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Thanks for the links. How would you translate the function:
y = cos(n*x*acos(x))
into POV syntax?
Thanks much,
Dennis
"gimi" <gim### [at] psico ch> wrote in message news:3E3### [at] psicoch...
> hi,
>
> i stumbled across this old scene files last week
> where i tried to implement an idea that Clifford
> Pickover mentions in one of his marvelous books
> ("Mazes for the Mind: Computers and the unexpected",
> Clifford A. Pickover, St. Martin's Press, New York).
>
> in chapter 45, "Squashed Worlds That Pack Infinity
> into a Cube", p.249), he describes a simple method
> to do exactly this.
>
> i was interested how various objects would look like
> in zenospace, and so i wrote this little scene.
> - feel free to improve or extend it!
>
> please note that there are two versions of the
> sphere function. - i guess that the second one
> is just a little faster. i did not verify this,
> though.
>
> BTW, there is more in cliff's books that also
> inspired me, he even did some raytracing himself.
> you'll find amazing pictures there! - to find out
> more, please see
> http://www.pickover.com/
> (his homepage)
> and
> http://RealityCarnival.Com
> (his newest homepage ;)
> and
> http://sprott.physics.wisc.edu/pickover/neoreality.html
> (a page about his neoreality novels)
> if you want to find out more about his work.
>
> ..and click on the links below to visit my own site,
> where you will find even more about raytracing,
> programming and other things i do!
>
>
> gimi
>
>
> - ok, and here is the source:
>
> <source>
> // zeno.pov
> // by gim### [at] psicoch - http://www.psico.ch
>
> #default {
> texture {
> pigment {
> color rgbt < .5, .5, .5, 0 >
> }
> finish {
> ambient .9 diffuse .1
> phong 0.4 phong_size 200
> specular .4 roughness .2
> }
> }
> }
>
>
> // infinite plane in a box
> // arguments:
> // a,b,c : plane (xyz) parameters,
> // r : plane distance,
> // as in "ax + by + cz = r"
> #declare f_zeno_plane = function(a,b,c, r, x,y,z) {
> a * atanh(x)
> + b * atanh(y)
> + c * atanh(z)
> + r
> }
>
>
> // finite sphere in a box - first version
> // arguments:
> // a,b,c : sphere center point
> // r : sphere radius
> #declare f_zeno_sphere1 = function(a,b,c, r, x,y,z) {
> sqrt(
> pow(atanh(x)-a, 2)
> + pow(atanh(y)-b, 2)
> + pow(atanh(z)-c, 2)
> ) - r
> }
>
>
> // finite sphere in a box - second version
> // arguments:
> // a,b,c : sphere center point
> // r : sphere radius
> #declare f_zeno_sphere2 = function(a,b,c, r, x,y,z) {
> (
> pow(atanh(x)-a, 2)
> + pow(atanh(y)-b, 2)
> + pow(atanh(z)-c, 2)
> ) - pow(r, 2)
> }
>
>
> isosurface {
>
> function {
> f_zeno_plane(
> 4, 16, -8, +2,
> x,y,z
> )
> }
>
> // cut off "noise"
> contained_by { box { -.999999, +.999999 } }
> threshold 0
> accuracy .01
> evaluate 1, 1.1, 0.90
> translate -2.1*x
> }
>
>
> isosurface {
>
> function {
> f_zeno_sphere1(
> 0.8, -0.5, -1, 1.5,
> x,y,z
> )
> }
>
> // cut off "noise"
> contained_by { box { -.999999, +.999999 } }
> threshold 0
> accuracy .01
> evaluate 10, 1.1, 0.90
> }
>
>
> isosurface {
>
> function {
> f_zeno_sphere2(
> 0.8, -0.5, +1, 1.5,
> x,y,z
> )
> }
>
> // cut off "noise"
> contained_by { box { -.999999, +.999999 } }
> threshold 0
> accuracy .01
> evaluate 10, 1.1, 0.90
> translate +2.1*x
> }
>
>
> sky_sphere {
> pigment {
> gradient y ramp_wave
> color_map {
> [ 0.000/6 color rgbft <1,1,0, 0,0> ]
> [ 1.000/6 color rgbft <0,1,0, 0,1> ]
> [ 1.001/6 color rgbft <0,1,0, 0,1> ]
> [ 2.000/6 color rgbft <0,1,1, 0,0> ]
> [ 3.000/6 color rgbft <0,0,1, 0,1> ]
> [ 3.001/6 color rgbft <0,0,1, 0,1> ]
> [ 4.000/6 color rgbft <1,0,1, 0,0> ]
> [ 5.000/6 color rgbft <1,0,0, 0,1> ]
> [ 5.001/6 color rgbft <1,0,0, 0,1> ]
> [ 6.000/6 color rgbft <1,1,0, 0,0> ]
> }
> }
> }
>
>
> camera {
> location <0,4,-8>
> look_at 0
> angle 45
> }
>
>
> light_source {
> <0,10,0>
> color rgb 1
> }
> </source>
>
> --
> mailto:gim### [at] psicoch
> http://www.psico.ch/
> http://psico.servehttp.com/
>
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