How to Find Intersections with Ellipses in PGF/TikZ
- by infblnpf
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!
