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> How do I split such a function into parts? For instance
It's already in parts.
What you can do is limit the range of U and V over which those functions are
evaluated.
If you limit U or V to the range from 0 to 0, then you will get a circle.
Swap U and V, and you get "the other" circle
Limit the ranges of both to a fraction of (2*pi), and you get a curved patch
that only covers part of the torus' surface.
Keep one full 2*pi range, and limit the other, and you get a "hoop sweep" around
the torus, one way or the other.
The set of macros takes this concept and just does it 4 times (0, +TStep,
+PStep, +both) to generate 4 corners, and fills that in with 2 smooth triangles.
See clipka's favorite link:
https://nylander.wordpress.com/2008/08/25/crosssectionofthequinticcalabiyaumanifold/
There is no magic.
Look back through the forums, and you can see that we've been exploring this
basic concept  for years.
#version version;
#include "colors.inc"
light_source {
<5, 10, 20>
color White
fade_distance 20
fade_power 2
}
camera {
location <0, 2, 35>
look_at <0, 0, 10>
right x*image_width/image_height
up y
}
#declare U1 = 0; // small radius
#declare U2 = 2*pi; //
#declare V1 = 0; // large radius
#declare V2 = 2*pi; //
#declare r0 = 10;
#declare r1 = 4;
#declare SphereRadius = 0.1;
// Create a set of points on the surface of a Torus
#declare X = function (T, P, R, r) {cos(T) * ( R + r * cos(P) )}
#declare Y = function (T, P, R, r) {sin(T) * ( R + r * cos(P) )}
#declare Z = function (T, P, r, n) {r * sin(P)}
#declare TStep = 0.02;
#declare PStep = 0.05;
#for (Theta, U1, U2, TStep)
#for (Phi, V1, V2, PStep)
#local XYandZResultOfParametricFunctionsEvaluatedForThisImmediateUandV =
<X (Theta, Phi, r0, r1), Y (Theta, Phi, r0, r1), Z (Theta, Phi, r0, r1)>;
sphere {XYandZResultOfParametricFunctionsEvaluatedForThisImmediateUandV
SphereRadius pigment {White}}
#end
#end
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On 9/13/2018 7:59 PM, Mike Horvath wrote:
> I have attached my scene file so far. It already calculates the
> positions of the planets. However, I want to create parametric tori
> showing the orbits of each planet over a span of time.
>
> I believe I have all the pieces already. But how do I convert the
> calculations into the functions a parametric object requires? For
> example, what do I use for u and v?
>
> Thanks.
>
>
> Mike
The latest version of the scene can now be downloaded from the Object
Collection.
http://lib.povray.org/searchcollection/index2.php?objectName=SolarSystemOrrery&version=1.0&contributorTag=SharkD
Mike
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I have textures, but do not know how to orient them with respect to the
axial tilt, orbit and sun. Is anyone familiar with how to do this?
Mike
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On 15/09/2018 11:43, Mike Horvath wrote:
> I have textures, but do not know how to orient them with respect to the
> axial tilt, orbit and sun. Is anyone familiar with how to do this?
>
>
> Mike
For Z up Left handed scenes.
texture {
pigment {
image_map{
png "F:\Graphics\B3D Data\Maps\Planets\Earth\EarthMap2.png"
interpolate 2
map_type 1
}
rotate <20.000,0.000,0.000>
}
Then for orientation in an orbit. Rotate the sphere the planet texture
will follow.

Regards
Stephen
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On 15/09/2018 11:58, Stephen wrote:
> rotate <20.000,0.000,0.000>
That might be 19 to 21 not rotate 20*x

Regards
Stephen
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On 9/15/2018 6:58 AM, Stephen wrote:
> On 15/09/2018 11:43, Mike Horvath wrote:
>> I have textures, but do not know how to orient them with respect to
>> the axial tilt, orbit and sun. Is anyone familiar with how to do this?
>>
>>
>> Mike
>
> For Z up Left handed scenes.
>
>
> texture {
> pigment {
> image_map{
> png "F:\Graphics\B3D Data\Maps\Planets\Earth\EarthMap2.png"
> interpolate 2
> map_type 1
> }
> rotate <20.000,0.000,0.000>
> }
>
> Then for orientation in an orbit. Rotate the sphere the planet texture
> will follow.
>
Thanks. But which direction does the axis tilt with respect to the Sun
on a given day?
Mike
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On 15/09/2018 13:11, Mike Horvath wrote:
> On 9/15/2018 6:58 AM, Stephen wrote:
>> On 15/09/2018 11:43, Mike Horvath wrote:
>>> I have textures, but do not know how to orient them with respect to
>>> the axial tilt, orbit and sun. Is anyone familiar with how to do this?
>>>
>>>
>>> Mike
>>
>> For Z up Left handed scenes.
>>
>>
>> texture {
>> pigment {
>> image_map{
>> png "F:\Graphics\B3D Data\Maps\Planets\Earth\EarthMap2.png"
>> interpolate 2
>> map_type 1
>> }
>> rotate <20.000,0.000,0.000>
>> }
>>
>> Then for orientation in an orbit. Rotate the sphere the planet texture
>> will follow.
>>
>
> Thanks. But which direction does the axis tilt with respect to the Sun
> on a given day?
>
>
Earth currently has an axial tilt of about 23.4° and the angle does not
change. With respect to the Sun on a given day, it depends on there it
is in its orbit.
https://en.wikipedia.org/wiki/Axial_tilt#Earth
So if you start your Planetarium at the summer or winter equinox. The
mechanics will take care of themselves.
I think. :)

Regards
Stephen
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Latest version is attached. It is *very* close, but the Earth is off by
about one month's worth of travel.
Here is the document I am using as a guide:
https://ssd.jpl.nasa.gov/txt/aprx_pos_planets.pdf
And I am using this website to compare my render to:
https://inthesky.org/solarsystem.php
Set it to JD 2458376.5, which is equivalent to A.D. 2018 Sep 15.
I am not sure where my calculations have gone wrong.
Mike
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Attachments:
Download 'orrery_sphere_trail_new.pov.txt' (25 KB)


 
 




 
 


On 9/16/2018 2:31 PM, Mike Horvath wrote:
> Latest version is attached. It is *very* close, but the Earth is off by
> about one month's worth of travel.
>
> Here is the document I am using as a guide:
>
> https://ssd.jpl.nasa.gov/txt/aprx_pos_planets.pdf
>
> And I am using this website to compare my render to:
>
> https://inthesky.org/solarsystem.php
>
> Set it to JD 2458376.5, which is equivalent to A.D. 2018 Sep 15.
>
> I am not sure where my calculations have gone wrong.
>
>
> Mike
If you zoom out, Jupiter is also in the wrong place, so Maybe my results
are *not* so close after all.
Mike
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Updated the scene. It is working correctly now.
:)
Mike
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Attachments:
Download 'orrery_sphere_trail_b.pov.txt' (29 KB)


 
 




 

