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From: Mike Horvath
Subject: Oblate spheroid cartography
Date: 18 Jul 2018 22:00:37
Message: <5b4fb885$1@news.povray.org>
Several types of latitude are described here:

https://en.wikipedia.org/wiki/Latitude

I have a sphere, with a texture of the Earth mapped to it, and 
latitude/longitude gridlines overlaid on top.

(See the "Circle of latitude" animation in p.b.a.)

This is easy to do. But what if I want to model the oblateness of the 
Earth WRT a true sphere? What if I want to also exaggerate it a great deal?

The naive thing to do would be to simply scale the sphere along the 
vertical axes without changing the horizontal axis. This is also pretty 
easy to do.

But would it be *more* proper to alter the texture map so that spherical 
latitude is converted to geodetic or geographic latitude? I.e. should I 
deform the map so that 60 degrees N remains 60 degees N after switching 
from a sphere to an oblate spheroid and geodetic latitude?

How do I do this with a texture map? What is the correct way to proceed? 
To my eyes, applying the texture map after deforming the sphere looks 
the same as applying the texture map before deforming the sphere.


Mike


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From: clipka
Subject: Re: Oblate spheroid cartography
Date: 18 Jul 2018 23:05:23
Message: <5b4fc7b3@news.povray.org>
Am 19.07.2018 um 00:02 schrieb Mike Horvath:
> Several types of latitude are described here:
> 
> https://en.wikipedia.org/wiki/Latitude

Wow. I never imagined latitude was that complex of a topic.


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From: Bald Eagle
Subject: Re: Oblate spheroid cartography
Date: 19 Jul 2018 01:00:00
Message: <web.5b4fe16e32871de6458c7afe0@news.povray.org>
clipka <ano### [at] anonymousorg> wrote:
> Am 19.07.2018 um 00:02 schrieb Mike Horvath:
> > Several types of latitude are described here:
> >
> > https://en.wikipedia.org/wiki/Latitude
>
> Wow. I never imagined latitude was that complex of a topic.

Ah reality.   So many details.

I suppose one should ask if making any corrections is appropriate and necessary,
or overkill for accomplishing the desired goal.

"The difference between the semi-major and semi-minor axes is about 21 km (13
miles) and as fraction of the semi-major axis it equals the flattening; on a
computer monitor the ellipsoid could be sized as 300 by 299 pixels. This would
barely be distinguishable from a 300-by-300-pixel sphere, so illustrations
usually exaggerate the flattening."

"On the reference ellipsoid for WGS84, the centre of the Eiffel Tower has a
geodetic latitude of 48° 51&#8242; 29&#8243; N, or 48.8583° N and longitude of
2° 17&#8242; 40&#8243; E or 2.2944°E. The same coordinates on the datum ED50
define a point on the ground which is 140 metres (460 feet) distant from the
tower.[citation needed] A web search may produce several different values for
the latitude of the tower; the reference ellipsoid is rarely specified."

What's the scale of the scene, and will +/- 460 feet be in any way significant?


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From: Thomas de Groot
Subject: Re: Oblate spheroid cartography
Date: 19 Jul 2018 06:46:42
Message: <5b5033d2$1@news.povray.org>
On 19-7-2018 2:55, Bald Eagle wrote:
[snip]
> What's the scale of the scene, and will +/- 460 feet be in any way significant?
> 
> 

...except as an intellectual exercise? I was going to answer like you 
did. I certainly believe that - except for very highly specific and 
specialised uses - this would be overkill. Why bother? Because the /true 
shape/ of the Earth is not even like that: it looks more like an 
(oblate) potato and its generalised, irregular, shape differences are 
certainly more than +/- 460 feet.

-- 
Thomas


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From: Mike Horvath
Subject: Re: Oblate spheroid cartography
Date: 19 Jul 2018 20:58:24
Message: <5b50fb70@news.povray.org>
On 7/18/2018 6:02 PM, Mike Horvath wrote:
> How do I do this with a texture map? What is the correct way to proceed? 
> To my eyes, applying the texture map after deforming the sphere looks 
> the same as applying the texture map before deforming the sphere.

On second appraisal, there is a difference in the texture based on 
whether it is applied before or after the sphere is scaled. But it's not 
the difference I was expecting...


