From 123a5f4a7d5afb554d17a6ffc795a7bf1921abf0 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sun, 22 Aug 2021 11:16:26 +0200 Subject: add additional image --- buch/chapters/95-homologie/images/Makefile | 17 ++- .../95-homologie/images/gausshomobasis.pdf | Bin 0 -> 24156 bytes .../95-homologie/images/gausshomobasis.tex | 109 ++++++++++++++ buch/chapters/95-homologie/images/gausshomoex.pdf | Bin 0 -> 15128 bytes buch/chapters/95-homologie/images/gausshomoex.tex | 120 ++++++++++++++++ .../95-homologie/images/homoboundaries.pdf | Bin 0 -> 17163 bytes .../95-homologie/images/homoboundaries.tex | 114 +++++++++++++++ buch/chapters/95-homologie/images/homoclasses.pdf | Bin 0 -> 11647 bytes buch/chapters/95-homologie/images/homoclasses.tex | 104 ++++++++++++++ buch/chapters/95-homologie/images/homocycles.pdf | Bin 0 -> 16779 bytes buch/chapters/95-homologie/images/homocycles.tex | 157 +++++++++++++++++++++ 11 files changed, 620 insertions(+), 1 deletion(-) create mode 100644 buch/chapters/95-homologie/images/gausshomobasis.pdf create mode 100644 buch/chapters/95-homologie/images/gausshomobasis.tex create mode 100644 buch/chapters/95-homologie/images/gausshomoex.pdf create mode 100644 buch/chapters/95-homologie/images/gausshomoex.tex create mode 100644 buch/chapters/95-homologie/images/homoboundaries.pdf create mode 100644 buch/chapters/95-homologie/images/homoboundaries.tex create mode 100644 buch/chapters/95-homologie/images/homoclasses.pdf create mode 100644 buch/chapters/95-homologie/images/homoclasses.tex create mode 100644 buch/chapters/95-homologie/images/homocycles.pdf create mode 100644 buch/chapters/95-homologie/images/homocycles.tex (limited to 'buch/chapters/95-homologie/images') diff --git a/buch/chapters/95-homologie/images/Makefile b/buch/chapters/95-homologie/images/Makefile index ac964ff..d14a3a2 100644 --- a/buch/chapters/95-homologie/images/Makefile +++ b/buch/chapters/95-homologie/images/Makefile @@ -3,7 +3,7 @@ # # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -all: dreieck.pdf polyeder.pdf +all: homocycles.pdf homoboundaries.pdf homoclasses.pdf gausshomoex.pdf gausshomobasis.pdf dreieck.pdf polyeder.pdf dreieck.pdf: dreieck.tex pdflatex dreieck.tex @@ -11,3 +11,18 @@ dreieck.pdf: dreieck.tex polyeder.pdf: polyeder.tex pdflatex polyeder.tex +gausshomobasis.pdf: gausshomobasis.tex + pdflatex gausshomobasis.tex + +gausshomoex.pdf: gausshomoex.tex + pdflatex gausshomoex.tex + +homocycles.pdf: homocycles.tex + pdflatex homocycles.tex + +homoboundaries.pdf: homoboundaries.tex + pdflatex homoboundaries.tex + +homoclasses.pdf: homoclasses.tex + pdflatex homoclasses.tex + diff --git a/buch/chapters/95-homologie/images/gausshomobasis.pdf b/buch/chapters/95-homologie/images/gausshomobasis.pdf new file mode 100644 index 0000000..07414bb Binary files /dev/null and b/buch/chapters/95-homologie/images/gausshomobasis.pdf differ diff --git a/buch/chapters/95-homologie/images/gausshomobasis.tex b/buch/chapters/95-homologie/images/gausshomobasis.tex new file mode 100644 index 0000000..ba21f54 --- /dev/null +++ b/buch/chapters/95-homologie/images/gausshomobasis.tex @@ -0,0 +1,109 @@ +% +% gaushomobasis.tex -- Bestimmung einer Basis der Homologiegruppen +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\s{0.5} +\def\inset{0.05} +\def\w{8} + +\def\zeile#1#2{ + \fill[color=#2] ({0+\inset},{(12-#1)*\s+\inset}) + rectangle ({\w*\s-\inset},{(13-#1)*\s-\inset}); +} +\def\marke#1#2{ +\node at ({0.5*\w*\s},{12.5-#1)*\s}) {$#2\mathstrut$}; +} + +\def\gauss{ +\draw (0,0) rectangle ({\w*\s},{12*\s}); +\draw (0,{7*\s}) -- ({\w*\s},{7*\s}); +} + +\draw[->,color=red,line width=1pt] ({0.1*\s},{(12.5-1)*\s}) + to[out=180,in=90] (-3.6,-2); +\draw[->,color=red,line width=1pt] ({0.1*\s},{(12.5-2)*\s}) + to[out=180,in=90] (-2.2,-2); +\draw[->,color=red,line width=1pt] ({0.1*\s},{(12.5-4)*\s}) + to[out=180,in=90] (-0.7,-2); + +\draw[->,color=darkgreen,line width=1pt] ({0.1*\s},{(12.5-7)*\s}) + to[out=180,in=90] (0.9,-2); +\draw[->,color=darkgreen,line width=1pt] ({0.1*\s},{(12.5-8)*\s}) + to[out=180,in=90] (1.6,-2); +\draw[->,color=darkgreen,line width=1pt] ({(\w-0.1)*\s},{(12.5-12)*\s}) + to[out=0,in=90] (2.6,-2); + +\draw[->,line width=2pt] ({\w*\s+0.1},{6*\s}) -- (5.4,{6*\s}); +\node at ({0.5*(\w*\s+5.5)},{6*\s}) [above] {Gauss}; + +\begin{scope} +\zeile{1}{red!30} +\zeile{2}{red!30} +\zeile{4}{red!30} +\zeile{7}{darkgreen!30} +\zeile{8}{darkgreen!30} +%\zeile{10}{darkgreen!30} +\zeile{12}{darkgreen!30} +\marke{1}{\scriptstyle\partial_{k+1}e_1^{(k+1)}} +\marke{2}{\scriptstyle\partial_{k+1}e_2^{(k+1)}} +\marke{3}{\scriptstyle\partial_{k+1}e_3^{(k+1)}} +\marke{4}{\vdots} +\marke{5}{\scriptstyle\partial_{k+1}e_{n_{k+1}}^{(k+1)}} +\marke{6}{\scriptstyle z_1^{(k)}} +\marke{7}{\scriptstyle z_2^{(k)}} +\marke{8}{\scriptstyle z_3^{(k)}} +\marke{9}{\scriptstyle z_4^{(k)}} +\marke{10}{\vdots} +\marke{11}{\scriptstyle z_{l-1}^{(k)}} +\marke{12}{\scriptstyle z_{l}^{(k)}} +\gauss +\end{scope} + +\begin{scope}[xshift=5.5cm] +\zeile{1}{black!20} +\zeile{2}{black!20} +\zeile{3}{black} +\marke{3}{\color{white}0} +\zeile{4}{black!20} +\zeile{5}{black} +\marke{5}{\color{white}0} +\zeile{6}{black} +\marke{6}{\color{white}0} +\zeile{7}{black!20} +\zeile{8}{black!20} +\zeile{9}{black} +\marke{9}{\color{white}0} +\zeile{10}{black} +\marke{10}{\color{white}0} +\zeile{11}{black} +\marke{11}{\color{white}0} +\zeile{12}{black!20} +\gauss +\end{scope} + +\node at (-4.4,-2) [below right] {$\{ +{\color{red}\partial_{k+1}e_1^{(k+1)}}, +{\color{red}\partial_{k+1}e_2^{(k+1)}}, +{\color{red}\partial_{k+1}e_{i_3}^{(k+1)}},\dots, +{\color{darkgreen}z_2^{(k)}}, +{\color{darkgreen}z_3^{(k)}}, +\dots +{\color{darkgreen}z_l^{(k)}} +\} = {\color{red}\mathcal{B}_k} \cup {\color{darkgreen}\mathcal{Z}_k'}$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/95-homologie/images/gausshomoex.pdf b/buch/chapters/95-homologie/images/gausshomoex.pdf new file mode 100644 index 0000000..bc0b766 Binary files /dev/null and b/buch/chapters/95-homologie/images/gausshomoex.pdf differ diff --git a/buch/chapters/95-homologie/images/gausshomoex.tex b/buch/chapters/95-homologie/images/gausshomoex.tex new file mode 100644 index 0000000..df53f70 --- /dev/null +++ b/buch/chapters/95-homologie/images/gausshomoex.tex @@ -0,0 +1,120 @@ +% +% gausshomoex.tex -- Beispiel für die Bestimmung einer Basis von H_1 +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\s{2.0} + +\def\punkt#1#2{({((#1)+0.5*(#2))*\s},{(#2)*\s*sqrt(3)/2})} + +\def\knoten#1#2#3{ + \fill[color=white] \punkt{#1}{#2} circle[radius=0.3]; + \node at \punkt{#1}{#2} {$#3$\strut}; + \draw \punkt{#1}{#2} circle[radius=0.3]; +} +\def\dreieck#1#2#3{ + \fill[color=gray] \punkt{#1}{#2} -- \punkt{#1+1}{#2} + -- \punkt{#1}{(#2)+1} -- cycle; + \node at \punkt{#1+0.3333}{#2+0.3333} {$#3$\strut}; + \draw[->,line width=1pt,shorten >= 0.3cm,shorten <= 0.3cm] + \punkt{#1}{#2} -- \punkt{#1+1}{#2}; + \draw[->,line width=1pt,shorten >= 0.3cm,shorten <= 0.3cm] + \punkt{#1+1}{#2} -- \punkt{#1}{#2+1}; + \draw[->,line width=1pt,shorten >= 0.3cm,shorten <= 0.3cm] + \punkt{#1}{#2+1} -- \punkt{#1}{#2}; +} + +\def\Dreieck#1#2#3{ + \fill[color=gray!50] \punkt{#1}{#2} -- \punkt{#1+1}{#2} + -- \punkt{#1+1}{(#2)-1} -- cycle; + \node at \punkt{#1+0.3333}{#2+0.3333} {$#3$\strut}; +} + +\def\kante#1#2#3{ + \fill[color=white,opacity=0.8] \punkt{#1}{#2} circle[radius=0.15]; + \node at \punkt{#1}{#2} {$\scriptstyle #3$}; +} + +\dreieck{0}{0}{1} +\dreieck{1}{0}{2} +\dreieck{2}{0}{3} +\dreieck{3}{0}{4} + +\dreieck{0}{1}{5} +\dreieck{2}{1}{6} + +\dreieck{0}{2}{7} +\dreieck{1}{2}{8} + +\dreieck{0}{3}{9} + + +\knoten{0}{0}{1} +\knoten{1}{0}{2} +\knoten{2}{0}{3} +\knoten{3}{0}{4} +\knoten{4}{0}{5} + +\knoten{0}{1}{6} +\knoten{1}{1}{7} +\knoten{2}{1}{8} +\knoten{3}{1}{9} + +\knoten{0}{2}{10} +\knoten{1}{2}{11} +\knoten