Re: [ATM] Raytracing Function

["Richard F.L.R. Snashall" <rflrs@rcn.com>]

Jim Burrows wrote:
> Let's get this based on reality.  The height y of the conic surface with 
> radius of curvature R, and conic constant b at zone radius x is the 
> solution of the quadratic equation
>
>          py² - 2Ry + x² = 0, with p = b + 1.
>
> If we assume R > 0, then the solution is y = x²/(R + sqrt( R² - 
> px²)).  Unfortunately in ray tracing, sign conventions may force R to be 
> negative - in that case, I'd use -R in the formula, then dredge up a mental 
> image to decide whether y is plus or minus.
>   
Actually, I don't bother; I have only considered solutions that
satisfy pcy < 1 (where c = 1/R).  The remaining cases with
solutions are extreme, I think; that's why I put out the question
about the magnitude -- if true, then I could use that as a
determining factor... I don't know how much more extreme the
cases could get.
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