Wasn't it Tom Melly who wrote:

>It occured to me that getting an iso-surface function to output a mesh-file
>rather than generating a scene could be a fairly trivial patch. Is this correct?
>What am I missing?

Such a facility is available for parametric isosurfaces.

Is it possible to convert an arbitrary isosurface function into
parametric co-orinates?

-- 
Mike Williams
Gentleman of Leisure

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> Such a facility is available for parametric isosurfaces.
>
> Is it possible to convert an arbitrary isosurface function into
> parametric co-orinates?

I've been there. There is no trivial method for achieving this. It gets ugly
just as soon as you leave the trigonometric domain.

Ruy

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Wasn't it Ruy who wrote:
>> Such a facility is available for parametric isosurfaces.
>>
>> Is it possible to convert an arbitrary isosurface function into
>> parametric co-orinates?
>
>I've been there. There is no trivial method for achieving this. It gets ugly
>just as soon as you leave the trigonometric domain.

I think it might be possible for functions that can be solved for one of
the variables. I.e. if you can convert from

                F(x,y,z) = 0
to
                z = G(x,y)

Then you should be able to express the function as the parametrics

                x = u
                y = v
                z = G(u,v)

For example, the sphere given by

        #declare  F = function {x*x + y*y + z*z - 1}

can be converted into the two sets of parametrics

        #declare Fx=function(U,V){U}
        #declare Fy=function(U,V){V}
        #declare Fz=function(U,V){sqrt(1-U*U-V*V)}
and
        #declare Fx=function(U,V){U}
        #declare Fy=function(U,V){V}
        #declare Fz=function(U,V){-sqrt(1-U*U-V*V)}

(One using the +ve sqrt and one the -ve)

Parts of this can be converted into a mesh using Ingo's include file.
Unfortunately it freaks out when asked to interpret regions of <U,V>
where the surface doesn't exist.

#include "functions.inc"

camera { location  <1, 1, -2> look_at <0, 0, 0>}

sky_sphere { pigment {
    function{abs(y)}
    color_map { [0.0 color blue 0.6] [1.0 color rgb 1] } 
  }
}

light_source {<-100,200,-100> colour rgb 1}


// a sphere
#declare  F = function {x*x + y*y + z*z - 1}

//converted to a parametric
#declare Fx=function(U,V){U}
#declare Fy=function(U,V){V}
#declare Fz=function(U,V){sqrt(1-U*U-V*V)}

#declare Umin=-0.7;
#declare Umax=0.7;
#declare Vmin=-0.7;
#declare Vmax=0.7;

#declare Iter_U = 20;
#declare Iter_V = 20;

//Converted to a mesh
#include "param.inc"
Parametric()

object {Surface
  pigment {rgb 0.9}
  finish {phong 0.5 phong_size 10}
  no_shadow
}


//The other side
#declare Fz=function(U,V){-sqrt(1-U*U-V*V)}

Parametric()

object {Surface
  pigment {rgb 0.9}
  finish {phong 0.5 phong_size 10}
  no_shadow
}

-- 
Mike Williams
Gentleman of Leisure

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Mike Williams <mik### [at] nospamplease> wrote:
: if you can convert from

:                 F(x,y,z) = 0
: to
:                 z = G(x,y)

... then it's just a heightfield which is pretty easy to create. You
can even use the function image feature for creating an actual height_field
object (which should render even faster than a mesh).

-- 
#macro M(A,N,D,L)plane{-z,-9pigment{mandel L*9translate N color_map{[0rgb x]
[1rgb 9]}scale<D,D*3D>*1e3}rotate y*A*8}#end M(-3<1.206434.28623>70,7)M(
-1<.7438.1795>1,20)M(1<.77595.13699>30,20)M(3<.75923.07145>80,99)// - Warp -

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Just as a thought, I think tha'ts true, but not all isosurface's are
representable with heightfields .. many of them are concave.

I think that gets back to 'tesselation isn't trivial'.

However, for many ISO's, I think this would be a good idea; it could reduce
rendering time.

                  == John ==

"Warp" <war### [at] tagpovrayorg> wrote in message
news:3c2b75cd@news.povray.org...
> Mike Williams <mik### [at] nospamplease> wrote:
> : if you can convert from
>
> :                 F(x,y,z) = 0
> : to
> :                 z = G(x,y)
>
> ... then it's just a heightfield which is pretty easy to create. You
> can even use the function image feature for creating an actual
height_field
> object (which should render even faster than a mesh).
>
> --
> #macro M(A,N,D,L)plane{-z,-9pigment{mandel L*9translate N color_map{[0rgb
x]
> [1rgb 9]}scale<D,D*3D>*1e3}rotate y*A*8}#end M(-3<1.206434.28623>70,7)M(
> -1<.7438.1795>1,20)M(1<.77595.13699>30,20)M(3<.75923.07145>80,99)// -
Warp -

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John D. Gwinner <jgw### [at] dazsicom> wrote:
: Just as a thought, I think tha'ts true, but not all isosurface's are
: representable with heightfields .. many of them are concave.

  All functions that can be reduced to z = G(x,y) are. Those that can't
be reduced to that, arent'. Simple :)

-- 
#macro M(A,N,D,L)plane{-z,-9pigment{mandel L*9translate N color_map{[0rgb x]
[1rgb 9]}scale<D,D*3D>*1e3}rotate y*A*8}#end M(-3<1.206434.28623>70,7)M(
-1<.7438.1795>1,20)M(1<.77595.13699>30,20)M(3<.75923.07145>80,99)// - Warp -

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