In article <cfh### [at] tritonimagicode>,
 Christoph Hormann <chr### [at] gmxde> wrote:

> I am quite sure you will miss some intersections this way (cases where 
> the function is negative only in a very small interval along the ray and 
> is positive otherwise for example).

You also miss roots with the bisection method. This is just one of the 
things you have to deal with when finding roots numerically.

However, if the function is monotonic on the interval you start with, 
either entirely increasing or entirely decreasing, there is only one 
root possible and this method will only tighten the interval closer to 
the root. If you break the function up into small enough intervals, for 
example with the variant of the bisection method the current solver 
uses, losing roots is rarely a problem. Neither method will find roots 
where the function just touches 0 without crossing it, though.

-- 
Christopher James Huff <cja### [at] earthlinknet>
http://home.earthlink.net/~cjameshuff/
POV-Ray TAG: <chr### [at] tagpovrayorg>
http://tag.povray.org/

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