Ian Jauslin
summaryrefslogtreecommitdiff
blob: 96b6bff86eabbd4711bb58825d823e8a863c8a95 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
\documentclass{standalone}

\usepackage{xcolor}

\definecolor{darkgreen}{HTML}{329D32}

\usepackage{tikz}

\begin{document}
\begin{tikzpicture}[scale=2.5]

\draw[color=blue](0,0)ellipse(1.5 and 1.0);

% angle of L
\def\tt{15}
% foci ae=sqrt(1-b^2/a^2)
\def\ae{1.118}
% collision point
\def\Px{0.5}
% Py=sqrt(1-Px^2/a^2)
\def\Py{0.943}
% slope Px/(a^2*sqrt(1-Px^2/a^2))
\def\slope{0.236}
% phi: atan(\Py/(\ae+\Px))
\def\ph{15.2}
% phi': pi-atan(\Py/(\ae-\Px))
\def\php{108.2}
% lambda: pi-atan(\slope)
\def\lam{151.7}
% psi: pi+phi-lambda
\def\ps{43.5}
% h=sin(\ph)*sqrt((\Px+\ae)^2+Py^2)
\def\h{0.491}

% foci
\path(-\ae,0)coordinate(F1);
\path(\ae,0)coordinate(F2);
% collision point
\path(\Px,\Py)coordinate(P);
%Q
\path(F1)++(90+\tt:\h)coordinate(Q);

\draw[densely dotted](F1)++(\tt:3)--++(180+\tt:3.5);
\draw[densely dotted](F2)++(\tt:0.7)--++(180+\tt:3.5);
\draw[line width=1](P)++(\tt:1)--++(180+\tt:3.5);

\draw[color=gray](F1)--(P)--(F2);

\draw[color=darkgreen,dashed](P)--++(1,-\slope);
\draw[color=darkgreen,dashed](P)--++(-1,\slope);

\draw[rotate=\tt](F1)++(0.4,0)arc(0:\ph:0.4);
\draw(F1)++(\tt+\ph/2:0.5)node{$\varphi$};
\draw[rotate=\tt](F2)++(0.15,0)arc(0:\php:0.15);
\draw(F2)++(\tt+\php/2:0.25)node{$\varphi'$};

\draw[rotate=\tt](P)++(0.1,0)arc(0:\lam:0.1);
\draw(P)++(\tt+\lam/2:0.2)node{$\lambda$};

\draw[rotate=\tt+\lam](P)++(0.2,0)arc(0:\ps:0.2);
\draw(P)++(\tt+\lam+\ps/2-7:0.3)node{$\psi$};
\draw[rotate=180+\tt+\lam](P)++(0.2,0)arc(0:-\ps:0.2);
\draw(P)++(\tt+180+\lam-\ps/2:0.3)node{$\psi$};


\fill[color=red](F1)circle(0.03);
\draw(F1)++(0,-0.15)node{$O$};
\fill(F2)circle(0.03);
\draw(F2)++(0,-0.15)node{$O'$};

\fill(P)circle(0.03);
\draw(P)++(\lam+\ps+90-\ps:0.15)node{$P$};

\fill(0,0)circle(0.03);
\draw(0,-0.15)node{$C$};

\fill(Q)circle(0.03);
\draw(Q)++(0,-0.15)node{$Q$};

\draw[dotted,<->](F1)++(\tt:-0.5)--++(90+\tt:\h);
\draw(F1)++(\tt:-0.6)++(90+\tt:\h/2)node{$h$};


\end{tikzpicture}
\end{document}