{2}{2}{12} + +\knoten{0}{3}{13} +\knoten{1}{3}{14} + +\knoten{0}{4}{15} + +\kante{0.5}{0}{1} +\kante{1.5}{0}{2} +\kante{2.5}{0}{3} +\kante{3.5}{0}{4} + +\kante{0}{0.5}{5} +\kante{0.5}{0.5}{6} +\kante{1}{0.5}{7} +\kante{1.5}{0.5}{8} +\kante{2}{0.5}{9} +\kante{2.5}{0.5}{10} +\kante{3}{0.5}{11} +\kante{3.5}{0.5}{12} + +\kante{0.5}{1}{13} +\kante{2.5}{1}{14} + +\kante{0}{1.5}{15} +\kante{0.5}{1.5}{16} +\kante{2}{1.5}{17} +\kante{2.5}{1.5}{18} + +\kante{0.5}{2}{19} +\kante{1.5}{2}{20} + +\kante{0}{2.5}{21} +\kante{0.5}{2.5}{22} +\kante{1}{2.5}{23} +\kante{1.5}{2.5}{24} + +\kante{0.5}{3}{25} + +\kante{0}{3.5}{26} +\kante{0.5}{3.5}{27} + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/95-homologie/images/homoboundaries.pdf b/buch/chapters/95-homologie/images/homoboundaries.pdf new file mode 100644 index 0000000..644f334 Binary files /dev/null and b/buch/chapters/95-homologie/images/homoboundaries.pdf differ diff --git a/buch/chapters/95-homologie/images/homoboundaries.tex b/buch/chapters/95-homologie/images/homoboundaries.tex new file mode 100644 index 0000000..ef8fd1a --- /dev/null +++ b/buch/chapters/95-homologie/images/homoboundaries.tex @@ -0,0 +1,114 @@ +% +% tikztemplate.tex -- template for standalon tikz images +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\s{0.4} + +\def\punkt#1#2{({((#1)+0.5*(#2))*\s},{(#2)*\s*sqrt(3)/2})} +\def\A{\punkt{0}{0}} +\def\B{\punkt{1}{0}} +\def\C{\punkt{2}{0}} +\def\D{\punkt{3}{0}} +\def\E{\punkt{4}{0}} +\def\F{\punkt{0}{1}} +\def\G{\punkt{1}{1}} +\def\H{\punkt{2}{1}} +\def\I{\punkt{3}{1}} +\def\J{\punkt{0}{2}} +\def\K{\punkt{1}{2}} +\def\L{\punkt{2}{2}} +\def\M{\punkt{0}{3}} +\def\N{\punkt{1}{3}} +\def\O{\punkt{0}{4}} + +\def\dreieck#1#2#3{ + \fill[color=gray] \punkt{#1}{#2} -- \punkt{#1+1}{#2} + -- \punkt{#1}{(#2)+1} -- cycle; +} + +\def\blau#1#2{ + \draw[color=blue] \punkt{#1}{#2} -- \punkt{#1+1}{#2} + -- \punkt{#1}{(#2)+1} -- cycle; +} + +\def\gebiet{ + \dreieck{0}{0}{1} + \dreieck{1}{0}{2} + \dreieck{2}{0}{3} + \dreieck{3}{0}{4} + \dreieck{0}{1}{5} + \dreieck{2}{1}{6} + \dreieck{0}{2}{7} + \dreieck{1}{2}{8} + \dreieck{0}{3}{9} +} + +\begin{scope} +\gebiet +\blau{0}{0} +\node[color=blue] at ({2*\s},-0.5) {$\partial_2e_1^{(2)}$}; +\end{scope} + +\begin{scope}[xshift=3cm] +\gebiet +\blau{1}{0} +\node[color=blue] at ({2*\s},-0.5) {$\partial_2e_2^{(2)}$}; +\end{scope} + +\begin{scope}[xshift=6cm] +\gebiet +\blau{2}{0} +\node[color=blue] at ({2*\s},-0.5) {$\partial_2e_3^{(2)}$}; +\end{scope} + +\begin{scope}[xshift=9cm] +\gebiet +\blau{3}{0} +\node[color=blue] at ({2*\s},-0.5) {$\partial_2e_4^{(2)}$}; +\end{scope} + +\begin{scope}[xshift=1.5cm,yshift=2.59cm] +\gebiet +\blau{0}{1} +\node[color=blue] at ({2*\s},-0.5) {$\partial_2e_5^{(2)}$}; +\end{scope} + +\begin{scope}[xshift=7.5cm,yshift=2.59cm] +\gebiet +\blau{2}{1} +\node[color=blue] at ({2*\s},-0.5) {$\partial_2e_6^{(2)}$}; +\end{scope} + +\begin{scope}[xshift=3cm,yshift=5.19cm] +\gebiet +\blau{0}{2} +\node[color=blue] at ({2*\s},-0.5) {$\partial_2e_7^{(2)}$}; +\end{scope} + +\begin{scope}[xshift=6cm,yshift=5.19cm] +\gebiet +\blau{1}{2} +\node[color=blue] at ({2*\s},-0.5) {$\partial_2e_8^{(2)}$}; +\end{scope} + +\begin{scope}[xshift=4.5cm,yshift=7.79cm] +\gebiet +\blau{0}{3} +\node[color=blue] at ({2*\s},-0.5) {$\partial_2e_9^{(2)}$}; +\end{scope} + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/95-homologie/images/homoclasses.pdf b/buch/chapters/95-homologie/images/homoclasses.pdf new file mode 100644 index 0000000..217ae75 Binary files /dev/null and b/buch/chapters/95-homologie/images/homoclasses.pdf differ diff --git a/buch/chapters/95-homologie/images/homoclasses.tex b/buch/chapters/95-homologie/images/homoclasses.tex new file mode 100644 index 0000000..e325d9b --- /dev/null +++ b/buch/chapters/95-homologie/images/homoclasses.tex @@ -0,0 +1,104 @@ +% +% tikztemplate.tex -- template for standalon tikz images +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\definecolor{darkgreen}{rgb}{0,0.6,0} +\def\s{0.4} + +\def\punkt#1#2{({((#1)+0.5*(#2))*\s},{(#2)*\s*sqrt(3)/2})} +\def\A{\punkt{0}{0}} +\def\B{\punkt{1}{0}} +\def\C{\punkt{2}{0}} +\def\D{\punkt{3}{0}} +\def\E{\punkt{4}{0}} +\def\F{\punkt{0}{1}} +\def\G{\punkt{1}{1}} +\def\H{\punkt{2}{1}} +\def\I{\punkt{3}{1}} +\def\J{\punkt{0}{2}} +\def\K{\punkt{1}{2}} +\def\L{\punkt{2}{2}} +\def\M{\punkt{0}{3}} +\def\N{\punkt{1}{3}} +\def\O{\punkt{0}{4}} + +%\def\knoten#1#2#3{ +% \fill[color=white] \punkt{#1}{#2} circle[radius=0.3]; +% \node at \punkt{#1}{#2} {$#3$\strut}; +% \draw \punkt{#1}{#2} circle[radius=0.3]; +%} +\def\dreieck#1#2#3{ + \fill[color=gray] \punkt{#1}{#2} -- \punkt{#1+1}{#2} + -- \punkt{#1}{(#2)+1} -- cycle; +% \node at \punkt{#1+0.3333}{#2+0.3333} {$#3$\strut}; +% \draw[->,line width=1pt,shorten >= 0.3cm,shorten <= 0.3cm] +% \punkt{#1}{#2} -- \punkt{#1+1}{#2}; +% \draw[->,line width=1pt,shorten >= 0.3cm,shorten <= 0.3cm] +% \punkt{#1+1}{#2} -- \punkt{#1}{#2+1}; +% \draw[->,line width=1pt,shorten >= 0.3cm,shorten <= 0.3cm] +% \punkt{#1}{#2+1} -- \punkt{#1}{#2}; +} + +%\def\Dreieck#1#2#3{ +% \fill[color=gray!50] \punkt{#1}{#2} -- \punkt{#1+1}{#2} +% -- \punkt{#1+1}{(#2)-1} -- cycle; +% \node at \punkt{#1+0.3333}{#2+0.3333} {$#3$\strut}; +%} + +%\def\kante#1#2#3{ +% \fill[color=white,opacity=0.8] \punkt{#1}{#2} circle[radius=0.15]; +% \node at \punkt{#1}{#2} {$\scriptstyle #3$}; +%} + +\def\gebiet{ + \dreieck{0}{0}{1} + \dreieck{1}{0}{2} + \dreieck{2}{0}{3} + \dreieck{3}{0}{4} + \dreieck{0}{1}{5} + \dreieck{2}{1}{6} + \dreieck{0}{2}{7} + \dreieck{1}{2}{8} + \dreieck{0}{3}{9} +} + +\begin{scope} +\gebiet +\draw[color=darkgreen] \B -- \G -- \J -- \F -- cycle; +\node[color=darkgreen] at ({2*\s},-0.5) {$z_5'$}; +\end{scope} + +\begin{scope}[xshift=2cm] +\gebiet +\draw[color=darkgreen] \D -- \I -- \L -- \H -- cycle; +\node[color=darkgreen] at ({2*\s},-0.5) {$z_6'$}; +\end{scope} + +\begin{scope}[xshift=4cm] +\gebiet +\draw[color=darkgreen] \C -- \L -- \N -- \K -- \M -- \J -- cycle; +\node[color=darkgreen] at ({2*\s},-0.5) {$z_9'$}; +\end{scope} + +\begin{scope}[xshift=6cm] +\gebiet +\draw[color=darkgreen] \K -- \N -- \O -- \M -- cycle; +\node[color=darkgreen] at ({2*\s},-0.5) {$z_{12}'$}; +\end{scope} + + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/95-homologie/images/homocycles.pdf b/buch/chapters/95-homologie/images/homocycles.pdf new file mode 100644 index 0000000..075bb65 Binary files /dev/null and b/buch/chapters/95-homologie/images/homocycles.pdf differ diff --git a/buch/chapters/95-homologie/images/homocycles.tex b/buch/chapters/95-homologie/images/homocycles.tex new file mode 100644 index 0000000..898cac6 --- /dev/null +++ b/buch/chapters/95-homologie/images/homocycles.tex @@ -0,0 +1,157 @@ +% +% tikztemplate.tex -- template for standalon tikz images +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\s{0.4} + +\def\punkt#1#2{({((#1)+0.5*(#2))*\s},{(#2)*\s*sqrt(3)/2})} +\def\A{\punkt{0}{0}} +\def\B{\punkt{1}{0}} +\def\C{\punkt{2}{0}} +\def\D{\punkt{3}{0}} +\def\E{\punkt{4}{0}} +\def\F{\punkt{0}{1}} +\def\G{\punkt{1}{1}} +\def\H{\punkt{2}{1}} +\def\I{\punkt{3}{1}} +\def\J{\punkt{0}{2}} +\def\K{\punkt{1}{2}} +\def\L{\punkt{2}{2}} +\def\M{\punkt{0}{3}} +\def\N{\punkt{1}{3}} +\def\O{\punkt{0}{4}} + +%\def\knoten#1#2#3{ +% \fill[color=white] \punkt{#1}{#2} circle[radius=0.3]; +% \node at \punkt{#1}{#2} {$#3$\strut}; +% \draw \punkt{#1}{#2} circle[radius=0.3]; +%} +\def\dreieck#1#2#3{ + \fill[color=gray] \punkt{#1}{#2} -- \punkt{#1+1}{#2} + -- \punkt{#1}{(#2)+1} -- cycle; +% \node at \punkt{#1+0.3333}{#2+0.3333} {$#3$\strut}; +% \draw[->,line width=1pt,shorten >= 0.3cm,shorten <= 0.3cm] +% \punkt{#1}{#2} -- \punkt{#1+1}{#2}; +% \draw[->,line width=1pt,shorten >= 0.3cm,shorten <= 0.3cm] +% \punkt{#1+1}{#2} -- \punkt{#1}{#2+1}; +% \draw[->,line width=1pt,shorten >= 0.3cm,shorten <= 