BIHARMONIC OPTIMIZATION OF PIECEWISE PLANAR SURFACES
A. V. Smurygin, I. V. Zhurbin
Physicotechnical Institute, Ural Branch of the Russian Academy of Sciences, ul. Kirova 132, Izhevsk, 426000 Russia
Keywords: simplicial scheme, subdivision of simplicial scheme, embedding function, biharmonic interpolation, discrete Laplace operator on the graph
Abstract
In this paper, we propose a method for optimizing geometric objects such as polygons and triangulated piecewise planar surfaces, for the purposes of greater detailing and providing visual smoothness of their images. The initial object is treated as a geometric realization of a simplicial scheme. The method involves refining the simplicial scheme and biharmonic interpolation of the embedding function of a subdivision of the simplicial scheme in Euclidean space.
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