7 papers · 1 filter
Visualization of curvature on curve and surface by tangential angle parametrization
Yutaro Kabata, Shigeki Matsutani, Yuta Ogata
We propose a unified method to visualize curvature on planar curves and surfaces of revolution using the tangential angle parameter. For plane curves, placing markers at equal incr…
Monodromy of Darboux transformations of polarised curves
Joseph Cho, Katrin Leschke, Yuta Ogata
We show that every finite type polarised curve in the conformal -sphere with a polynomial conserved quantity admits a resonance point, under a non-orthogonality assumption on th…
Discrete constant mean curvature cylinders and isothermic tori
Joseph Cho, Katrin Leschke, Yuta Ogata
We consider the monodromy problem of Darboux transforms of discrete isothermic surfaces using the integrable theory of discrete polarised curves. Then we provide, for the first tim…
Periodic discrete Darboux transforms
Joseph Cho, Katrin Leschke, Yuta Ogata
We express Darboux transformations of discrete polarised curves as parallel sections of discrete connections in the quaternionic formalism. This immediately leads to the linearisat…
On discrete constant principal curvature surfaces
Y. Kabata, S. Matsutani, Y. Ogata
Recently, it is discovered that a certain class of nanocarbon materials has geometrical properties related to the discrete geometry, pre-constant discrete principal curvature [9] b…
New explicit CMC cylinders and same-lobed CMC multibubbletons
Joseph Cho, Katrin Leschke, Yuta Ogata
We provide explicit parametrisations of all Darboux transforms of Delaunay surfaces. Using the Darboux transformation on a multiple cover, we obtain this way new closed CMC surface…