SharkD schrieb:
> The following function transforms a sphere such that it is expanded
> logarithmically along the y axis. What I would like to do next is to
> expand a sphere based on its distance from the origin instead. Any 
> ideas? Of course, if the sphere is located a the origin like my example 
> it will still look like a sphere.

You'd need to (a) define the center of the sphere, (b) compute the 
desired radius from the distance to the origin, (c) redefine your 
Temp_fnc1 to take into account a radius, and (e) offset the parameters 
to Temp_fnc1 by the center, as in:

#local Center = <...>; // (a)
#local Radius = log(vlength(Center)+1) / log(2); // (b)
#local Temp_fnc1 = function
{
     1 - min(1, sqrt(x*x + y*y + z*z)/Radius) // (c)
}
#local Temp_fnc3 = function
{
     Temp_fnc1(x-Center.x,y-Center.y,z-Center.z) // (d)
}

I guess this definition for Temp_fnc3 might run into problems though, 
due to POV-Ray's general inability to use vector stuff in functions; you 
may need to define temporary variables for the Center vector components, 
as in:

#local CenterX = Center.x;
#local CenterY = Center.y;
#local CenterZ = Center.z;
#local Temp_fnc3 = function
{
     Temp_fnc1(x-CenterX,y-CenterY,z-CenterZ)
}


Note that this will produce just a single sphere. To get multiples of 
them, you might want to add multiple instances of that function, as in:

#macro Temp_Fnc(Center)
   #local Radius = log(vlength(Center)+1)
   #local Temp_fnc1 = function
   {
     1 - min(1, sqrt(x*x + y*y + z*z)/Radius)
   }
   #local CenterX = Center.x;
   #local CenterY = Center.y;
   #local CenterZ = Center.z;
   ( Temp_fnc1(x-CenterX,y-CenterY,z-CenterZ) )
#end

#local Temp_fnc3 = function
{
   Temp_Fnc(<0,1,0>) +
   Temp_Fnc(<0,3,0>) +
   Temp_Fnc(<0,10,0>) +
   ...
}

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