Thank you very much
didnt think of the if function and isosurfaces
its exactly what i need...

Mike Williams <mik### [at] nospamplease> wrote in message
news:0o0### [at] econymdemoncouk...
> Wasn't it Oded who wrote:
> >This is more of of a mathematical problem than a practical one:
> >can any one think of a better way to create the following object type:
> >I was thinking, while trying to convert a dodchahedron to a 3d star, of
an
> >object that will give the user higher control of defining 'in' and 'out'
in
> >CSG objects. in pov-ray you can only define intersections, inverses and
> >unions.
> >I was thinking of more complicated rules, eg:
> >    a point A is "inside" function (a1....a12) if it is         inside 11
> >out of 12 objects.
> >what i needed to do for that was to define a union of 12 intersections of
6
> >objects which was was quite dirty (mathematically speaking)
> >eventually i ended up writing a c program to raytrace these objects
defined
> >soly by the 12 objects.
>
> Here's a method using MegaPov.
>
> Use the "if" isosurface operator 12 times and set the threshold to 1.5.
>
> First of all you need to express each of your objects a1 to a12 as
> isosurface functions. In the case of a stellated dodecahedron your
> objects are planes, so that's not too hard. It helps if you ensure that
> the point <0,0,0> is always on the "inside" of your objects, i.e.
> a1(0,0,0)<0. E.g. for the two horizontal planes "y-1=0" and "y+1=0" use
> functions  "y-1" and "-y-1"; the second plane is inverted so that
> <0,0,0> is on the inside.
>
> The expression "if (a1, 1, 0)" returns the value 1 when a1>0 and returns
> 0 when a1<0. I.e. it returns 1 for points outside the a1 object and
> returns 0 for points that are inside.
>
> If we add together several "if"s, like
>  "function {if(a1,1,0) + if(a2,1,0) + ... + if(a12,1,0)}"
> we get the number of objects which the point is outside. Set the
> Threshold to 1.5 and you get the set of points which are outside at
> least 1 but less than 2 of the objects. (If you set the threshold to an
> integer value then there's a volume of points which satisfy the function
> and you get slightly different results.)
>
> Use "method 1". "method 2" gives awful results because the max_gradient
> needs to be set to infinity. "method 2 eval" gives good results but
> takes a very long time because it evaluates the max_gradient to have a
> very high value.
>
> A slight problem with this method is that some parts of the object seem
> to be erroneously unlit. I guess it's getting confused about which side
> of the surface is the interior.
>
>
> --
> Mike Williams
> Gentleman of Leisure

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