diff options
Diffstat (limited to 'buch/chapters/95-homologie/images')
| -rw-r--r-- | buch/chapters/95-homologie/images/Makefile | 9 | ||||
| -rw-r--r-- | buch/chapters/95-homologie/images/approx.m | 77 | ||||
| -rw-r--r-- | buch/chapters/95-homologie/images/approximation.pdf | bin | 0 -> 32134 bytes | |||
| -rw-r--r-- | buch/chapters/95-homologie/images/approximation.tex | 69 | ||||
| -rw-r--r-- | buch/chapters/95-homologie/images/homoboundaries.pdf | bin | 17163 -> 17362 bytes | |||
| -rw-r--r-- | buch/chapters/95-homologie/images/homoboundaries.tex | 3 | ||||
| -rw-r--r-- | buch/chapters/95-homologie/images/homoclasses.pdf | bin | 11647 -> 11791 bytes | |||
| -rw-r--r-- | buch/chapters/95-homologie/images/homoclasses.tex | 17 | ||||
| -rw-r--r-- | buch/chapters/95-homologie/images/homocycles.pdf | bin | 16779 -> 17039 bytes | |||
| -rw-r--r-- | buch/chapters/95-homologie/images/homocycles.tex | 15 |
10 files changed, 181 insertions, 9 deletions
diff --git a/buch/chapters/95-homologie/images/Makefile b/buch/chapters/95-homologie/images/Makefile index 50c2b0d..bc85c55 100644 --- a/buch/chapters/95-homologie/images/Makefile +++ b/buch/chapters/95-homologie/images/Makefile @@ -4,7 +4,8 @@ # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # all: complexbasis.pdf homocycles.pdf homoboundaries.pdf homoclasses.pdf \ - gausshomoex.pdf gausshomobasis.pdf dreieck.pdf polyeder.pdf + gausshomoex.pdf gausshomobasis.pdf dreieck.pdf polyeder.pdf \ + approximation.pdf dreieck.pdf: dreieck.tex pdflatex dreieck.tex @@ -30,3 +31,9 @@ homoclasses.pdf: homoclasses.tex complexbasis.pdf: complexbasis.tex pdflatex complexbasis.tex +approximation.pdf: approximation.tex approx.tex + pdflatex approximation.tex + +approx.tex: approx.m + octave approx.m + diff --git a/buch/chapters/95-homologie/images/approx.m b/buch/chapters/95-homologie/images/approx.m new file mode 100644 index 0000000..0db41c2 --- /dev/null +++ b/buch/chapters/95-homologie/images/approx.m @@ -0,0 +1,77 @@ +# +# approx.m +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +x = zeros(7,7); +y = zeros(7,7); + +s = 1.05; + +for i = (1:7) + winkel = (i-1) * 8.333333 + 20; + for j = (1:7) + radius = (j-1) * 0.5 + 3; + x(i,j) = 1.05 * radius * cosd(winkel); + y(i,j) = 1.05 * radius * sind(winkel); + endfor +endfor + +X = x; +Y = y; +for i = (1:7) + for j = (1:7) + X(i,j) = round(2 * x(i,j)) / 2; + Y(i,j) = round(2 * y(i,j)) / 2; + endfor +endfor + +fn = fopen("approx.tex", "w"); + + +for i = (1:6) + for j = (1:6) + winkel = (i-1+0.6666) * 8.33333 + 20; + radius = (j-1+0.3333) * 0.5 + 3; + fprintf(fn, "\\definecolor{mycolor}{rgb}{%.2f,%.2f,%.2f};\n", + (winkel - 20) / 50, 0.8, (radius-3)/3); + fprintf(fn, "\\fill[color=mycolor] (%.3f,%.3f) -- (%.3f,%.3f) -- (%.3f,%.3f) -- cycle;\n", + X(i,j), Y(i,j), + X(i+1,j+1), Y(i+1,j+1), + X(i+1,j), Y(i+1,j)); + winkel = (i-1+0.3333) * 8.33333 + 20; + radius = (j-1+0.6666) * 0.5 + 3; + fprintf(fn, "\\definecolor{mycolor}{rgb}{%.2f,%.2f,%.2f};\n", + (winkel - 20) / 50, 0.8, (radius-3)/3); + fprintf(fn, "\\fill[color=mycolor] (%.3f,%.3f) -- (%.3f,%.3f) -- (%.3f,%.3f) -- cycle;\n", + X(i,j), Y(i,j), + X(i,j+1), Y(i,j+1), + X(i+1,j+1), Y(i+1,j+1)); + endfor +endfor + +linewidth = 0.4; + +fprintf(fn, "\\gitter\n"); + +for i = (1:7) + for j = (1:6) + fprintf(fn, "\\draw[color=darkred,line width=%.1fpt] (%.3f,%.3f) -- (%.3f,%.3f);\n", linewidth, + X(i,j), Y(i,j), X(i,j+1), Y(i,j+1)); + endfor +endfor +for i = (1:6) + for j = (1:7) + fprintf(fn, "\\draw[color=darkred,line