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

On 21/01/2026 19:01, R.Wieser wrote:
> Paul,
> 
>>   ln(2.097283) = 0.740643   # Via the ln() button on my calculator
> 
> And that 0.740643 points to somewhere between the northpole and canada on an
> ice plate.  Where I'm quite sure Washington DC isn't located.
> 
> Which was why I started to doubt that "ln()" equals "log()".  But if not,
> what is it ?
> 
>> The plot origin must not be where we think it is.
> 
> Well, thats easy to check : Just calculate the result for a Latitude of Zero
> degrees.  It should point at the equator.
> 
>> Notice how in a lot of these mathematics discussions, nobody labels a damn
>> thing.
> 
> Just mathematics ?    A couple of weeks ago I tried to find example code for
> OpenSLL.  I could find some, but with zero indication which version of the
> DLL it was for - and it matters a *lot*.  It frustrates me to no end.
> 
>>> 0.117959 is *way* to low
>>
>> But it is 0.5 minus that number, so 0.382 .
> 
> In my previous message I mentioned that I multiply the result by half the
> height of the map, and subtract it from the equator (again, half the height
> of the map).  That is the same, right ?
> 
> Actually, it isn't.  :-)
> 
> Now you have shown that the log() in the formule you presented is exactly
> that (and not a elog() (natural log?) ) I had some solid ground from which I
> could look further.
> 
> The whole problem is that your formule multiplies by the full height of the
> map, and my "simplified" one multiplied by *half* the maps height (and than
> subtracts from the equator).
> 
> When I multiplied my result by two the result was the same as what came
> outof your formule.
> 
> Thank you for that. :-)
> 
> mea culpa : after noticing that my implementation of the formule didn't work
> I *should* have first tried to implement it as provided. :-|
> 
> 
> Than only one thing remains : Any idea why the first formule doesn't give
> the expected result ?<whistle>
> 
> Regards,
> Rudy Wieser
> 
> 
> 
> 
I would expect most people would think that log(A) means log to base 10 
of A while ln(B) is natural log of B if they were just shown without any 
explanation.