0.3cm] +% \punkt{#1}{#2+1} -- \punkt{#1}{#2}; +} + +%\def\Dreieck#1#2#3{ +% \fill[color=gray!50] \punkt{#1}{#2} -- \punkt{#1+1}{#2} +% -- \punkt{#1+1}{(#2)-1} -- cycle; +% \node at \punkt{#1+0.3333}{#2+0.3333} {$#3$\strut}; +%} + +%\def\kante#1#2#3{ +% \fill[color=white,opacity=0.8] \punkt{#1}{#2} circle[radius=0.15]; +% \node at \punkt{#1}{#2} {$\scriptstyle #3$}; +%} + +\def\gebiet{ + \dreieck{0}{0}{1} + \dreieck{1}{0}{2} + \dreieck{2}{0}{3} + \dreieck{3}{0}{4} + \dreieck{0}{1}{5} + \dreieck{2}{1}{6} + \dreieck{0}{2}{7} + \dreieck{1}{2}{8} + \dreieck{0}{3}{9} +} + +\begin{scope} +\gebiet +\draw[color=red] \A -- \B -- \F -- cycle; +\node[color=red] at ({2*\s},-0.5) {$z_1$}; +\end{scope} + +\begin{scope}[xshift=2cm] +\gebiet +\draw[color=red] \B -- \C -- \G -- cycle; +\node[color=red] at ({2*\s},-0.5) {$z_2$}; +\end{scope} + +\begin{scope}[xshift=4cm] +\gebiet +\draw[color=red] \C -- \D -- \H -- cycle; +\node[color=red] at ({2*\s},-0.5) {$z_3$}; +\end{scope} + +\begin{scope}[xshift=6cm] +\gebiet +\draw[color=red] \D -- \E -- \I -- cycle; +\node[color=red] at ({2*\s},-0.5) {$z_4$}; +\end{scope} + +\begin{scope}[xshift=8cm] +\gebiet +\draw[color=red] \A -- \B -- \G -- \F -- cycle; +\node[color=red] at ({2*\s},-0.5) {$z_5$}; +\end{scope} + +\begin{scope}[xshift=10cm] +\gebiet +\draw[color=red] \C -- \D -- \I -- \H -- cycle; +\node[color=red] at ({2*\s},-0.5) {$z_6$}; +\end{scope} + +\begin{scope}[xshift=12cm] +\gebiet +\draw[color=red] \A -- \B -- \G -- \J -- \F -- cycle; +\node[color=red] at ({2*\s},-0.5) {$z_7$}; +\end{scope} + +\begin{scope}[xshift=0cm,yshift=-3cm] +\gebiet +\draw[color=red] \C -- \D -- \I -- \L -- \H -- cycle; +\node[color=red] at ({2*\s},-0.5) {$z_8$}; +\end{scope} + +\begin{scope}[xshift=2cm,yshift=-3cm] +\gebiet +\draw[color=red] \A -- \B -- \C -- \H -- \L -- \K -- \J -- \F -- cycle; +\node[color=red] at ({2*\s},-0.5) {$z_9$}; +\end{scope} + +\begin{scope}[xshift=4cm,yshift=-3cm] +\gebiet +\draw[color=red] \J -- \K -- \M -- cycle; +\node[color=red] at ({2*\s},-0.5) {$z_{10}$}; +\end{scope} + +\begin{scope}[xshift=6cm,yshift=-3cm] +\gebiet +\draw[color=red] \A -- \B -- \C -- \H -- \L -- \N -- \K -- \J -- \F -- cycle; +\node[color=red] at ({2*\s},-0.5) {$z_{11}$}; +\end{scope} + +\begin{scope}[xshift=8cm,yshift=-3cm] +\gebiet +\draw[color=red] \J -- \K -- \N -- \M -- cycle; +\node[color=red] at ({2*\s},-0.5) {$z_{12}$}; +\end{scope} + +\begin{scope}[xshift=10cm,yshift=-3cm] +\gebiet +\draw[color=red] \J -- \K -- \N -- \O -- \M -- cycle; +\node[color=red] at ({2*\s},-0.5) {$z_{13}$}; +\end{scope} + + +\end{tikzpicture} +\end{document} + -- cgit v1.2.1