On 9/15/2018 1:07 PM, Mike Horvath wrote:
> I'm trying to adapt the following PDF to POV-Ray code for my 
> planetarium/orrery.
> 
> https://ssd.jpl.nasa.gov/txt/aprx_pos_planets.pdf
> 

In Step 6 of that PDF, it gives an equation on how to convert between 
ecliptic coordinates and J2000 coordinates.

What is the inverse of that equation, and how do I change it into a 
series of `rotate` commands instead?

Thanks.



Mike

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On 9/20/2018 8:17 PM, Mike Horvath wrote:
> On 9/15/2018 1:07 PM, Mike Horvath wrote:
>> I'm trying to adapt the following PDF to POV-Ray code for my 
>> planetarium/orrery.
>>
>> https://ssd.jpl.nasa.gov/txt/aprx_pos_planets.pdf
>>
> 
> In Step 6 of that PDF, it gives an equation on how to convert between 
> ecliptic coordinates and J2000 coordinates.
> 
> What is the inverse of that equation, and how do I change it into a 
> series of `rotate` commands instead?
> 
> Thanks.
> 
> 
> 
> Mike

I found the inverse on Wikipedia.

https://en.wikipedia.org/wiki/Ecliptic_coordinate_system#Conversion_between_celestial_coordinate_systems

Still not sure how to replace the equation with a series of `rotate` 
commands though.


Mike

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Found a document with a table of values:

https://astropedia.astrogeology.usgs.gov/download/Docs/WGCCRE/WGCCRE2009reprint.pdf

The pertinent variables are alpha, delta and W. What do I do with these 
variables? Dunno for sure. This document provides a formula:

https://depositonce.tu-berlin.de/bitstream/11303/6237/4/burmeister_steffi.pdf

I /think/ I need to rotate around the z-axis by W, around the x-axis by 
(90-δ), and around the z-axis again by (90+α), in that order. Lastly, an 
additional rotation (around the x-axis?) by 23.43928 degrees must be 
done to get the body out of the ICRF frame and into the ecliptic frame.

But I still don't know the starting conditions. I.e. before applying the 
transformations, should the globe's North Pole point upward? Should the 
intersection of the Prime Meridian and Equator lie along the x-axis? 
Also, am I wrong, and should I perform the inverse matrix calculations 
instead? Either way, I have not gotten results that match what I see in 
Celestia for the same Julian Date.


Mike

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Le 25/09/2018 à 07:39, Mike Horvath a écrit :
> Found a document with a table of values:
> 
> https://astropedia.astrogeology.usgs.gov/download/Docs/WGCCRE/WGCCRE2009reprint.pdf 
> 
> 
> The pertinent variables are alpha, delta and W. What do I do with these 
> variables? Dunno for sure. This document provides a formula:
> 
> https://depositonce.tu-berlin.de/bitstream/11303/6237/4/burmeister_steffi.pdf 
> 

Read start of 1.3, alpha, delta & W are defined there.

> 
> I /think/ I need to rotate around the z-axis by W, around the x-axis by 
> (90-δ), and around the z-axis again by (90+α), in that order.

W is the "day" part of the planet, adjusting the prime meridian.
Right-handed system, so, yes, W is for z-axis when applied first.
Otherwise, it would be applied along the rotation axis of the planet 
once transformed from z by alpha & delta.

Figure 1.3 , page 11

 From the point gamma on ICRF equator, starting sphere, the axis of 
rotation of the planet is located at 90°+alpha, for an amount of 
90°-delta. (a single tilting of the planet axis, along a single 
perpendicular axis)

If I assert +x is gamma at start, +z north, you have to apply a rotation 
along v_rotate( y, alpha*z) of 90°-delta, then a rotation of W along the 
new pole axis.

You can of course transfer the W part before the other rotation, as it 
is simpler to use z.


> Lastly, an 
> additional rotation (around the x-axis?) by 23.43928 degrees must be 
> done to get the body out of the ICRF frame and into the ecliptic frame.

