This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Computing Discrete Minimal Surfaces Using a Nonlinear Spring Model
November/December 2010 (vol. 12 no. 6)
pp. 74-79

A new algorithm can derive one or more minimal surfaces from an initial arbitrary surface with a fixed boundary.

1. J. Douglas, "Solution of the Problem of Plateau," Trans. Am. Math. Soc., vol. 33, no. 1, 1931, pp. 263–321.
2. T. Radó, "On Plateau's Problem," Ann. Math., vol. 31, no. 3, 1930, pp. 457–469.
3. J.X. Chen, Y. Yang, and X. Wang, "Physics-Based Modeling and Real-Time Simulation," Computing in Science & Eng., vol. 3, no. 3, 2001, pp. 98–102.
4. G. Dziuk and J.E. Hutchinson, "The Discrete Plateau Problem: Algorithm and Numerics," Math. Computation, vol. 68, no. 225, 1999, pp. 1–23.
5. U. Pinkall and K. Polthier, "Computing Discrete Minimal Surface and their Conjugates," Experimental Math., vol. 2, no. 1, 1993, pp. 15–36.
6. M. Meyer et al., "Discrete Differential-Geometry Operators for Triangulated 2-Manifolds," Proc. VisMath, Springer-Verlag, 2002, pp. 34–57.
7. R.W. Clough and J. Penzien, Dynamics of Structures, McGraw Hill, 1975.
8. G.S. Chaim and J.M. Sullivan, "Cubic Polyhedra," arXiv.org, 14 May 2002; http://arxiv.org/abs/math0205145.
1. L. Walter and J.R. Wilson, "On Discrete Dirichlet and Plateau Problem," Numerische Mathematik, vol. 3, 1961, pp. 359–373.
2. P. Concus, "Numerical Solution of the Minimal Surface Equation," Math. Computation, vol. 21, 1967, pp. 340–350.
3. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed. Springer-Verlag, 1984.
4. P.G. Ciarlet, The Finite Element Method for Elliptic Problems, North Holland, 1978, pp. 301–311.
5. T. Tsuchiya, "On Two Methods for Approximating Minimal Surfaces in Parametric Form," Math. Computation, vol. 46, no. 174, 1986, pp. 517–529.
6. U. Pinkall and K. Polthier, "Computing Discrete Minimal Surface and their Conjugates," Experimental Math., vol. 2, no. 1, 1993, pp. 15–36.
7. D. Chopp, "Computing Minimal Surfaces via Level Set Curvature Flow," J. Computational Physics, vol. 106, no. 1, 1993, pp. 77–91.
8. G. Dziuk and J.E. Hutchinson, "The Discrete Plateau Problem: Algorithm and Numerics," Math. Computation, vol. 68, no. 225, 1999, pp. 1–23.
9. T. Cecil, "A Numerical Method for Computing Minimal Surfaces in Arbitrary Dimension," J. Computational Physics, vol. 206, no. 2, 2005, pp. 650–660.
10. G. Xu and Q. Pan, "Geometric Modeling by Discrete Surfaces Patches Based on Geometric Partial Differential Equations," J. Computer-Aided Design & Computer Graphics, vol. 17, no. 12, 2005, pp. 2596–2606.

Index Terms:
Discrete minimal surface, nonlinear spring model, mean curvature normal, degenerated triangles
Citation:
Yongquan Jiang, Li Chen, Qishu Chen, Qiang Peng, Jim X. Chen, "Computing Discrete Minimal Surfaces Using a Nonlinear Spring Model," Computing in Science and Engineering, vol. 12, no. 6, pp. 74-79, Nov.-Dec. 2010, doi:10.1109/MCSE.2010.127
Usage of this product signifies your acceptance of the Terms of Use.