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Biconic surface

The biconic surface is an asymmetric surface that has indpendent curvature and conic constant in each of the x and y directions. The sag of the biconic surface is given by the following equation

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In the x-direction (y=0) the sag is a conic with curvature cx and conic constant kx. In the y-direction (x=0) the sag is a conic with curvature cy and conic constant ky.

The y curvature and conic constant are specified on the surface table of the surface data editor. The x curvature and conic constant are specified on the parameters table.

Parameters

Rx
Radius of curvature in the x direction, equal to 1/cx
kx
Conic constant in the x direction

By setting one of the curvature parameters to zero, a cylindrical surface results.

The shape of a conic is given by the following table:

k>0 ε>1 oblate ellipse
k=0 ε=1 circle
-1<k<0 0<ε<1 prolate ellipse
k =-1 ε=0 parabola
k<-1 ε<0 hyperbola

See also