کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1702792 1012354 2016 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the construction of minimal surfaces from geodesics
ترجمه فارسی عنوان
درباره ساخت سطوح حداقلی از geodesics
کلمات کلیدی
مشکل Björling؛ Catenoid؛ نقشه برداری؛ سطح حداقل؛ مشکل فلوت؛ Helicatenoid
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مکانیک محاسباتی
چکیده انگلیسی

In a recent article (2013), Li et al. [1] approximate minimal surfaces from geodesic boundaries, with applications to garment design in mind. We go over this work and existing methods for constructing minimal surfaces from geodesics. First, we justify why minimal surfaces and the problem of finding the surface with minimal area (i.e., solving Plateau's problem) have little to do with garment design. Second, we recall that Plateau's problem makes little sense for boundaries such as those considered in [1], composed of unclosed curves of finite length or disconnected pieces of them (with no other positional restriction). Finally, we note that the construction of a minimal surface (with zero mean curvature) from a prescribed geodesic is a particular instance of a classical problem in differential geometry, already solved by Björling. In particular, for a geodesic circle or helix the resulting minimal surfaces are well-known (catenoid and helicatenoid, respectively), so no approximations are required.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematical Modelling - Volume 40, Issue 2, 15 January 2016, Pages 1676–1682
نویسندگان
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