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June 20th, 2009, 05:25 AM   #1
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Lambert -> Latitude and Longitude?

Hi all...

I have no idea if this is the right place to be posting this question - I've browsed through the different topics and well, I'm completely lost. Let's just say math is not my strong suit. Anywho, what I'm trying to do is transform 78,216 Lambert Coordinates to Lat / Long. I have the following information:

Longitude of Origin: -91:52:00.120
Latitude of Origin: 63:23:26.520
Standard Parallel 1: 77:00:00.00
Standard Parallel 2: 49:00:00.00
False X: 6200000.00
False Y: 3000000.00
(false x and y representing the offset)

I also have a list of 10 formulae that when used will apparently give me the transformation - unfortunately they're on a fax, so I can't upload them here (no scanner at home). They look extraordinarily complex to me, and I'm hesitant to start using them if they're not what I actually need. (As an example, and I'll type out the names of the Greek letters, I have x = rho sin [n(phi - phi 0)], y = rho 0 - rho cos [n(phi - phi 0)]....where rho = sgn(n)(sqr rt(x^2 + (rho 0 -y)^2)). HUH?)
What I was hoping to do is write a program or use an Excel spreadsheet or something to work through the huge amount of data I have. I'm really hoping someone can help me out here...Thanks in advance and I hope you have a great day!
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June 20th, 2009, 11:40 AM   #2
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Re: Lambert -> Latitude and Longitude?

I'm going to move this topic to Applied Math, since this really goes beyond what a high schooler would be expected to know.
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June 20th, 2009, 12:12 PM   #3
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Re: Lambert -> Latitude and Longitude?

Those complicated formulas are, unfortunately, exactly what you need. (You might need only half of them -- the rest might be the formulas for going the other direction.)

The formulas should be essentially those here:
http://mathworld.wolfram.com/LambertCon ... ction.html

If you do this in a spreadsheet, you can put the x and y data (the Lambert coordinates) in one sheet and the reference data (reference latitude, reference longitude, standard parallel 1, etc.) in another. Any calculation relying only on the reference data can be done in the second sheet -- no need to repeat it. Then on the main sheet you can put the formulas for rho and theta, relying on the x and y coordinates in the first row along with the reference data. With rho and theta you can use the formulas for latitude (phi) and longitude (lambda) and you have the first row done. Check to make sure it makes sense, then drag the formulas for rho, theta, phi, and lambda down to the 78,215 other rows.
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June 21st, 2009, 04:40 AM   #4
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Re: Lambert -> Latitude and Longitude?

Hi CRGreathouse,

Thank you very much for your reply - that link you gave me are the formulae I'm looking at on my fax paper, so I guess I had everything I need. Your help is much appreciated and hopefully I'll get this figured out - I'll let you know how it goes!
Have a great day and take care...
Chris

"Geek till it Hz. Geek till it MHz."
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June 21st, 2009, 04:44 PM   #5
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Re: Lambert -> Latitude and Longitude?

In the not-unlikely case that you run into troubles, post here and I'll try to get you unstuck. Otherwise, pat yourself on the back -- a tangled mess of formulas like that can be a pain to code.
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June 22nd, 2009, 04:42 PM   #6
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Re: Lambert -> Latitude and Longitude?

Durn it, I'm stuck LOL.

Using the mathworld.wolfram site you've provided, I have established that I need to use the Inverse formulae, as I have the Lambert Coordinates and need the lat/long. Sweet. So I have starting plugging in the full formulae for each of the symbols to see what I come up with (and to get more comfortable with these calculations, it's been a long time...). So question...

I am putting in the formulae for the values of theta. In the calculation it's using [(F/rho)]; however, in the calculation of rho, you need to use theta. Hunh? Would that not consitute a circular reference and therefore an error? Great, two rows of formulae and I'm already confused.

Please tell me that either a) I'm correct and what I would need to use (I'm assuming theta1, but don't want to go down that path unless someone more adept in math tells me to do so) or b) I'm completely off base and how I would actually go about doing this.

Your assistance is, as always, very much appreciated.
Chris

...Edit: Now that I'm looking a little more carefully at the equations, I've noticed something else. In the calculation of F, you use (1/4 pi + 1/2 theta1). In the calculation of rho, you use (1/4 pi + 1/2 theta). So if I'm correct and supposed to use theta1, these would then cancel out, leaving ( cos theta1 * tan ^ n / n ) / F cot ^ n). And because F is in the denominator, and F is in the numerator (written out in full), does this not mean that the calculation in the square brackets reduces to 1 / cot ^ n? Man am I lost....and my parents wondered why I never did well in math in school - I confuse the hell out of myself!
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June 22nd, 2009, 09:44 PM   #7
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Re: Lambert -> Latitude and Longitude?

