission Problems of the Russian Academy of Sciences, Bolshoy Karetny 19 bld.1, Moscow 127051, Russia
dc.contributor.institution	School of Computer Science and Technology, Harbin Institute of Technology, West Wenhua Str. 2, 264209 Weihai, China
dc.contributor.institution	BCAM – Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Basque Country, Spain
dc.identifier.arxivid	2001.01444
kaust.person	Pottmann, Helmut
refterms.dateFOA	2020-01-14T13:03:11Z
dc.date.published-online	2020-10-16
dc.date.published-print	2020-11
dc.date.posted	2020-01-06