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Distribution Parameter

The distribution parameter of a Noncylindrical Ruled Surface parameterized by

{\bf x}(u,v)=\boldsymbol{\sigma}(u)+v\boldsymbol{\delta}(u),
\end{displaymath} (1)

where $\boldsymbol{\sigma}$ is the Striction Curve and $\boldsymbol{\delta}$ the Director Curve, is the function $p$ defined by
p={\mathop{\rm det}(\boldsymbol{\sigma}' \boldsymbol{\delta}...
...\delta}')\over \boldsymbol{\delta}'\cdot\boldsymbol{\delta}'}.
\end{displaymath} (2)

The Gaussian Curvature of a Ruled Surface is given in terms of its distribution parameter by
\end{displaymath} (3)

See also Noncylindrical Ruled Surface, Striction Curve


Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 347-348, 1993.

© 1996-9 Eric W. Weisstein