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A

is a 4th order quartic polynomial shape that looks like a donut or inner tube. Because this shape is so useful and quartics are difficult to define, POV-Ray lets you take a short-cut and define a torus by:**torus**

*TORUS:***torus {***Major***,***Minor [TORUS_MODIFIER...]***}***TORUS_MODIFIER:*

|**sturm***OBJECT_MODIFIER*

**
**

where *Major* is a float value giving the major radius and *Minor* is a float specifying the minor radius. The major radius extends from the center of the hole to the mid-line of the rim while the minor radius is the radius of the cross-section of the rim. The torus is centered at the origin and lies in the x-z-plane with the y-axis sticking through the hole.

Major and minor radius of a torus.

The torus is internally bounded by two cylinders and two rings forming a thick cylinder. With this bounding cylinder the performance of the torus intersection test is vastly increased. The test for a valid torus intersection, i.e. solving a 4th order polynomial, is only performed if the bounding cylinder is hit. Thus a lot of slow root solving calculations are avoided.

Calculations for all higher order polynomials must be very accurate. If the torus renders improperly you may add the keyword

to use POV-Ray's slower-yet-more-accurate Sturmian root solver.**sturm**

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