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Seashell

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ConicalSpiral1
ConicalSpiral2

A conical surface modeled after the shape of a seashell. One parameterization (left figure) is given by

x=2[1-e^(u/(6pi))]cosucos^2(1/2v)
(1)
y=2[-1+e^(u/(6pi))]sinucos^2(1/2v)
(2)
z=1-e^(u/(3pi))-sinv+e^(u/(6pi))sinv,
(3)

where v in [0,2pi), and u in [0,6pi) (Wolfram Research).

Another parameterization (von Seggern 2007) is given by

x=[(1-v/(2pi))(1+cosu)+c]cos(nv)
(4)
y=[(1-v/(2pi))(1+cosu)+c]sin(nv)
(5)
z=(bv)/(2pi)+asinu(1-v/(2pi))
(6)

for u,v in [0,2pi] (right figure with a=0.2, b=1, c=0.1, and n=2).

See also

Conical Spiral

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References

Gray, A. "Sea Shells." §13.6 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 308-309, 1997.Nordstrand, T. "Conic Spiral or Seashell." http://jalape.no/math/shelltxt.von Seggern, D. CRC Standard Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 2007. Wolfram Research, Inc. "Mathematica Version 2.0 Graphics Gallery." http://library.wolfram.com/infocenter/Demos/4664/.

Cite this as:

Weisstein, Eric W. "Seashell." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Seashell.html

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