87 lines
1.9 KiB
TeX
87 lines
1.9 KiB
TeX
\documentclass{standalone}
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\usepackage{xcolor}
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\definecolor{darkgreen}{HTML}{329D32}
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\usepackage{tikz}
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\begin{document}
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\begin{tikzpicture}[scale=2.5]
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\draw[color=blue](0,0)ellipse(1.5 and 1.0);
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% angle of L
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\def\tt{15}
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% foci ae=sqrt(1-b^2/a^2)
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\def\ae{1.118}
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% collision point
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\def\Px{0.5}
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% Py=sqrt(1-Px^2/a^2)
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\def\Py{0.943}
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% slope Px/(a^2*sqrt(1-Px^2/a^2))
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\def\slope{0.236}
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% phi: atan(\Py/(\ae+\Px))
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\def\ph{15.2}
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% phi': pi-atan(\Py/(\ae-\Px))
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\def\php{108.2}
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% lambda: pi-atan(\slope)
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\def\lam{151.7}
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% psi: pi+phi-lambda
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\def\ps{43.5}
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% h=sin(\ph)*sqrt((\Px+\ae)^2+Py^2)
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\def\h{0.491}
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% foci
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\path(-\ae,0)coordinate(F1);
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\path(\ae,0)coordinate(F2);
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% collision point
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\path(\Px,\Py)coordinate(P);
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%Q
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\path(F1)++(90+\tt:\h)coordinate(Q);
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\draw[densely dotted](F1)++(\tt:3)--++(180+\tt:3.5);
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\draw[densely dotted](F2)++(\tt:0.7)--++(180+\tt:3.5);
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\draw[line width=1](P)++(\tt:1)--++(180+\tt:3.5);
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\draw[color=gray](F1)--(P)--(F2);
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\draw[color=darkgreen,dashed](P)--++(1,-\slope);
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\draw[color=darkgreen,dashed](P)--++(-1,\slope);
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\draw[rotate=\tt](F1)++(0.4,0)arc(0:\ph:0.4);
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\draw(F1)++(\tt+\ph/2:0.5)node{$\varphi$};
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\draw[rotate=\tt](F2)++(0.15,0)arc(0:\php:0.15);
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\draw(F2)++(\tt+\php/2:0.25)node{$\varphi'$};
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\draw[rotate=\tt](P)++(0.1,0)arc(0:\lam:0.1);
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\draw(P)++(\tt+\lam/2:0.2)node{$\lambda$};
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\draw[rotate=\tt+\lam](P)++(0.2,0)arc(0:\ps:0.2);
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\draw(P)++(\tt+\lam+\ps/2-7:0.3)node{$\psi$};
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\draw[rotate=180+\tt+\lam](P)++(0.2,0)arc(0:-\ps:0.2);
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\draw(P)++(\tt+180+\lam-\ps/2:0.3)node{$\psi$};
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\fill[color=red](F1)circle(0.03);
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\draw(F1)++(0,-0.15)node{$O$};
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\fill(F2)circle(0.03);
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\draw(F2)++(0,-0.15)node{$O'$};
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\fill(P)circle(0.03);
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\draw(P)++(\lam+\ps+90-\ps:0.15)node{$P$};
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\fill(0,0)circle(0.03);
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\draw(0,-0.15)node{$C$};
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\fill(Q)circle(0.03);
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\draw(Q)++(0,-0.15)node{$Q$};
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\draw[dotted,<->](F1)++(\tt:-0.5)--++(90+\tt:\h);
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\draw(F1)++(\tt:-0.6)++(90+\tt:\h/2)node{$h$};
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\end{tikzpicture}
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\end{document}
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