Category: 
October 16, 2006
The level surfaces pictured here are periodic in three dimensions. The equations whose solutions they represent are composed of trigonometric functions, and are shown to the left of the surface images. See animations and VRML models of these surfaces ont the accompanying page.
Several of these surfaces closely approximate known minimal surfaces. In particular the P, G, D, and Neovius minimal surfaces are frequently referred to by the same name as their level surface counterparts. The closeness of the P,G, and D minimal and level surfaces is depicted visually on the page titled Level Sets Approximating Minimal Surfaces.
The surfaces were generated using SolSurf. The images were rendered using VPS.
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P (“Schwarz P”)
cos x + cos z + cos y = 0 |
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D (“Diamond”)
sin x * sin y * sin z + sin x * cos y * cos z + cos x * sin y * cos z + cos x * cos y * sin z = 0 |
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G (“Gyroid”)
cos x * sin y + cos y * sin z + cos z * sin x = 0 |
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N (“Neovius”)
3*(cos x + cos y + cos z) + 4* cos x * cos y * cos z = 0.0 |
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W (“iWP”)
cos x * cos y + cos y * cos z + cos z * cos x - cos x * cos y * cos z = 0 |
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P_W (P W Hybrid)
4*(cos x * cos y +
cos y * cos z +
cos z * cos x) -
3* cos x * cos y * cos z = -2.4
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http://www.msri.org/about/sgp/jim/geom/level/library/triper/mainc.html
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