









 
 




 
 


How would I create a tube in the shape of a logarithmic spiral? It
should have an even thickness. Do I need to use an isosurface once
again? Thanks.
Mike
Post a reply to this message


 
 




 
 


Mike Horvath <mik### [at] gmailcom> wrote:
> How would I create a tube in the shape of a logarithmic spiral? It
> should have an even thickness. Do I need to use an isosurface once
> again? Thanks.
If you have the parametric equation already for a spiral isosurface and you just
a need a smooth tube, then a difference of two sphere sweeps would render *much*
faster than an isosurface.
Just make the radius of the outer one a bit larger and the length of the
differenced sweep a bit longer, so you get open ends (or just use other
differencing objects to snip off the ends).
Maybe something like this nonlogarithmic spiral:
#macro Spherical_Spiral(turns, outer_rad, tube_rad, incr)
#local pt_cnt = int(pi/incr+0.5);
#local tt = 0;
sphere_sweep {
cubic_spline
pt_cnt
#while (tt < pi)
#local xt = outer_rad * cos(turns*2*tt) * sin(tt);
#local yt = outer_rad * sin(turns*2*tt) * sin(tt);
#local zt = outer_rad * cos(tt);
<xt, yt, zt> tube_rad
#local tt = tt + incr;
#end
tolerance 0.1
}
#end
difference {
object { Spherical_Spiral(5, 3, 0.12, 0.03) pigment {color Red} }
object { Spherical_Spiral(5, 3, 0.10, 0.03) pigment {color Blue} }
box {1, 1 scale 12 translate x*12}
rotate y*40
}
Cheers,
Rob
Post a reply to this message


 
 




 
 


Mike Horvath <mik### [at] gmailcom> wrote:
> How would I create a tube in the shape of a logarithmic spiral? It
> should have an even thickness. Do I need to use an isosurface once
> again? Thanks.
>
>
> Mike
I think you HAVE TO use a parametric or a loop, since you're going to need angle
values in your equation greater than tau, else you'll get a "circle of values"
rather than a "spiral of values" due to the atan2 in the implicit form required
for evaluating an isosurface.
so following:
http://news.povray.org/povray.newusers/thread/%3Cweb.59c7e943ff4768ea832bdcda0%40news.povray.org%3E/?mtop=418031&moff=1
0
this didn't work  it just gives an Archimedian spiral.
camera {orthographic
location <0,10,0.1>
look_at 0
angle 90}
light_source {<0, 10, 10> rgb 1 shadowless}
plane {y, 1 pigment { checker rgb 0.5, rgb 1 }}
#declare RADIUS = 5;
#declare Thickness = 0.1;
#declare Freq = 2;
#declare Spirals = 1;
#declare Logarithmic =
function {
Thickness  y*y*Freq 
pow (
sin (
sqrt (x*x+z*z) * Freq 
(pi * exp (0.15 * atan2 (z,x) ) )
)
, 2)
}
#declare Archimedian = function {(Thickness  y*y*Freq 
pow(sin(sqrt(x*x+z*z)*Freq 
(0.5*Spirals*atan2(z,x)) ),2))}
isosurface {
function {Logarithmic (x, y, z)}
accuracy 0.01
threshold 0 // default value
max_gradient 102
contained_by {sphere {<0,0,0>, RADIUS}}
open
texture {pigment {rgb <1, 0, 0>} finish {specular 0.4}}
}
So you'll need to adapt the parametric equations to a sphere sweep or a
parametric, or just a loop of spheres.
#declare SpiralX = function (Theta) {exp(0.15*Theta)*0.1*cos(Theta)};
#declare SpiralY = function (Theta) {exp(0.15*Theta)*0.1*sin(Theta)};
#for (T, 0, 10*tau, 0.01)
#local X = SpiralX (T);
#local Z = SpiralY (T);
sphere {<X, 0, Z> 0.1 pigment {rgb <1, 0, 0>}}
#end
[* Caution, this conclusion is based on a processor functioning on less than 1
cup of coffee]
Post a reply to this message


 
 




 
 


On 1/26/2021 7:42 PM, Robert McGregor wrote:
> Mike Horvath <mik### [at] gmailcom> wrote:
>> How would I create a tube in the shape of a logarithmic spiral? It
>> should have an even thickness. Do I need to use an isosurface once
>> again? Thanks.
>
> If you have the parametric equation already for a spiral isosurface and you just
> a need a smooth tube, then a difference of two sphere sweeps would render *much*
> faster than an isosurface.
>
> Just make the radius of the outer one a bit larger and the length of the
> differenced sweep a bit longer, so you get open ends (or just use other
> differencing objects to snip off the ends).
>
> Maybe something like this nonlogarithmic spiral:
>
> #macro Spherical_Spiral(turns, outer_rad, tube_rad, incr)
> #local pt_cnt = int(pi/incr+0.5);
> #local tt = 0;
> sphere_sweep {
> cubic_spline
> pt_cnt
> #while (tt < pi)
> #local xt = outer_rad * cos(turns*2*tt) * sin(tt);
> #local yt = outer_rad * sin(turns*2*tt) * sin(tt);
> #local zt = outer_rad * cos(tt);
> <xt, yt, zt> tube_rad
> #local tt = tt + incr;
> #end
> tolerance 0.1
> }
> #end
>
> difference {
> object { Spherical_Spiral(5, 3, 0.12, 0.03) pigment {color Red} }
> object { Spherical_Spiral(5, 3, 0.10, 0.03) pigment {color Blue} }
> box {1, 1 scale 12 translate x*12}
> rotate y*40
> }
>
>
> Cheers,
> Rob
>
>
Good idea thank you!
Another option is to create a mesh parametrically.
Mike
Post a reply to this message


 
 




 

