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Distribution Parameter

The distribution parameter of a noncylindrical ruled surface parameterized by

x(u,v)=sigma(u)+vdelta(u),
(1)

where sigma is the striction curve and delta the director curve, is the function p defined by

p=(det(sigma^'deltadelta^'))/(delta^'·delta^').
(2)

The Gaussian curvature of a ruled surface is given in terms of its distribution parameter by

K=-([p(u)]^2)/({[p(u)]^2+v^2}^2).
(3)

See also

Noncylindrical Ruled Surface, Ruled Surface, Striction Curve

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References

Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, p. 447, 1997.

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Distribution Parameter

Cite this as:

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

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