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PEDAL OF A SURFACE OR A CURVE
The pedal (surface) of a surface or a curve
with respect to a point O is the locus of the feet of the lines passing by O perpendicular to the tangent planes of the surface
or the osculating planes of the curve
.
In the case of a surface, the pedal is the envelope of the spheres with diameter [OM0], when
M0 describes
(property that provides a construction of the tangent plane of the pedal).
In the case of a curve, the pedal is the circled surface composed of the circles with diameter [OM0],
perpendicular to the tangent to the curve at M0
, when M0 describes .
Example: the pedal of the ellipsoid with respect to its center is Fresnel's elasticity surface.
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© Robert FERRÉOL
2017