Add closed-form expression of the inverse stereographic projection

problems/inverse-stereographic-projection.py

+# The inverse stereographic projection through the north pole, and its derivative
+def f(x):
+    normSquared = x[0]*x[0]+x[1]*x[1]
+    return [2*x[0] / (normSquared+1), 2*x[1] / (normSquared+1), (normSquared-1)/ (normSquared+1)]
+    #a = 20
+    #normSquared = a*a*(x[0]*x[0]+x[1]*x[1])
+    #return [a*2*x[0] / (normSquared+1), a*2*x[1] / (normSquared+1), (normSquared-1)/ (normSquared+1)]
+
+def df(x):
+    normSquared = x[0]*x[0]+x[1]*x[1]
+    denominator = (1+normSquared)*(1+normSquared)
+
+    return (( (2*(1+normSquared) - 4*x[0]*x[0]) / denominator, (-4*x[0]*x[1]) / denominator),
+            ( (-4*x[1]*x[0]) / denominator, (2*(1+normSquared) - 4*x[1]*x[1]) / denominator),
+            (4*x[0]/denominator,4*x[1]/denominator))
+
+fdf = (f, df)