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Cornu
Spiral Animation with Rhombus Substitution
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The
Spiral of Cornu is named for the French scientist Marie Alfred
Cornu (1841 - 1902). He studied this curve, also known as a
clothoid or Euler's Spiral, in connection with diffraction. Euler
applied a similar figure while measuring the elasticity of a spring.
The parametric equations for a generalized Cornu spiral are on the
right.
Similar integrals are named for Augustin Jean Fresnel (1788-1827), one
of the founders of the wave theory of light.
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The Spiral of
Cornu, a.k.a. Clothoids "are important curves used in
freeway and railroad construction. For example, a clothoid is
needed to make the gradual transition from a highway; which has zero
curvature, to the midpoint of a freeway exit, which has nonzero
curvature. A clothoid is clearly preferable to a path consisting
of straight lines and circles, for which the curvature is
discontinuous." (!!)
Alfred Gray
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Copyright Notice:
This
animation and all images within are under copyright by Cye Waldman and
may not be copied, electronically or otherwise, without his espress
permission.
Dr.
Cye Waldman
cye@att.net
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