A noncylindrical ruled surface always
has a parameterization of the form

(1)

where ,
, and is called the striction curve of . Furthermore, the striction curve does not depend on the choice
of the base curve. The striction and director curves
of the helicoid

(2)

are

For the hyperbolic paraboloid

(5)

the striction and director curves are

See also Director Curve ,

Distribution Parameter ,

Noncylindrical Ruled Surface ,

Ruled Surface
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References Gray, A. "Noncylindrical Ruled Surfaces" and "Examples of Striction Curves of Noncylindrical Ruled Surfaces." §19.3 and 19.4 in
Modern
Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca
Raton, FL: CRC Press, pp. 445-449, 1997. Referenced on Wolfram|Alpha Striction Curve
Cite this as:
Weisstein, Eric W. "Striction Curve."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/StrictionCurve.html

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