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Curve and Surface Smoothing Using a Modified Cahn-Hilliard Equation

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  • Yongho Choi
  • Darea Jeong
  • Junseok Kim

Abstract

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.

Suggested Citation

  • Yongho Choi & Darea Jeong & Junseok Kim, 2017. "Curve and Surface Smoothing Using a Modified Cahn-Hilliard Equation," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-9, October.
    • Handle: RePEc:hin:jnlmpe:5971295
    DOI: 10.1155/2017/5971295
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