plot a point which is in form of lat and long in a pixel map

Question

I need to plot a point which is in form of lat and long

this point is equivalent to a screen coordinate on pixels on my map.

I want to make a relation in these two point so if you want to plot a lat,long

I can know what is this position on map.

here a graphical representation of the markers [little wheels] on the corners of the map and the values for X and Y; and the equivalent points in lat long.

so here is the X and Y pixel coordinates on my map and the relationship on lat long

I have some equations to represent this relationship but I havent figure out how to make it work so if I get given any long, lat coordinate how to represent it in my pixel x and y.

How to establish this relationship in an equation?

thanks!

Answer 1

The practical answer is to linearly interpolate it. The error for a spherical earth will not matter, and as the user zooms in you will get more accurate. At small scales the earth is flat, and at large scales you don't care. The fact that you think a rectangle has corners that match supports this (this ignores the fact that distance east-west for a given range of longitude decreases as the latitude increases). So given $long=116.7, x=20+\frac {long-116.671221}{116.741259-116.671221}(1117-20)$