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Ask Norm - August 1999

Question 1: Perhaps you can help me with a datum related question. For some time I have been searching for a reference to a datum called "Camacupa" which is used in Angola. Please tell me if there is some method to work with this datum definition inside of Tralaine?

Question 2: I wondered if someone could help me with the math to Calculate the distance between a set of Lat/Long dec Co-Ordinates, and as well get a Bearing in Degrees between the two?

Question 3: What zone does Sacramento County, California fall into using NAD83?

Question 4: An office sent me some coordinates in WGS-84 (in AutoCAD). These should be represented in a Lambert Conformal projection with latitude and longitude lines. Could you help me to solve this problem? Thank you in advance.

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Q1. I always enjoy the newsletter. I have been aware of Mentor Software products for a number of years. During college, I had used at the time, what I believed was one of the earlier versions of Tralaine back in 1988 or so, when I was at Hunter College in NYC.

That was a long time ago....

Perhaps you can help me with a datum related question. For some time I have been searching for a reference to a datum called "Camacupa" which is used in Angola and is present on various topo maps produced by the Angolan Institute of Cartography and Geodesy. I downloaded new current version of Tralaine from your website, but i did not see a reference to that datum. I had once found some mention of it through the web at the DIGIT (spelling) site in Canada and also the EPSG site, but I could not find the complete descriptions, only mention of the name. Any information you may have about this would be greatly appreciated. please tell me if there is some method to work with this datum definition inside of Tralaine.

Please respond at your convenience.

Best regards,

-- Reese W. Plews rplews@tkb.att.ne.jp

A. Hello Reese . . .

I don't have any more information then you already have. You'll notice that there are a lot of datums referenced in the EPSG database which have no real information other then possibly the ellipsoid. This not uncommon for countries which were primarily in the Soviet sphere of influence. If the oil companies weren't exploring there, there is little information available.

If you have a point or two of correspondence, you can use our Molodensky Freebie to get some approximate numbers which you can use. That is, possibly you have a new GPS coordinates for a point which you also have Camacupa coordinates. The Molodensky utility will give you some approximate delta X, delta Y, and delta Z numbers you can use.

Sorry I can't be of any more assistance.

Norm

Q2. I wondered if someone could help me with the math to Calculate the distance between a set of Lat/Long dec Co-Ordinates, and as well get a Bearing in Degrees between the two?

Thanks,

J. Wilson

A. On a sphere, it is relatively simple. From Snyder's, Map Projections Page 30:

cos (c) = sin(lat1) * sin(lat2) + cos(lat1) * cos(lat2) * cos (lng2 - lng1)

lat's and lng's in radians, of course. c is the angular distance between the two points in radians. Use the radius of the sphere to convert to linear measurments. For the azimuth, again from page 30 of Snyder:

cos (Az) = [cos(lat1) * sin(lat2) - sin(lat1) * cos(lat2) * cos(lng2 - lng1)] / sin(c)

or, a form suitable for use with atan2 which will provide a full 360 degree azimuth:

tan(Az) = cos(lat2) * sin(lng2 - lng1) / [cos(lat1) * sin(lat2) - sin(lat1) * cos(lat2) * cos(lng2 - lng1)]

Again, all angles are in radians. This is an Azimuth, rather than a bearing, and is positive east of north.

On an ellipsoid, the situation gets very complex. Best I can do for you here is to point you to:

ftp.ngs.noaa.gov/pub/pcsoft/for_inv.3d/source

This site contains FORTRAN source code to a program which does this calculation. This is non-trivial stuff.

You can download our Forward/Inverse program (it's free) too.

Hope this helps.

Norm

Q3. What zone does Sacramento County, California fall into using NAD83?

Dave

A. Zone 2, or in the Mentor Software vernacular, CS83-II.

We have posted a freebie, for the month of June I think, which is a State Plane Zone Locator. It provides the NAD83 State Plane zone number for all counties in the 48 states (and Hawaii, I think; Alaska doesn't really have counties).

Norm

Q4. An office sent me some coordinates in WGS-84 (in AutoCAD). These should be represented in a Lambert Conformal projection with latitude and longitude lines. Could you help me to solve this problem? Thank you in advance.

Juan Gonzalez

A. I presume the coordinates they gave you are latitude and longitude numbers. Converting to Lambert Conformal Conic is complicated. Our whole business is based on this type of problem.

You will first need to obtain a definition of the coordinate system.  The projection, Lambert Conformal Conic in this case, is just one piece of the puzzle. You will need to obtain information about the origin latitude, origin longitude, standard parallels, etc.

Second, you will probably want to find a program which can accept such numbers and do the calculations for you. Our Tralaine software is one such product. If you download Tralaine from our web site, you will be given a temporary license. The temporary license will be sufficient for a single job such as the one you describe.

Proceed as follows:

1> Obtain the information necessary about the coordinate system and enter it into the Coordinate System Editor.

2> Use the Coordinate System test screen to convert a few points to verify the validity of the definition.

3> Then use Tralaine to convert the data points. Tralaine will convert coordinates in autocad .DWG files, so this may be the most convenient way of converting them.

It is quite likely that the Lambert Conformal system you have been asked to work with is a national coordinate system of sorts. If you have some documentation on this system, I will be glad to put the numbers into Tralaine and provide you with a system which has been tested to meet the national grid requirements. I could also convert a file which has the coordinates in it.

Norm


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