Mathematically speaking, isn't it true you can compute the coordinate transformation (with your choice of map projection, perhaps ignoring the poles)? The real

Mathematically speaking, isn't it true you can compute the coordinate transformation (with your choice of map projection, perhaps ignoring the poles)? The real problem is that your metric / notion of distance has changed, so you can't simply compute distance as sqrt((x2-x1)^2 + (y2-y1)^2) and expect it to map neatly to a circle on the globe.