Discrete differential geometry
Nhà xuất bản : Birkhäuser Basel
Năm xuất bản : 2008
Mô tả vật lý : 441 p.
Số phân loại : 516.36
Chủ đề : 1. Circle patterns. 2. Circular nets. 3. Discrete curvature lines. 4. Discrete minimal surfaces. 5. Discrete Willmore energy. 6. isothermicsurfaces. 7. Book.
Thông tin chi tiết
Tóm tắt : | In the search for appropriate discretizations of surface theory it is crucial to preserve fundamental properties of surfaces such as their invariance with respect to transformation groups. We discuss discretizations based on Mobius-invariant building blocks such as circles and spheres. Concrete problems considered in these lectures include the Willmore energy as well as conformal and curvature-line parametrizations of surfaces. In particular we discuss geometric properties of a recently found discrete Willmore energy. The convergence to the smooth Willmore functional is shown for special refinements of triangulations originating from a curvature-line parametrization of a surface. Further we treat special classes of discrete surfaces such as isothermic, minimal, and constant mean curvature. The construction of these surfaces is based on the theory of circle patterns, in particular on their variational description. |
Thông tin dữ liệu nguồn
Thư viện | Ký hiệu xếp giá | Dữ liệu nguồn |
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Đại học quốc gia Hà Nội |
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https://repository.vnu.edu.vn/handle/VNU_123/31574 |