% Author: Prof. Dr. Matthias Jung, DL9MJ
% Year: 2024
\begin{tikzpicture}
    % Theta (Elevation von Oben), Phi (Azimuth)
    \def\toCoords#1#2{
        {sin(#1)*cos(#2)},%
        {sin(#1)*sin(#2)},%
        {cos(#1)}%
    }
    %% Script to calculate parameters: https://www.nosco.ch/mathematics/en/great-circle.php
    %import numpy as np
    %import math
    %#   theta phi
    %a = [30, -20]
    %b = [70, -90]
    %p1 = [
    %    math.sin(math.radians(a[0]))*math.cos(math.radians(a[1])),
    %    math.sin(math.radians(a[0]))*math.sin(math.radians(a[1])),
    %    math.cos(math.radians(a[0]))
    %]
    %p2 = [
    %    math.sin(math.radians(b[0]))*math.cos(math.radians(b[1])),
    %    math.sin(math.radians(b[0]))*math.sin(math.radians(b[1])),
    %    math.cos(math.radians(b[0]))
    %]
    %u = p1
    %w = np.cross(p1,p2)
    %v = (np.cross(u,w))/(np.linalg.norm(w))
    %print(u)
    %print(v)
    \begin{axis}
        [
            width=\linewidth*\getDarcImageFactor,
            height=\linewidth*\getDarcImageFactor,
            scale only axis,
            axis equal,
            enlargelimits=false,
            axis lines=none,
            domain=0:180,
            samples=32,
            y domain=0:360,
            samples y=21,
            %view={25}{30} % default
        ]
        \addplot3 [
            surf,
            z buffer=sort,
            draw=DARCgray,
            fill=white,
            colormap={bw}{color=(DARCgray) color=(DARCgray)}
        ] (
            {sin(x)*cos(y)},
            {sin(x)*sin(y)},
            {cos(x)}
        );
        \addplot3 [
            draw=DARCblue,
            very thick,
            samples y=100,
            y domain=296.5:360,
        ] (
            {cos(y)*0.46984631039295416  + sin(y)*0.24133274},
            {cos(y)*-0.17101007166283433 + sin(y)*0.96856549},
            {cos(y)*0.8660254037844387   + sin(y)*0.06032751}
        );

        \addplot3 [
            draw=DARCred,
            thick,
            samples y=100,
            y domain=45:0,
        ] (
            {cos(y)*0.46984631039295416  + sin(y)*0.24133274},
            {cos(y)*-0.17101007166283433 + sin(y)*0.96856549},
            {cos(y)*0.8660254037844387   + sin(y)*0.06032751}
        );

        \addplot3 [
            draw=DARCred,
            thick,
            samples y=100,
            y domain=296.5:235, 
        ] (
            {cos(y)*0.46984631039295416  + sin(y)*0.24133274},
            {cos(y)*-0.17101007166283433 + sin(y)*0.96856549},
            {cos(y)*0.8660254037844387   + sin(y)*0.06032751}
        );

        \addplot3 [
            draw=DARCred,
            thick,
            dashed,
            samples y=100,
            y domain=235:45,
        ] (
            {cos(y)*0.46984631039295416  + sin(y)*0.24133274},
            {cos(y)*-0.17101007166283433 + sin(y)*0.96856549},
            {cos(y)*0.8660254037844387   + sin(y)*0.06032751}
        );

        \fill[black] (axis cs:\toCoords{30}{-20}) circle (2pt);% node[below right](){a};
        \fill[black] (axis cs:\toCoords{70}{-90}) circle (2pt);% node[above left](){b};
        \path[DARCblue](axis cs:\toCoords{30}{-20}) -- (axis cs:\toCoords{70}{-90}) node[pos=0.5,anchor=north,rotate=45](){Kurzer Weg};
        \path[DARCred](axis cs:\toCoords{70}{-90}) node[anchor=south east,rotate=53](){Langer Weg};
    \end{axis}
\end{tikzpicture}