First of all, let's make sure we're on the same page with the notation: ? is phi and ? is theta.

Quote:
Originally Posted by darth_pathos
Durn it, I'm stuck LOL.
Don't worry about it -- we both knew this was going to be a bit complicated.

Quote:
Originally Posted by darth_pathos
I am putting in the formulae for the values of theta. In the calculation it's using [(F/rho)]; however, in the calculation of rho, you need to use theta.
The calculation of phi (?) does use rho, that's right. But ignore the "direct" formula for rho and use the "inverse" calculation below it on the MathWorld page. Note that sgn(n) is 1 if n is positive, -1 if n is negative, and 0 if n is zero. In Excel, you can code this as
=IF(varN<0,-1,IF(varN>0,1,0))
if you've labeled the 'n' value varN.

Quote:
Originally Posted by darth_pathos
In the calculation of F, you use (1/4 pi + 1/2 theta1). In the calculation of rho, you use (1/4 pi + 1/2 theta). So if I'm correct and supposed to use theta1, these would then cancel out, leaving ( cos theta1 * tan ^ n / n ) / F cot ^ n). And because F is in the denominator, and F is in the numerator (written out in full), does this not mean that the calculation in the square brackets reduces to 1 / cot ^ n?
Yeah, there are a few things you're confused on here.

Most importantly, don't use that formula for rho: use the one below starting with sgn(n) * sqrt(...). Second, tan^n (stuff) isn't tan to the power of n times stuff; it's the tangent of stuff to the power of n. In Excel:
=TAN(stuff)^varN
(replacing stuff with the appropriate things, of course).

Quote:
Originally Posted by darth_pathos
Man am I lost....and my parents wondered why I never did well in math in school - I confuse the hell out of myself!
And just think, once you lick this thing you'll have come full circle. How many people have even heard of Lambert coordinates, let alone written a spreadsheet to convert thousands of Lambert coordinates to latitude and longitude?

Just so you understand, when I saw your post the first thing I did was to search Google for Lambert coordinates. I didn't know how to work with them myself!
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June 23rd, 2009, 03:50 AM   #8
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Re: Lambert -> Latitude and Longitude?

Hey there CRGreathouse.....thanks for the detailed and extremely supportive reply, I'm going to go back and rethink on things (not entirely sure how I missed the Inverse Calculations for rho - can't exactly blame "missing the obvious" on being a math n00b LOL). The only question that I have right now is regarding the sgn function; according to wikipedia, it's the Sign function, used to determine the sign value of a real number. OK, fine and good. Now what the heck does it mean, and how to I calculate it? Going to have to spend time thinking about this (remember Winnie the Pooh? I need a Thinking Place...).
I have printed off the thread as well as a couple of other web pages and will get me a coffee and start reading.

Is it sick to admit that although this is really frustrating I'm loving it at the same time?

Thanks
Chris

...I also realised this morning I inadvertantly called Phi Theta. Bad, bad me, especially considering I'm such a huge fan of the Good Ol' Golden Ratio. Oops.
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June 23rd, 2009, 04:21 AM   #9
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Re: Lambert -> Latitude and Longitude?

Quote:
Originally Posted by darth_pathos
The only question that I have right now is regarding the sgn function; according to wikipedia, it's the Sign function, used to determine the sign value of a real number. OK, fine and good. Now what the heck does it mean, and how to I calculate it?
I knew that would be a problem, so I explained it above.

It's 1 when the number is positive, -1 when negative, and 0 if it's 0.

Quote:
Originally Posted by darth_pathos
Is it sick to admit that although this is really frustrating I'm loving it at the same time?
That just means you're out of practice. It wouldn't be nearly as frustrating if you had to do it again.
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June 23rd, 2009, 06:49 PM   #10
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Re: Lambert -> Latitude and Longitude?

Ok, soooooo here I am again with another question

I've read everything over carefully you've replied. Awesome info. Slight bump in the road, however.

n = ln (cos theta1 sec theta2)
ln(tan(1/4 pi + 1/2 theta2)cot(1/4 pi + 1/2 theta1))

So based on my information, I have theta1 = 77:00:00.00 and theta2 = 49:00:00.00 (Standard Parallels 1 and 2).

I'm using Excel and secant isn't a function available, but it appears 1/cos is the same thing, so I'm using that. However, when I do the calculations, I get cos(77) = -0.03098, and 1/cos(49) = 3.326762. However, when I do

ln(-0.03098 * 3.326762)

, I get an error in Excel. When I remove the negative, I get an answer. I'm so close (I think) to having a decent understanding of this and then run into something as silly as this. Argh. Suggestions? Am I supposed to assume that I drop the negative sign and take the absolute value? Or have I once again missed something?

Thanks again for your time.....
Chris
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