Calculus and Plot of a simple polar stereographic projection

Question

Valentin Reichel 2019-8-1

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https://ww2.mathworks.cn/matlabcentral/answers/474379-calculus-and-plot-of-a-simple-polar-stereographic-projection

回答： Divya Yerraguntla 2019-8-7

Hey I wonder if anyone could give me a hand or some tips, since i am new to matlab trying to figure out the following problem.

I wanted to create a small programm which represents a polar stereographic projection. It should contain a sphere, with polarcoordinates ( latitude lambda, longitude phi). The projection centre should be in the north pole and on the opposing side there should be a tangent plane with coordinates ( alpha and m ). I want to insert any point A on the sphere with coordinates ( lambda and phi) and the programm calculates the procetion point A' on the tangental plane with coordinates ( alpha and m).

Calculus for coordinates of the Procetion point A'(m,alpha)

m=2 r (radius of the sphere) tan(((pi/2)-phi)/2) where phi is the first coordinate of the inserted point A

alpha = lambda where lambda is the second coordinate of the inserted point A

And i wanted to plot the sphere, the projection centre, the tangental plane and both points A and A'.

I would be happy about an answer. Have a great day, Valentin