Mike


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From: Bald Eagle
Subject: Re: Oblate spheroid cartography
Date: 20 Jul 2018 00:40:01
Message: <web.5b512f1132871de6458c7afe0@news.povray.org>
https://www.youtube.com/watch?v=yJZP_-40KVw

You could give one of the authors an email, and see if they have any
suggestions.  They clearly know how to flip around equations for spheres and
geometric inversion like aces.

You might also check out various other fora like Mathematica, stackexchange,
etc. and see if this has been asked and answered there.


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From: Mike Horvath
Subject: Re: Oblate spheroid cartography
Date: 20 Jul 2018 01:12:30
Message: <5b5136fe$1@news.povray.org>
On 7/19/2018 8:38 PM, Bald Eagle wrote:
> https://www.youtube.com/watch?v=yJZP_-40KVw
> 
> You could give one of the authors an email, and see if they have any
> suggestions.  They clearly know how to flip around equations for spheres and
> geometric inversion like aces.
> 

Interesting. Did they use POV-Ray to make the video? It looks very much 
like it.


> You might also check out various other fora like Mathematica, stackexchange,
> etc. and see if this has been asked and answered there.
> 
> 

I already mirrored my question to stack exchange. I use that site daily! 
Not sure about the mathematica forum. They might be annoyed if I know 
nothing about using Mathematica.


Mike


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From: Stephen
Subject: Re: Oblate spheroid cartography
Date: 20 Jul 2018 06:09:55
Message: <5b517cb3$1@news.povray.org>
On 20/07/2018 02:13, Mike Horvath wrote:
> On 7/19/2018 8:38 PM, Bald Eagle wrote:
>> https://www.youtube.com/watch?v=yJZP_-40KVw
>>
>> You could give one of the authors an email, and see if they have any
>> suggestions.  They clearly know how to flip around equations for 
>> spheres and
>> geometric inversion like aces.
>>
> 
> Interesting. Did they use POV-Ray to make the video? It looks very much 
> like it.
> 
From:

http://www.dimensions-math.org/Dim_merci_E.htm

Most of the images were created in Povray
Fractal images were created in Ultrafractal

The whole series is worth watching. Even if just for the graphics and 
the smoothness of the animations.

IIRC They made an announcement on the newsgroups. When they released the 
videos.



> 
>> You might also check out various other fora like Mathematica, 
>> stackexchange,
>> etc. and see if this has been asked and answered there.
>>
>>
> 
> I already mirrored my question to stack exchange. I use that site daily! 
> Not sure about the mathematica forum. They might be annoyed if I know 
> nothing about using Mathematica.
> 

You got a really helpful answer from amd


> 
> Mike


-- 

Regards
     Stephen


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From: Mike Horvath
Subject: Re: Oblate spheroid cartography
Date: 20 Jul 2018 07:32:38
Message: <5b519016$1@news.povray.org>
On 7/20/2018 2:09 AM, Stephen wrote:
> On 20/07/2018 02:13, Mike Horvath wrote:
>> I already mirrored my question to stack exchange. I use that site 
>> daily! Not sure about the mathematica forum. They might be annoyed if 
>> I know nothing about using Mathematica.
>>
> 
> You got a really helpful answer from amd
> 
> 

Yeah... I get that a lot. The people on stack exchange don't want to 
answer questions that don't garner them lots of points I think. (I'm not 
sure what their business model is.) Or they don't explain how to improve 
a question before closing/holding it.


Mike


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From: Stephen
Subject: Re: Oblate spheroid cartography
Date: 20 Jul 2018 10:42:37
Message: <5b51bc9d$1@news.povray.org>
On 20/07/2018 08:34, Mike Horvath wrote:
> On 7/20/2018 2:09 AM, Stephen wrote:
>> On 20/07/2018 02:13, Mike Horvath wrote:
>>> I already mirrored my question to stack exchange. I use that site 
>>> daily! Not sure about the mathematica forum. They might be annoyed if 
>>> I know nothing about using Mathematica.
>>>
>>
>> You got a really helpful answer from amd
>>
>>
> 
> Yeah... I get that a lot. The people on stack exchange don't want to 
> answer questions that don't garner them lots of points I think. (I'm not 
> sure what their business model is.) Or they don't explain how to improve 
> a question before closing/holding it.
> 
> 

They need to grow up and stop thinking of themselves as cleaver. ;)


-- 

Regards
     Stephen


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