Issue No.06 - November/December (2010 vol.12)
pp: 74-79
<p>A new algorithm can derive one or more minimal surfaces from an initial arbitrary surface with a fixed boundary.</p>
Discrete minimal surface, nonlinear spring model, mean curvature normal, degenerated triangles
Li Chen, Qishu Chen, Yongquan Jiang, Jim X. Chen, "Computing Discrete Minimal Surfaces Using a Nonlinear Spring Model", Computing in Science & Engineering, vol.12, no. 6, pp. 74-79, November/December 2010, doi:10.1109/MCSE.2010.127
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,", 14 May 2002;