Toroidal Surface
A toroidal surface consists of a rectangular surface with a possibly aspheric toroidal shape. A toroidal 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 is defined by:
where c is the reciprocal of the radius of curvature in YZ plane.
The toroidal surface is defined by 14 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 - 14 | 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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