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POHow to Find Intersections with Ellipses in PGF/TikZ
 

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  1. POHow to Find Intersections with Ellipses in PGF/TikZ
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    <p>I am trying to display a sphere in PGF/TikZ to illustrate the idea of great circles.</p> <p>The code for my current result is:</p> <pre><code>\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 [&lt;-&gt;, dashed] (0,-5) -- (0,5); % y-axis \draw [-&gt;, dashed] (0, 0) -- (20:5); % x-axis \draw [-&gt;, dashed] (0, 0) -- (200:5); % x-axis \draw [-&gt;, dashed] (0, 0) -- (340:5); % z-axis \draw [-&gt;, 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} </code></pre> <p>How do I</p> <ol> <li>find the two points of intersection of the two red ellipses (commented as great circle 1 and 2), </li> <li>find the point of intersection of a line (originating at the center (0,0)) with a ellipse, and</li> <li>place a little circle or rectangle there?</li> </ol> <p>Placing a little circle or rectangle there is not an issue. Thank you very much!</p>
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