I am interested in calculating a box, based on a center point and its ∆ values. The box is an excerpt of the earth' surface. Note that I am not working with a projection of the earth (2D), but with values accounting for its original form - being a sphere (3D).
Given is the center (
c) point - in geographical coordinates (latitude (
x) / longitude (
c(x/y). Another information I am having is ∆ latitude (
∆y) and ∆ longitude (
Here an abstraction of the earth and how the points are located.
_______90°______ / \ ∆(y) \ / \ c(x/y) --- ∆(x)--------\ / \ Longitude / \ |--------0° Equator --------| \ / \ / \----- latitude ------/ \ / \ / ------ -90°----
Given this information, I can calculate
p2 = x + ∆x or
p4 = x - ∆x. Once I have
p1...p4, I have the coordinates for
x1...x4 which are the corners.
x1------p1------x2 | | | | ∆y | | | | p4--∆x--c(x/y)--p2 | | | | | | | | | x4------p3------x3
When I draw the polygon created from
x1...x4, it covers more than it should. This gets more extreme the closer I am to north - or south pole. I assume this is because of the curvature of the earth. The more I am moving north or south, the more distance is between two latitude lines
How would I correct the calculated polygon regarding the curvature of the earth? I tried a linear function
f(x) = 1/90 * x but that only approximates it roughly.