POV-Ray : Newsgroups : povray.advanced-users : Square roots of negative numbers in isosurfaces? : Re: Square roots of negative numbers in isosurfaces? Server Time
5 Sep 2024 20:57:55 EDT (-0400)
  Re: Square roots of negative numbers in isosurfaces?  
From: Mike Williams
Date: 14 Jan 2000 21:20:24
Message: <FslWUEAg43f4EwTB@econym.demon.co.uk>
Wasn't it David Fontaine who wrote:
>What I think POV *should* do is not include these areas in the graph. Say I
>want to graph a hemisphere on my TI-89, I do x^2+y^2+z^2=1, z^2=-x^2-y^2+1,
>z=sqrt(1-x^2-y^2), and graph it and it gives me my hemisphere, and the area
>*outside* the hemisphere is ignored (not rendered) because it is sqrt(neg).
>Because if people want it to work the other way they can always just make
>it sqrt(abs(x)) instead of sqrt(x).

That might be possible when using the function as an isosurface, but
such a function can also be used as a pattern for a pigment or normal.
When a function has no solution in a region of space you could ignore it
if you're using that function to define a surface, but what could you do
if there's a point where the surface exists but the pigment and/or
normal doesn't. E.g.

sphere {0,1
        pigment {
            function {noise3d(x^0.5/K, y/K, z/K)}
            colour_map{[0 rgb <1,0,0>][1 rgb <1,1,0>]}
            }    
        normal {
            function {noise3d(x^0.5/K, y/K, z/K)}
            }
       }     

-- 
Mike Williams + #
Gentleman of Leisure


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