2016
DOI: 10.1007/s00208-016-1424-z
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Isothermic triangulated surfaces

Abstract: Abstract. We found a class of triangulated surfaces in Euclidean space which have similar properties as isothermic surfaces in Differential Geometry. We call a surface isothermic if it admits an infinitesimal isometric deformation preserving the mean curvature integrand locally. We show that this class is Möbius invariant. Isothermic triangulated surfaces can be characterized either in terms of circle patterns or based on conformal equivalence of triangle meshes. This definition generalizes isothermic quadrila… Show more

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Cited by 14 publications
(22 citation statements)
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“…(6) ("version 1") behaves differently from normality according to Eq. (6 * ) ("version 2"), while there is hardly any difference between conditions (6 * ) and (11). with χ = f + v − e as the Euler characteristic.…”
Section: Resultsmentioning
confidence: 99%
See 2 more Smart Citations
“…(6) ("version 1") behaves differently from normality according to Eq. (6 * ) ("version 2"), while there is hardly any difference between conditions (6 * ) and (11). with χ = f + v − e as the Euler characteristic.…”
Section: Resultsmentioning
confidence: 99%
“…The theory presented in [2] is restricted to offset-like pairs of polyhedral surfaces where corresponding edges and faces are parallel. There are ongoing efforts to extend this theory to more general situations (we point to recent work on quad meshes [10] and on isothermic triangle meshes of constant mean curvature [11]). It is therefore remarkable that at least for the situation described here, triangle meshes allow an approach to curvatures and even a shape operator which is likewise guided by the Steiner formula, but without the rather restrictive property of parallelity (which for triangle meshes would be even more restrictive).…”
Section: Relevance For Discrete Differential Geometrymentioning
confidence: 99%
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“…The results on planar triangular meshes in this paper are closely related to isothermic triangulated surfaces in Euclidean space [8].…”
Section: Thus We Indeed Havefmentioning
confidence: 99%
“…A similar formula for quadrilateral meshes with factorized real cross ratios was established by Bobenko and Pinkall [1]. Here we will use the definition of a discrete minimal surface f with Gauß map n given in [8]:…”
Section: The Holomorphic Quadratic Differential Q := Hg Z Dz 2 Is Calmentioning
confidence: 99%