I think it should still be possible to define a perfect circle from 3 points on a globe, tho
Imagine the 3 points on the globe defining a plane, and then just intersecting the globe by that plane, you’d have a perfect circle on a sphere that still goes through the original 3 points if I’m visualizing this in my head correctly, might try this in blender or something
Stereographic projection is the one (and only) thatballows that. You can draw any circle (or a straight line) on a stereographic map and it will remain a circle on the globe.
Looking at the stereographic projection, there is a longer distance between points the father you get from the center of the map. Although the latitude lines remain circular in a polar projection, the map scales to avoid distortion father from the constant growth of the map once you leave the projected hemisphere. The northern hemisphere in an artic projection still must distort, making geometry a mess.
Goode homolosine projection is closer to keeping that distortion down, but all maps are an estimate due to the way a 3d curve is translated to a flat surface.
All that said, and I know I’m being pedantic, you could come really close by calculating the center of the circle in a sphere, then projecting the map stereographically from the center. That specific projection would come the closest, given the irregular shape of the Earth.
I wonder what size the circle would be if you took in to account the earth’s curvature.
Are there any map projections that allow for accurate projection of circles across arbitrary points?
That theorem only applies 2d from my understanding
I think it should still be possible to define a perfect circle from 3 points on a globe, tho
Imagine the 3 points on the globe defining a plane, and then just intersecting the globe by that plane, you’d have a perfect circle on a sphere that still goes through the original 3 points if I’m visualizing this in my head correctly, might try this in blender or something
Stereographic projection is the one (and only) thatballows that. You can draw any circle (or a straight line) on a stereographic map and it will remain a circle on the globe.
https://en.wikipedia.org/wiki/Stereographic_map_projection#Properties
If you drew in on a globe, it would look deformed in this projection. I think the radius wouldn’t change, but it would look “wider” towards the north
All map projections are arbitrary. The only way to do this is on a globe.
Different projections preserve different properties. From memory there are ones that leave circles circular, so would allow this.
Edit: It’s stereographic projection that maps circles to circles.
Looking at the stereographic projection, there is a longer distance between points the father you get from the center of the map. Although the latitude lines remain circular in a polar projection, the map scales to avoid distortion father from the constant growth of the map once you leave the projected hemisphere. The northern hemisphere in an artic projection still must distort, making geometry a mess.
Goode homolosine projection is closer to keeping that distortion down, but all maps are an estimate due to the way a 3d curve is translated to a flat surface.
All that said, and I know I’m being pedantic, you could come really close by calculating the center of the circle in a sphere, then projecting the map stereographically from the center. That specific projection would come the closest, given the irregular shape of the Earth.