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ViewsConvert coordinates to corresponding place in table
I have a table with data of an area from west europe. I want to convert coordinates to a value in this table. The problem is similar to this question, but I'm not sure how to work this out as I've never done something similar like this.
Let's say I want to get the value in the table for Amsterdam (lat: 52.35, long: 4.83). How would I convert that into the proper x and y values in the table? I first tried linear interpolation but found out that doesn't work because of the projection. I know of proj4js but I'm unsure how to define these values for the projection.
Per the docs I'm guessing I need to do something like this:
const firstProjection = "something something";
const secondProjection = "WGS84"; // ?
proj4(firstProjection, secondProjection, [52.35, 4.83]);
// [x?, y?]
Some calibration values I have are:
Row (x) Column (y) Latitude Longitude
173 157 54.429 2.352
273 530 53.276 7.694
245 412 53.640 6.038
464 545 51.624 7.546
262 130 53.663 1.903
226 223 53.939 3.293
236 563 53.555 8.244
244 208 53.790 3.058
248 289 53.710 4.240
206 361 54.022 5.348
233 372 53.779 5.472
2 answers
Answer question0
There is no exact way to convert the surface of a sphere to a plane, particularly a rectangular one. There are a number of approximate solutions which are explored in answers to this question.
If the area you are looking at is small you can use the approximation given there by MvG:
x = r * longitude * cos(φ0)
y = r * latitude
Where cos(φ0) = the aspect ratio and φ0 is a latitude close to the center of your map.
I also found a solution using UTM which you can find here. Lower on the page they give their underlying code.
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Your "projection" will be done in two steps:
- From WGS84 to some projected Coordinate Reference System (most common is Web Mercator GMaps are using https://en.wikipedia.org/wiki/Web_Mercator_projection). So it will be from Epsg:4326 to Epsg:3857.
const projection = proj4("EPSG:4326", "EPSG:3857");
const geographicCoordinates = [52.35, 4.83]; // lat, lon
const cartographicCoordinates = projection.forward(geographicCoordinates);
- Project x and y values from cartographic coordinates to screen coordinates using transformation:
xScreen = (cartographicX - cartographicXMin) / (cartographicXMax - cartographicXMin) * (screenXMax - screenXMin);
yScreen = (cartographicY - cartographicYMin) / (cartographicYMax - cartographicYMin) * (screenYMax - screenYMin);
To get cartographic X and Y min maxes use the same transformation.
You need to note, however, that Mercator projection expands areas endlessly closer the latitude is to the poles which means one must not use this projection if the coordinates are in the north (Greenland, for example). For these areas you need to use conic projections.