Converting longitude/latitude to x/y

  • Thread starter MasterX
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In summary, Earth is not a sphere, and the coordinates x, y calculated using the spherical coordinate system do not correspond to the x, y coordinates calculated using the latitude/longitude system.
  • #1
MasterX
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I hope I am posting in the right section.

Up to today I was assuming that Earth is a sphere, and I was using the spherical coordinates to convert longitude/latitude to x/y. But, I wanted to use a more accurate transformation, and I wanted to calculate x/y by considering the actual shape of the planet. Thus, I found that 1 degree of latitude is equal to 111km or 60 nautical miles. One degree of longitude, is equal to the same distance times the cosine of the latitude. Therefore, I can easily compute the x,y coordinates of all the points, if I set one point to be the origin.

Once I have the x,y coordinates of all the points, I compare them. To my surprise the coordinates of these points do not only differ in magnitude but sometimes in sign. More importantly, the relative difference between two points is not the same for these two methods.

Can someone explain to me why I am getting this awkward results. Is there a logic behind this counter intuitive result?

Thank you.
 
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  • #2
I just realized that I am trying to compare the solution from two different coordinate systems. The only thing I could compare is the distance between two points, but even that would not be the same, due to the enormous radius of the planet.
 
  • #3
To get to some two dimensional x/y coordinates (as opposed to three dimensional x/y/z) you are also going through some kind of projection or map transform.

That said, you shouldn't be getting a change in sign. There is no difference between geodetic and geocentric longitude. Geodetic and geocentric latitude are equal at the poles (±90°) and at the equator (0°). In other words, your map will change in shape a little bit at mid-latitudes (±45°).
 
  • #4
Actually, I do not do any kind of projection. All the points are close to each other, and I could assume that they have the same z. I believe that z is important when you go from one hemisphere to the other. Otherwise, you won't find two different points on the surface of a sphere that have the same (x,y).

First of all, these two methods should not (and they are not) give the same map nor the same distances between two points. The two maps do not have the same area, but the points are oriented on the map in a similar way. One thing that was a surprise to me, and I was struggling to find the bug in my calculations, was that the two maps looked like one was vertical to the other (this does not mean that if I rotate the maps the points will coincide).

I believe that I get these two different maps because I computed the x,y coordinates of the points with two completely different coordinate systems. The spherical coordinate system describes the entire volume of an object, whereas the other coordinate system allows one to move on the surface of that object. So, the origin of the former coordinate system is the center of the object, whereas is a point on the surface of the object for the latter coordinate system.
 
  • #5
Its a bit hard to comment on what you did since you haven't said what you did mathematically.
 
  • #6
D H said:
Its a bit hard to comment on what you did since you haven't said what you did mathematically.

I thought that my first post had made this clear!

I am using http://en.wikipedia.org/wiki/Geodetic_system" [Broken]
 
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1. What is the purpose of converting longitude/latitude to x/y?

Converting longitude/latitude to x/y allows us to plot geographic locations on a 2-dimensional map or graph. This makes it easier to analyze and visualize spatial data.

2. How is longitude/latitude converted to x/y?

Longitude/latitude can be converted to x/y using mathematical formulas that take into account the curvature of the Earth and the projection of the map or graph being used.

3. What units are used for x/y coordinates?

The units for x/y coordinates can vary and depend on the map or graph being used. Common units include meters, feet, and degrees.

4. Is converting longitude/latitude to x/y accurate?

The accuracy of converting longitude/latitude to x/y depends on the method used and the scale of the map or graph. In general, the conversion can introduce some distortion, but it can be minimized through careful selection of the projection and scale.

5. Can longitude/latitude be directly converted to x/y without any calculations?

No, longitude/latitude cannot be directly converted to x/y without any calculations. As mentioned earlier, there are mathematical formulas that need to be used to account for the curvature of the Earth and the projection of the map or graph.

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