Convert a list of surveyor points in Longitude and Latitude near equatorial to Cartesian system

Question

I have a list of surveyor points in longitude and latitude, obtained from Google Maps, and now I want to convert them to X and Y coordinate system ( in meter). My surveyor points cover around 10 km^2, at most. My surveyor points located near or at the equatorial.

I understand that there are a few ways to do this. But I want a quick way. can I then use spherical approximation, given that my points are located near or at the equatorial?

I am asking whether can I use spherical approximation, given that my points are located near or at the equatorial? And why is it closed "too broad"? This is terrible — Graviton, Jun 19 '17 at 04:41

MBo · Accepted Answer · 2017-06-19T06:43:05.293

1

Yes, for quick and dirty "projection" of small region near equator you can use simple approximation.

If your region has border values Lat0, Lon0, Lat1, Lon1 and you want to get meters:

LatDiff = Lat1 - Lat0
Londiff = Lon1 - Lon0

Scale = 10 000 000 meters / 90 degrees = 111 111 m/degree
// 1/4 part of meridian length

y = (latitude - Lat0) * Scale
x = (longitude - Lon0) * Cos(average_latitude) * Scale

Cosine of latitude (same value for the whole region) compensates error near 1.5% for lat 10 degrees, 6% for lat 20 degrees, and might be omitted if needed.

edited Jun 19 '17 at 06:43

answered Jun 19 '17 at 05:20

MBo

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What is `scale`? – Graviton Jun 19 '17 at 05:41
Coefficient to make a map of defined size. For example, if coordinate difference is about angular minute, and picture should be about 1000 pixels width, `scale = 1000px / (1/60)` – MBo Jun 19 '17 at 05:45
I wrote more detailed example – MBo Jun 19 '17 at 05:53
Sorry, I still don't get it. The `Width` and `Height` refer to? – Graviton Jun 19 '17 at 06:21
As far as I understand, you want to draw/show a map with points. Map is picture, it has desired size - width and height, hasn't it? – MBo Jun 19 '17 at 06:26
Ah, I want to convert the lat/long. into Cartesian coordinate ( in meter). Question updated, sorry for the unclear question. – Graviton Jun 19 '17 at 06:34
No problem. You just have to change a scale. Look at edit – MBo Jun 19 '17 at 06:43

Convert a list of surveyor points in Longitude and Latitude near equatorial to Cartesian system

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