diff options
Diffstat (limited to '')
| -rw-r--r-- | buch/chapters/030-geometrie/images/kegelschnitte.jpg | bin | 158373 -> 174074 bytes | |||
| -rw-r--r-- | buch/chapters/030-geometrie/images/kegelschnitte.pdf | bin | 179256 -> 194994 bytes | |||
| -rw-r--r-- | buch/chapters/030-geometrie/images/kegelschnitte.pov | 46 | ||||
| -rw-r--r-- | buch/chapters/030-geometrie/images/kegelschnitte.tex | 88 |
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 Binary files differindex 5d0b329..75fc133 100644 --- a/buch/chapters/030-geometrie/images/kegelschnitte.jpg +++ b/buch/chapters/030-geometrie/images/kegelschnitte.jpg diff --git a/buch/chapters/030-geometrie/images/kegelschnitte.pdf b/buch/chapters/030-geometrie/images/kegelschnitte.pdf Binary files differindex aa697f4..c2205bf 100644 --- a/buch/chapters/030-geometrie/images/kegelschnitte.pdf +++ b/buch/chapters/030-geometrie/images/kegelschnitte.pdf 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 Örter +% \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} |
