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-rw-r--r--buch/chapters/030-geometrie/images/kegelschnitte.jpgbin158373 -> 174074 bytes
-rw-r--r--buch/chapters/030-geometrie/images/kegelschnitte.pdfbin179256 -> 194994 bytes
-rw-r--r--buch/chapters/030-geometrie/images/kegelschnitte.pov46
-rw-r--r--buch/chapters/030-geometrie/images/kegelschnitte.tex88
4 files changed, 100 insertions, 34 deletions
diff --git a/buch/chapters/030-geometrie/images/kegelschnitte.jpg b/buch/chapters/030-geometrie/images/kegelschnitte.jpg
index 5d0b329..75fc133 100644
--- a/buch/chapters/030-geometrie/images/kegelschnitte.jpg
+++ b/buch/chapters/030-geometrie/images/kegelschnitte.jpg
Binary files differ
diff --git a/buch/chapters/030-geometrie/images/kegelschnitte.pdf b/buch/chapters/030-geometrie/images/kegelschnitte.pdf
index aa697f4..c2205bf 100644
--- a/buch/chapters/030-geometrie/images/kegelschnitte.pdf
+++ b/buch/chapters/030-geometrie/images/kegelschnitte.pdf
Binary files differ
diff --git a/buch/chapters/030-geometrie/images/kegelschnitte.pov b/buch/chapters/030-geometrie/images/kegelschnitte.pov
index 60e6964..6b6388b 100644
--- a/buch/chapters/030-geometrie/images/kegelschnitte.pov
+++ b/buch/chapters/030-geometrie/images/kegelschnitte.pov
@@ -13,6 +13,7 @@ global_settings {
#declare imagescale = 0.090;
#declare r = 0.03;
#declare R = 1.3 * r;
+#declare rkurve = 0.6 * r;
camera {
location <-33, 20, 50>
@@ -77,6 +78,7 @@ union {
#declare kurvenfarbe = rgb<0.4,0.8,0>;
#declare leitfarbe = rgb<0.8,0.2,0.8>;
#declare ebenenfarbe = rgbt<0.6,0.4,0.2,0.0>;
+#declare mantelfarbe = rgb<0.2,0.6,1.0>;
#declare kegelhoehe = 3;
#declare kegelradius = 1.4;
@@ -150,6 +152,32 @@ intersection {
}
}
+#declare ymantel = kegelradius - 1;
+#declare xmantel = sqrt(kegelradius*kegelradius-ymantel*ymantel);
+
+union {
+ cylinder {
+ <3+xmantel,-kegelhoehe,ymantel>,
+ <3-xmantel,kegelhoehe,-ymantel>,
+ 0.5 * rkurve
+ }
+ sphere { <3+xmantel,-kegelhoehe,ymantel>, 0.5 * rkurve }
+ sphere { <3-xmantel,kegelhoehe,-ymantel>, 0.5 * rkurve }
+ cylinder {
+ <3-xmantel,-kegelhoehe,ymantel>,
+ <3+xmantel,kegelhoehe,-ymantel>,
+ 0.5 * rkurve
+ }
+ sphere { <3-xmantel,-kegelhoehe,ymantel>, 0.5 * rkurve }
+ sphere { <3+xmantel,kegelhoehe,-ymantel>, 0.5 * rkurve }
+ pigment {
+ color mantelfarbe
+ }
+ finish {
+ specular 0.5
+ metallic
+ }
+}
#declare e3 = <0, 1, 0>;
#declare tunten = -offsethyperbel / vdot(nparabel-nhyperbel, e3);
@@ -185,7 +213,6 @@ intersection {
Origin + (-a * cosh(s) * xaxis + b * sinh(s) * yaxis)
#end
-#declare rkurve = 0.6 * r;
// Hyperbel
union {
@@ -279,6 +306,23 @@ intersection {
}
}
+union {
+ cylinder {
+ <0,-kegelhoehe,kegelradius>,
+ <0,kegelhoehe,-kegelradius>,
+ 0.5 * rkurve
+ }
+ sphere { <0,-kegelhoehe,kegelradius>, 0.5 * rkurve }
+ sphere { <0,kegelhoehe,-kegelradius>, 0.5 * rkurve }
+ pigment {
+ color mantelfarbe
+ }
+ finish {
+ specular 0.5
+ metallic
+ }
+}
+
ebene(0, nparabel, offsetparabel, 0.5)
#declare tcenter = 0.5 * offsetparabel / vdot(nparabel, e3);
diff --git a/buch/chapters/030-geometrie/images/kegelschnitte.tex b/buch/chapters/030-geometrie/images/kegelschnitte.tex
index b8067ad..bb91d0d 100644
--- a/buch/chapters/030-geometrie/images/kegelschnitte.tex
+++ b/buch/chapters/030-geometrie/images/kegelschnitte.tex
@@ -18,6 +18,7 @@
\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}
@@ -37,38 +38,56 @@
\fill (0,0) circle[radius=0.05];
}{}
+%
+% Lage der Schnittebene
+%
\begin{scope}[yshift=-7.5cm]
-
-\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}
-\end{scope}
-
-\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}
-\end{scope}
-
-\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}
+ % 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});
@@ -97,15 +116,18 @@
\marke{5.3}{-0.0}{scheitelfarbe}{$S_2$}
\node[color=yellow] at (4.8,-2.7) [below right] {$P$};
+%
+% Beschriftung und geometrische Ă–rter
+%
\begin{scope}[yshift=-5.5cm]
-\node at (-4.5,0)
+ \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] (-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)
+ \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}