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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 5971295, 9 pages
Research Article

Curve and Surface Smoothing Using a Modified Cahn-Hilliard Equation

Department of Mathematics, Korea University, Seoul 02841, Republic of Korea

Correspondence should be addressed to Junseok Kim;

Received 19 April 2017; Revised 23 July 2017; Accepted 14 September 2017; Published 25 October 2017

Academic Editor: Ruben Specogna

Copyright © 2017 Yongho Choi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a new method using the modified Cahn-Hilliard (CH) equation for smoothing piecewise linear shapes of two- and three-dimensional objects. The CH equation has good smoothing dynamics and it is coupled with a fidelity term which keeps the original given data; that is, it does not produce significant shrinkage. The modified CH equation is discretized using a linearly stable splitting scheme in time and the resulting scheme is solved by using a Fourier spectral method. We present computational results for both curve and surface smoothing problems. The computational results demonstrate that the proposed algorithm is fast and efficient.