منابع مشابه
Symmetry of Embedded Genus-one Helicoids
In this note, we use the Lopez-Ros deformation introduced in [9] to show that any embedded genus-one helicoid must be symmetric with respect to rotation by 180 around a normal line. This partially answers a conjecture of Bobenko from [3]. We also show this symmetry holds for an embedded genus-k helicoid Σ, provided the underlying conformal structure of Σ is hyperelliptic. In [3], Bobenko conjec...
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Recently, Savadjiev et al. introduced a generalized helicoid as an osculating object to characterize near parallel 3D curve patterns. This new model allows for patterns of different kinds to be examined and generated via three curvature parameters. The parameterization can be efficiently used to model hair strands. We present an investigation of the usability of the generalized helicoid model f...
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In computer graphics, modeling the geometry of hair and hair-like patterns such as grass and fur remains a significant challenge. Hair strands can exist in an extensive variety of arrangements and the choice of an appropriate representation for tasks such as hair synthesis, fitting, editing, or reconstruction from samples, is non-trivial. To support such applications we present a novel mathemat...
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We investigate the instabilities of a flat elastic ribbon subject to twist under tension and develop an integrated phase diagram of the observed shapes and transitions. We find that the primary buckling mode switches from being localized longitudinally along the length of the ribbon to transverse above a triple point characterized by a crossover tension that scales with ribbon elasticity and as...
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For more then 200 years the helicoid was the only known infinite total curvature embedded minimal surface of finite topology. The situation changed in 1993, when Hoffman, Karcher and Wei [9] discovered the genus one helicoid a minimal torus with one end, which has a form of the helicoid at infinity. The genus one helicoid was constructed using the Weierstrass representation. Karcher, Wei and Ho...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2002
ISSN: 0026-2285
DOI: 10.1307/mmj/1022636758