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Sturm

Some of POV-Ray's objects allow you to choose between a fast but sometimes inaccurate root solver and a slower but more accurate one. This is the case for all objects that involve the solution of a cubic or quartic polynomial. There are analytic mathematical solutions for those polynomials that can be used.

Lower order polynomials are trivial to solve while higher order polynomials require iterative algorithms to solve them. One of those algorithms is the Sturmian root solver. For example:

  blob {

    threshold .65

    sphere { <.5,0,0>, .8, 1 }

    sphere { <-.5,0,0>,.8, 1 }

    sturm

  }

The keyword may optionally be followed by a float expression which is interpreted as a boolean value. For example sturm off may be used to force it off. When the keyword is specified alone, it is the same as sturm on. The default no sturm is specified is off.

The following list shows all objects for which the Sturmian root solver can be used.

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