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- W3195036812 abstract "We prove (under some technical assumptions) that each surface in R3 containing two arcs of parabolas with axes parallel to Oz through each point has a parametrization (P(u,v)R(u,v),Q(u,v)R(u,v),Z(u,v)R2(u,v)) for some P,Q,R,Z∈R[u,v] such that P,Q,R have degree at most 1 in u and v, and Z has degree at most 2 in u and v. The proof is based on the observation that one can consider a parabola with vertical axis as an isotropic circle; this allows us to use methods of the recent work by M. Skopenkov and R. Krasauskas in which all surfaces containing two Euclidean circles through each point are classified. Such approach also allows us to find a similar parametrization for surfaces in R3 containing two arbitrary isotropic circles through each point (under the same technical assumptions). Finally, we get some results concerning the top view (the projection along the Oz axis) of the surfaces in question." @default.
- W3195036812 created "2021-08-30" @default.
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- W3195036812 date "2021-10-01" @default.
- W3195036812 modified "2023-09-26" @default.
- W3195036812 title "Surfaces containing two isotropic circles through each point" @default.
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- W3195036812 doi "https://doi.org/10.1016/j.cagd.2021.102035" @default.
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