Tem P.

asked • 02/19/15

What happens to a line/curve from a flat map to a spherical map?

The scenario starts from the Earth (assumed as a sphere with radius r). The sphere is turned into a square map (cartography) and now I measure a curve on that map (gaining a polynomial function to describe it) then now I want to know its length when its converted back into a spherical (3D) map.

What would happen to my 2D polynomial, can it be described as a 3D polynomial which I can find the length of?

I need to know for my maths exploration. Please, any info would help, you may use any variable, tell me what I need to know (e.g. radius of Earth, etc). If there are multiple answers with different additional assumptions please inform me. Thank you for any mathematicians out there that can help me on this. I actually used a beach satellite image and used data points plotted on a graph to interpolate a polynomial out of it, then found the arc length.

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