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
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
|
%
% kegelschnitt.tex
%
% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
%
\documentclass[tikz]{standalone}
\usepackage{times}
\usepackage{amsmath}
\usepackage{txfonts}
\usepackage[utf8]{inputenc}
\usepackage{graphics}
\usetikzlibrary{arrows,intersections,math,calc}
\usepackage{ifthen}
\begin{document}
\definecolor{kegelfarbe}{rgb}{0.2,0.6,0.6}
\definecolor{ebenenfarbe}{rgb}{0.6,0.4,0.2}
\definecolor{fokusfarbe}{rgb}{0.8,0.0,0.0}
\definecolor{scheitelfarbe}{rgb}{0,0.6,0}
\definecolor{leitfarbe}{rgb}{0.8,0.2,0.8}
\definecolor{mantelfarbe}{rgb}{0.2,0.6,1.0}
\newboolean{showgrid}
\setboolean{showgrid}{false}
\def\breite{7}
\def\hoehe{5}
\begin{tikzpicture}[>=latex,thick]
% Povray Bild
\node at (0,0) {\includegraphics[width=14cm]{kegelschnitte.jpg}};
% Gitter
\ifthenelse{\boolean{showgrid}}{
\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
\draw (-\breite,-\hoehe) grid (\breite, \hoehe);
\fill (0,0) circle[radius=0.05];
}{}
%
% Lage der Schnittebene
%
\begin{scope}[yshift=-7.5cm]
% Hyperbel
\begin{scope}[xshift=-4.5cm]
\clip (-2,-2.5) rectangle (2,1.5);
\fill[color=kegelfarbe!40]
(-1.4,-3) -- (1.4,-3) -- (-1.4,3) -- (1.4,3) -- cycle;
\begin{scope}[xshift=-0.3cm]
\draw[color=ebenenfarbe,line width=1.4pt]
(-0.4,-3) -- (0.4,3);
\end{scope}
\begin{scope}
\draw[color=mantelfarbe,line width=1.2pt]
(-0.4,-3) -- (0.4,3);
\end{scope}
\end{scope}
% Parabel
\begin{scope}
\clip (-2,-2.5) rectangle (2,1.5);
\fill[color=kegelfarbe!40]
(-1.4,-3) -- (1.4,-3) -- (-1.4,3) -- (1.4,3) -- cycle;
\begin{scope}[xshift=0.5cm]
\draw[color=ebenenfarbe,line width=1.4pt]
(-1.4,-3) -- (1.4,3);
\end{scope}
\begin{scope}
\draw[color=mantelfarbe,line width=1.2pt]
(-1.4,-3) -- (1.4,3);
\end{scope}
\end{scope}
% Ellipse
\begin{scope}[xshift=4.5cm]
\clip (-2,-2.5) rectangle (2,1.5);
\fill[color=kegelfarbe!40]
(-1.4,-3) -- (1.4,-3) -- (-1.4,3) -- (1.4,3) -- cycle;
\begin{scope}[xshift=0.9cm]
\draw[color=ebenenfarbe,line width=1.4pt]
(-3.4,-3) -- (3.4,3);
\end{scope}
\end{scope}
\end{scope}
%
% Beschriftung der 3D-Abbildung
%
\def\marke#1#2#3#4{
\fill[color=white,opacity=0.5]
({#1-0.25},{#2-0.2}) rectangle ({#1+0.20},{#2+0.2});
\node[color=#3] at ({#1},{#2}) {#4};
}
\node[color=fokusfarbe] at (-5,0.5) {$F_1$};
\node[color=fokusfarbe] at (-4.5,4.4) {$F_2$};
%\node[color=scheitelfarbe] at (-4.5,4.1) [below left] {$S_2$};
%\node[color=scheitelfarbe] at (-4.7,0.8) [above left] {$S_1$};
\marke{-4.9}{3.7}{scheitelfarbe}{$S_2$}
\marke{-5.1}{1.1}{scheitelfarbe}{$S_1$}
\node[color=yellow] at (-3.9,-0.9) [right] {$P$};
\node[color=fokusfarbe] at (0.05,0.75) {$F$};
%\node[color=scheitelfarbe] at (0.4,1.0) [above left] {$S$};
\marke{0.35}{1.4}{scheitelfarbe}{$S$};
\node[color=yellow] at (0.95,-0.6) [right] {$P$};
\node[color=leitfarbe] at (2.2,1.2) {$l$};
\node[color=fokusfarbe] at (3.5,-2.9) {$F_1$};
\node[color=fokusfarbe] at (4.4,-0.8) {$F_2$};
%\node[color=scheitelfarbe] at (3.6,-3.5) [below left] {$S_1$};
%\node[color=scheitelfarbe] at (4.8,-0.4) [above right] {$S_2$};
\marke{3.05}{-3.85}{scheitelfarbe}{$S_1$}
\marke{5.3}{-0.0}{scheitelfarbe}{$S_2$}
\node[color=yellow] at (4.8,-2.7) [below right] {$P$};
%
% Beschriftung und geometrische Örter
%
\begin{scope}[yshift=-5.5cm]
\node at (-4.5,0)
{Hyperbel: $\overline{F_1P}-\overline{F_2P}=\text{const}$\strut};
\fill[color=white,opacity=0.7] (-1.3,-0.25) rectangle (1.3,0.25);
\node at (0,0) {Parabel: $\overline{FP}=\overline{lP}$\strut};
\fill[color=white,opacity=0.7] (2.4,-0.25) rectangle (6.6,0.25);
\node at (4.5,0)
{Ellipse: $\overline{F_1P}+\overline{F_2P}=\text{const}$\strut};
\end{scope}
\end{tikzpicture}
\end{document}
|