width=%.1fpt] (%.3f,%.3f) -- (%.3f,%.3f);\n", linewidth, + X(i,j), Y(i,j), X(i+1,j), Y(i+1,j)); + endfor +endfor +for i = (1:6) + for j = (1:6) + fprintf(fn, "\\draw[color=darkred,line width=%.1fpt] (%.3f,%.3f) -- (%.3f,%.3f);\n", linewidth, + X(i,j), Y(i,j), X(i+1,j+1), Y(i+1,j+1)); + endfor +endfor + +fclose(fn) + diff --git a/buch/chapters/95-homologie/images/approximation.pdf b/buch/chapters/95-homologie/images/approximation.pdf Binary files differnew file mode 100644 index 0000000..8bdd2e7 --- /dev/null +++ b/buch/chapters/95-homologie/images/approximation.pdf diff --git a/buch/chapters/95-homologie/images/approximation.tex b/buch/chapters/95-homologie/images/approximation.tex new file mode 100644 index 0000000..042f0e2 --- /dev/null +++ b/buch/chapters/95-homologie/images/approximation.tex @@ -0,0 +1,69 @@ +% +% approximation.tex -- Approximation einer Abbildung durch eine simpliziale +% +% (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{1.3} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\definecolor{darkred}{rgb}{0.8,0,0} +\definecolor{darkred}{rgb}{0,0,0} + +\def\gitter{ + \foreach \x in {1,1.5,...,6}{ + \draw[color=gray] (\x,1) -- (\x,6); + \draw[color=gray] (1,\x) -- (6,\x); + } +} + +\def\s{1.05} + +\def\colorsector{ + \foreach \r in {3,3.2,...,5.8}{ + \foreach \a in {20,...,69}{ + \pgfmathparse{(\a-20)/50} + \xdef\rot{\pgfmathresult} + \pgfmathparse{(\r-3)/3} + \xdef\blau{\pgfmathresult} + \definecolor{mycolor}{rgb}{\rot,0.8,\blau} + \fill[color=mycolor] + (\a:{\s*\r}) -- (\a:{\s*(\r+0.2)}) -- ({\a+1}:{\s*(\r+0.2)}) -- ({\a+1}:{\s*\r}) -- cycle; + } + } +} + +\begin{scope}[xshift=0cm] +\colorsector +\gitter +\foreach \r in {3,3.5,...,6.0}{ + \draw[color=black,line width=0.4pt] (20:{\s*\r}) arc (20:70:{\s*\r}); +} +\foreach \a in {20,28.3333,...,70}{ + \draw[color=black,line width=0.4pt] (\a:{\s*3}) -- (\a:{\s*6}); +} +\begin{scope} +\clip (20:{\s*3}) -- (20:{\s*6}) arc (20:70:{\s*6}) -- (70:{\s*3}); +\foreach \a in {-5,...,5}{ + \draw[color=black,line width=0.4pt] + plot[domain={20+8.33333*\a}:{70+8.3333*\a},samples=100] + (\x:{\s*(3+3*(\x-(20+8.3333*\a))/50)}); +} +\end{scope} + +\end{scope} + +\begin{scope}[xshift=5.5cm] +\input{approx.tex} +\end{scope} + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/95-homologie/images/homoboundaries.pdf b/buch/chapters/95-homologie/images/homoboundaries.pdf Binary files differindex 644f334..fb94ec8 100644 --- a/buch/chapters/95-homologie/images/homoboundaries.pdf +++ b/buch/chapters/95-homologie/images/homoboundaries.pdf diff --git a/buch/chapters/95-homologie/images/homoboundaries.tex b/buch/chapters/95-homologie/images/homoboundaries.tex index ef8fd1a..53087fa 100644 --- a/buch/chapters/95-homologie/images/homoboundaries.tex +++ b/buch/chapters/95-homologie/images/homoboundaries.tex @@ -14,7 +14,7 @@ \def\skala{1} \begin{tikzpicture}[>=latex,thick,scale=\skala] -\def\s{0.4} +\def\s{0.55} \def\punkt#1#2{({((#1)+0.5*(#2))*\s},{(#2)*\s*sqrt(3)/2})} \def\A{\punkt{0}{0}} @@ -41,6 +41,7 @@ \def\blau#1#2{ \draw[color=blue] \punkt{#1}{#2} -- \punkt{#1+1}{#2} -- \punkt{#1}{(#2)+1} -- cycle; + \draw[->,color=blue] \punkt{#1}{#2} -- \punkt{#1+1}{#2}; } \def\gebiet{ diff --git a/buch/chapters/95-homologie/images/homoclasses.pdf b/buch/chapters/95-homologie/images/homoclasses.pdf Binary files differindex 217ae75..fbbaedd 100644 --- a/buch/chapters/95-homologie/images/homoclasses.pdf +++ b/buch/chapters/95-homologie/images/homoclasses.pdf diff --git a/buch/chapters/95-homologie/images/homoclasses.tex b/buch/chapters/95-homologie/images/homoclasses.tex index e325d9b..4467f08 