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