In newusers there was recently a post about creating an isosurface with 
the function "cos(x) + cos(y) + cos(z)". I decided to grab that function 
and play with the new to povr fork's f_boxb(). A function intended for 
use in specifically with isosurfaces.

f_boxb() is a function which takes another function as an input and 
encloses it in a box which in part or in total is expected to be smaller 
than the isosurface contained_by shape.

The contained_by shape can itself be used to clip away sides of the now 
boxed original function to expose an inner structure. I did this on the 
top and front in the attached image.

Bill P.

Aside: The gradient of "cos(x) + cos(y) + cos(z)" is relatively high as 
isosurface functions go.

// Code ONLY works with the povr fork
...
#include "functions.inc"
// Function f_boxb defined in functions.inc
#declare Fn03 = function (x,y,z) { (cos(x) + cos(y) + cos(z))*-1 }
#declare Fn04 = function (x,y,z) {
     f_boxb(x,y,z,0.6,0.667,1,-0.02,0,0,Fn03(x*20,y*20,z*20),0.010)
}
#declare Iso99 = isosurface {
     function { Fn04(x,y,z) }
     contained_by { box { <-1,-1,-0.95>,<1,1/3,1> } }
     threshold 0
     accuracy 0.00017
     max_gradient 33.3
}
#declare SorrellBrown = srgb <0.80784,0.72549,0.56078>;
#declare Pigment02 = pigment { color SorrellBrown }
#declare Normal02 = normal { granite  0.31 scale 0.177 }
#declare Finish02 = finish { phong 0.33 }
#declare Texture02 = texture {
     pigment { Pigment02 }
     finish { Finish02 }
     normal { Normal02 }
}
#declare Obj02 = object { Iso99 texture { Texture02 } }
...

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Attachments:
Download 'threecosiso.jpg' (108 KB)

Preview of image 'threecosiso.jpg'

William F Pokorny <ano### [at] anonymousorg> wrote:

> f_boxb() is a function which takes another function as an input and
> encloses it in a box which in part or in total is expected to be smaller
> than the isosurface contained_by shape.
>
> The contained_by shape can itself be used to clip away sides of the now
> boxed original function to expose an inner structure. I did this on the
> top and front in the attached image.


That looks cool.

Now all you need to do is interlace that function with some white ovoids with
micronormals, and you sell those by the case for $50+ each.

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On 2/19/23 14:38, Bald Eagle wrote:
> That looks cool.

Thanks.

> 
> Now all you need to do is interlace that function with some white ovoids with
> micronormals, and you sell those by the case for $50+ each.

:-)

---

 > Aside: The gradient of "cos(x) + cos(y) + cos(z)" is relatively high
 > as isosurface functions go.

Aside to my aside... We can lower the gradient in the above case. By 
noticing the function values swing between -3 and 3 in a symmetrical 
way, we can code:

#declare Fn03 = function (x,y,z) {
     (cos(x) + cos(y) + cos(z))*(1/3)
}

Which re-maps the values to -1 to 1. Why not *1/9 you ask for an even 
lower gradient? Well, you can, but it gets to be a gradient game with 
isosurfaces after some point. It tends' to help to get everything into a 
more common value space - and I aim for -1 to 1 as a rule - as in that 
space functions tend to play better together.

Bill P.

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