Re: Worldmap mercator projection - Latitude to Y calculation. - last try

On 2026/1/24 8:28:44, R.Wieser wrote:
> John,
> 
>> There are three stages to this
> ...
>> 1. The mathematical conversion from latitude (and longitude) to the
>> position on the plane map *relative to its centre*
> 
> Nope.  There is no rule that that center must be taken as the origin.   Take 
> the formule Paul provided for instance.  It returns a result in the range of 
> 0 to 1 .

It makes it easier to understand what's going on if done in these three
stages. And assuming we're talking of the Web Mercator image as shown at
https://upload.wikimedia.org/wikipedia/commons/e/ec/Web_maps_Mercator_projection_SW.jpg,
0 degrees latitude and longitude _is_ at its centre.

> 
>> 2. The _scaling_ required, depending on the size of the map image.
>> Which again will depend on the size of the image (and may be different
>> for X and Y).
> 
> Worse : Mercator maps go from +85 to -85 latitude.  That must be part of the 

(Or 85.051129.)

> formule (I've found several maps where the south-pole is cut off, and a bit 
> of the north too. iow, useless without further information).

No, just because the map is cut off at those latitudes, that figure does
NOT have to appear in the formula. The poles _have_ to be cut off,
otherwise the map would be infinitely tall, and very distorted at the poles.

> 
> But again no.   The result of the formule *is* the scaling (in your and my 
> usage ranging from +1 to -1, in Pauls formule case, from 0 to +1).  You just 
> apply it on whatever size Mercator-style map you have handy.

The above image, according to my browser, is 2068 by 2060 pixels.

> 
>> I think _most_ of those contributing to this discussion know that,
>> but have not been making it very clear which bits of their formula(e)
>> do what.
> 
> I do not need to know what all the parts of a car do, as long as I can drive 
> it.  The same goes for these two formules.   Latitude goes in, something I 
> can apply comes out.
> 
True, if that really is all you want. As a scientist/engineer/just
enquiring mind, I don't like to blindly use a formula without knowing
what it does - or perhaps _why_.

Yes, you can drive a car without knowing what each bit does. But knowing
at least some of them will improve your longevity (wear and tear on the
mechanisms), fuel economy, performance ... as you drive.

> 
> Though the whole problem isn't that nobody understood what you said there, 
> but that nobody was willing to compare the (intermediate) results I posted 
> with what they got themselves, allowing me to locate where I made my 
> mistake(s?).

That is indeed one of many problems.

It would be good to see where the following points come out on e. g. the
above image, using any formula (longitude given first):
0, 0
+/- 180, 85
+/-180, -85
and some known place, such as London or New York.

> 
> Not when I asked for it in my first post, and not when I rather explicitily 
> asked for it a few days back. :-(
> 
> Regards,
> Rudy Wieser
> 
> 
I guess if you just want a formula that works, and _aren't_ bothered
about the three steps - the mathematical conversion from angle to linear
dimension, the scaling, and the offset - then we're very different
minds. Which is of course fine; if we were all the same, it'd be a
boring world.

-- 
J. P. Gilliver. UMRA: 1960/<1985 MB++G()ALIS-Ch++(p)Ar++T+H+Sh0!:`)DNAf

We no longer make things, but sell each other consultancy on how to run
consulatancies better. (Michael Cross, Computing 1999-3-4 [p. 28].)