That's a change of referential, the matrix should be well-known. (i.e. I 
have no clue)
I do not know the x,y,z of ICRF(2) compared to the ecliptic plan and the 
vernal point.

> 
> But I still don't know the starting conditions. I.e. before applying the 
> transformations, should the globe's North Pole point upward? Should the 
> intersection of the Prime Meridian and Equator lie along the x-axis? 

Yes. x2.

> Also, am I wrong, and should I perform the inverse matrix calculations 
> instead? Either way, I have not gotten results that match what I see in 
> Celestia for the same Julian Date.
> 
> 
> Mike

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Thanks for taking a look!


> Figure 1.3 , page 11
> 
>  From the point gamma on ICRF equator, starting sphere, the axis of 
> rotation of the planet is located at 90°+alpha, for an amount of 
> 90°-delta. (a single tilting of the planet axis, along a single 
> perpendicular axis)
> 
> If I assert +x is gamma at start, +z north, you have to apply a rotation 
> along v_rotate( y, alpha*z) of 90°-delta, then a rotation of W along the 
> new pole axis.
> 

I can't quite understand your steps. Do you want me to do this?

   #declare sphere_coo = vrotate(y, (90+alpha_0) * z);
   #declare sphere_coo = vrotate(sphere_coo, (90-delta_0) * x);

OTOH, I have attached my scene so far if you would please look at it. 
The result is not similar to what I see in the program Celestia for the 
same Julian day. (I have attached a screenshot of that program as well.)


Mike

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Attachments:
Download 'do_not_delete.pov.txt' (5 KB) Download '2k_earth_daymap.jpg' (453 KB) Download 'celestia_screenshot_01.png' (130 KB)

Preview of image '2k_earth_daymap.jpg'

Preview of image 'celestia_screenshot_01.png'

Oops, here are the files once again. (Ignore the previous ones.)


Mike

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Attachments:
Download 'celestia_screenshot_01.png' (130 KB) Download 'do_not_delete.pov.txt' (5 KB) Download '2k_earth_daymap.jpg' (453 KB)

Preview of image 'celestia_screenshot_01.png'

Preview of image '2k_earth_daymap.jpg'

Le 26/09/2018 à 08:52, Mike Horvath a écrit :
> Oops, here are the files once again. (Ignore the previous ones.)
> 
> 
> Mike

I added the tilting axis (yellow) of the planet and the relevant
transformation.

I do not touch obliquity.

#declare TILT_AXIS = vrotate( x, (90+alpha_0)*z );
/* same as
#declare TILT_AXIS = vrotate( y, alpha_0*z );
*/
#include "transforms.inc"

#declare sphere_trans = transform
{
	rotate z * W
  Axis_Rotate_Trans( TILT_AXIS, 90-delta_0 )
	//rotate x * (90-delta_0)
	//rotate z * (90+alpha_0)
	rotate x * -obliquity
}

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Attachments:
Download 'step.png' (163 KB) Download 'step.pov.txt' (4 KB)

Preview of image 'step.png'

Thanks again for the help!

A couple of comments:

1. What is the significance of the long yellow cylinder?

2. The render of "step.pov" you posted still does not look like the 
Celestia screenshot. The Celestia screenshot in my last post is what the 
scene *should* look like, and the scene is off by quite a bit. I'm not 
sure what's wrong, either.


Mike

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Am 26.09.2018 um 19:45 schrieb Mike Horvath:

> 1. What is the significance of the long yellow cylinder?

Looks like direction to the sun.

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On 9/26/2018 1:47 PM, clipka wrote:
> Am 26.09.2018 um 19:45 schrieb Mike Horvath:
> 
>> 1. What is the significance of the long yellow cylinder?
> 
> Looks like direction to the sun.
> 

No, on Julian Date 2458383.5 the Sun should be directly along the -x axis.


Mike

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