Toroidal Surface Odd Asphere

A toroidal odd asphere surface consist of a rectangular surface with a possibly aspheric toroidal shape. This is similar to a toroidal surface but includes odd asphere terms and only includes terms up to y⁸. The surface is defined by a curve in the YZ plane which is then rotated about an axis parallel to the Y axis but displaced by a distance R; the radius of rotation. The curve in the YZ plane for this surface is defined by:

where c is the reciprocal of the radius of curvature in YZ plane.

The surface is defined by 13 parameters:

Parameter #	Description	Face Name	Face #
1	The X Half-Width in lens units.	All Faces	0
2	The Y Half-Width in lens units.	All Faces	0
3 - 4	Unused.	All Faces	0
5, 6, 7	The radius of rotation, radius of curvature, and conic for the surface.	All Faces	0
8 - 15	The coefficients on the powers of y for the surface.	All Faces	0

To make either the radius of rotation or radius of curvature flat; use a value of zero. Note a cylindrical surface results if the radius of rotation is set to zero.

The reference coordinate is the center of the front face. Face Numbers: All faces Face 0.

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• Torus Surface