100644 --- a/buch/chapters/95-homologie/images/homoclasses.tex +++ b/buch/chapters/95-homologie/images/homoclasses.tex @@ -1,5 +1,5 @@ % -% tikztemplate.tex -- template for standalon tikz images +% homoclasses.tex -- template for standalon tikz images % % (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule % @@ -11,11 +11,12 @@ \usepackage{csvsimple} \usetikzlibrary{arrows,intersections,math} \begin{document} -\def\skala{1} +\def\skala{1.4} \begin{tikzpicture}[>=latex,thick,scale=\skala] \definecolor{darkgreen}{rgb}{0,0.6,0} \def\s{0.4} +\def\h{-0.3} \def\punkt#1#2{({((#1)+0.5*(#2))*\s},{(#2)*\s*sqrt(3)/2})} \def\A{\punkt{0}{0}} @@ -77,25 +78,29 @@ \begin{scope} \gebiet \draw[color=darkgreen] \B -- \G -- \J -- \F -- cycle; -\node[color=darkgreen] at ({2*\s},-0.5) {$z_5'$}; +\draw[->,color=darkgreen] \B -- \G; +\node[color=darkgreen] at ({2*\s},{\h}) {$z_5'$}; \end{scope} \begin{scope}[xshift=2cm] \gebiet \draw[color=darkgreen] \D -- \I -- \L -- \H -- cycle; -\node[color=darkgreen] at ({2*\s},-0.5) {$z_6'$}; +\draw[->,color=darkgreen] \D -- \I; +\node[color=darkgreen] at ({2*\s},{\h}) {$z_6'$}; \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) {$z_9'$}; +\draw[->,color=darkgreen] \C -- \L; +\node[color=darkgreen] at ({2*\s},{\h}) {$z_9'$}; \end{scope} \begin{scope}[xshift=6cm] \gebiet \draw[color=darkgreen] \K -- \N -- \O -- \M -- cycle; -\node[color=darkgreen] at ({2*\s},-0.5) {$z_{12}'$}; +\draw[->,color=darkgreen] \K -- \N; +\node[color=darkgreen] at ({2*\s},{\h}) {$z_{12}'$}; \end{scope} diff --git a/buch/chapters/95-homologie/images/homocycles.pdf b/buch/chapters/95-homologie/images/homocycles.pdf Binary files differindex 075bb65..b68519e 100644 --- a/buch/chapters/95-homologie/images/homocycles.pdf +++ b/buch/chapters/95-homologie/images/homocycles.pdf diff --git a/buch/chapters/95-homologie/images/homocycles.tex b/buch/chapters/95-homologie/images/homocycles.tex index 898cac6..8f20a0c 100644 --- a/buch/chapters/95-homologie/images/homocycles.tex +++ b/buch/chapters/95-homologie/images/homocycles.tex @@ -75,79 +75,92 @@ \begin{scope} \gebiet -\draw[color=red] \A -- \B -- \F -- cycle; +\draw[->,color=red] \A -- \B -- \F -- cycle; +\draw[->,color=red] \A -- \B; \node[color=red] at ({2*\s},-0.5) {$z_1$}; \end{scope} \begin{scope}[xshift=2cm] \gebiet \draw[color=red] \B -- \C -- \G -- cycle; +\draw[->,color=red] \B -- \C; \node[color=red] at ({2*\s},-0.5) {$z_2$}; \end{scope} \begin{scope}[xshift=4cm] \gebiet \draw[color=red] \C -- \D -- \H -- cycle; +\draw[->,color=red] \C -- \D; \node[color=red] at ({2*\s},-0.5) {$z_3$}; \end{scope} \begin{scope}[xshift=6cm] \gebiet \draw[color=red] \D -- \E -- \I -- cycle; +\draw[->,color=red] \D -- \E; \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; +\draw[<-,color=red] \A -- \B; \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; +\draw[<-,color=red] \C -- \D; \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; +\draw[->,color=red] \A -- \B; \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; +\draw[->,color=red] \C -- \D; \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; +\draw[<-,color=red] \A -- \B; \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; +\draw[->,color=red] \J -- \K; \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; +\draw[->,color=red] \A -- \B; \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; +\draw[<-,color=red] \J -- \K; \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; +\draw[->,color=red] \J -- \K; \node[color=red] at ({2*\s},-0.5) {$z_{13}$}; \end{scope} |