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Minimal Surfaces from Triangular Meshes

Vos, J. (2016) Minimal Surfaces from Triangular Meshes. Bachelor's Thesis, Computing Science.

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In this thesis I investigate the novel use of the centroidal Voronoi tessellation (CVT) concept as a surface mesh smoothing operation. I carry out extensive literature research to find the most promising way for implementing the computation of such tessellations on $2$-manifold triangular meshes embedded in three-dimensional space. I detail my mesh visualisation application which implements this operator, as well as Loop subdivision, Laplacian smoothing, and dual mesh generation. I perform experimental research to find out how the new smoothing operator can best be combined with these other three, more traditional ones. For this purpose I focus on open meshes, so that boundary vertices can be kept fixed in order to obtain a smooth mesh surface between the boundaries. I search for the optimal strategy of converging to surfaces that still resemble the input mesh while appearing smooth to the human observer, without requiring too high a mesh density or too long a computation time. I report my findings in a coherent conclusion, and specify remaining future work on the subject.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Computing Science
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 08:13
Last Modified: 15 Feb 2018 08:13

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