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Approximating Manifolds by Meshes: Asymptotic Bounds in Higher Codimension

Laat, D. de (2011) Approximating Manifolds by Meshes: Asymptotic Bounds in Higher Codimension. Master's Thesis / Essay, Mathematics.

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We discuss asymptotic upper bounds on the Hausdorff distance between manifolds and optimal meshes. Here a mesh is a geometric simplicial complex whose carrier is topologically equivalent to the manifold and whose vertices lie on the manifold. By equipping manifolds with new curvature induced metrics we generalize a method of Clarkson, which uses nets and the second fundamental form to mesh hypersurfaces, to higher codimension. This yields new upper bounds for manifolds which admit global nonoriented normal frame fields, and these bounds compare well to bounds which are already known in special cases. Our approach yields an explicit expression for the constant in the asymptotic upper bound.

Item Type: Thesis (Master's Thesis / Essay)
Degree programme: Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 15 Feb 2018 07:46
Last Modified: 15 Feb 2018 07:46

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