12 citations · 25 across the 7 of their papers we have counts for
7 papers
Patchwork: A compact representation for 3D polygonal shapes
Ruichen Zheng, Biao Zhang, Michael Birsak +2
We introduce Patchwork, a new general-purpose shape representation capable of modeling 2D and 3D geometry with a small number of parameters. Patchwork is grounded in a rigorous mat…
Approximation by Quad Meshes in Laguerre Geometry
A. Ramos-Cisneros, M. Skopenkov, H. Pottmann
We study analogs of planar-quadrilateral meshes in Laguerre sphere geometry and the approximation of smooth surfaces by them. These new Laguerre meshes can be viewed as watertight…
Quasi-symmetric nets: A constructive approach to the equimodular elliptic type of Kokotsakis polyhedra
A. Nurmatov, M. Skopenkov, F. Rist +2
A Kokotsakis polyhedron is a polyhedral mesh in three-dimensional Euclidean space formed by a central n-gonal face (the base), n quadrilateral faces each sharing one edge with the…
Families of surfaces with constant ratio of principal curvatures and Plateau's problem
Mikhail Skopenkov, Khusrav Yorov
This work is on surfaces with a constant ratio of principal curvatures. These CRPC surfaces generalize minimal surfaces but are much more challenging to construct. We propose a con…
Incidences, tilings, and fields
P. Pylyavskyy, M. Skopenkov
The master theorem, introduced by Richter-Gebert and generalized by Fomin and the first author, provides a method for proving incidence theorems of projective geometry using triang…
Surfaces containing two circles through each point
Mikhail Skopenkov, Rimvydas Krasauskas
We find all analytic surfaces in space such that through each point of the surface one can draw two transversal circular arcs fully contained in the surface. The pro…
Surfaces containing two circles through each point and Pythagorean 6-tuples
M. Skopenkov, R. Krasauskas
We study analytic surfaces in 3-dimensional Euclidean space containing two circular arcs through each point. The problem of finding such surfaces traces back to the works of Darbou…