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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. A. Rokhlin and D. B. Fuks, Initial Course of Topology. Geometric Chapters (Nauka, Moscow, 1977) [in Russian].
E. I. Yakovlev, Computational Topology: Textbook (Nizhny Novgorod University, Nizhny Novgorod, 2003) [in Russian].
S. P. Novikov and A. T. Fomenko, Elements of Differential Geometry and Topology (Nauka, Moscow, 1987) [in Russian].
E. Catmull and J. Clark, “Recursively Generated B-Spline Surfaces on Arbitrary Topological Meshes,” Computer-Aided Design 10 (6), 350–355 (1978).
A. V. Smurygin and I. V. Zhurbin, “Combined Method of Convex Hulls for the Reconstruction of a Polyhedron from Given Planar Sections,” Geoinformatika, No. 1, 64–67 (2012).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.V. Smurygin, I.V. Zhurbin, 2015, published in Avtometriya, 2015, Vol. 51, No. 2, pp. 77–82.
About this article
Cite this article
Smurygin, A.V., Zhurbin, I.V. Biharmonic optimization of piecewise planar surfaces. Optoelectron.Instrument.Proc. 51, 170–174 (2015). https://doi.org/10.3103/S8756699015020107
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S8756699015020107