Hello, I am trying to display a sphere in PGF/TikZ to illustrate the idea of great circles. The code for my current result is: \begin{tikzpicture} \tikzfading[name=fade right, left color=transparent!20, right color=transparent!90] \tikzfading[name=fade out, inner color=transparent!100, outer color=transparent!10] \tikzfading[name=fade right gc, left color=transparent!0, right color=transparent!70] \draw [<->, dashed] (0,-5) -- (0,5); % y-axis \draw [->, dashed] (0, 0) -- (20:5); % x-axis \draw [->, dashed] (0, 0) -- (200:5); % x-axis \draw [->, dashed] (0, 0) -- (340:5); % z-axis \draw [->, dashed] (0, 0) -- (160:5); % z-axis \fill [color=cyan, opacity=0.15, path fading=fade out] (0,0) circle (4cm); % bounding circle \fill [color=cyan, opacity=0.25, path fading=fade right, fading angle=90] (0,0) ellipse (4cm and 1cm); % x-y-axis area % great circle 1 \draw [rotate=-40, color=red, path fading=fade right gc, fading angle=40] (0,0) ellipse (4cm and 1cm); % great circle 2 \draw[rotate=5, color=red, path fading=fade right gc, fading angle=5] (0,0) ellipse (1.5cm and 4cm); \end{tikzpicture} How do I find the two points of intersection of the two red ellipses (commented as great circle 1 and 2), find the point of intersection of a line (originating at the center (0,0)) with a ellipse, and place a little circle or rectangle there? Placing a little circle or rectangle there is not an issue. Thank you very much!