aboutsummaryrefslogtreecommitdiffstats
path: root/buch/chapters/95-homologie/images
diff options
context:
space:
mode:
authorAndreas Müller <andreas.mueller@ost.ch>2021-08-24 17:21:53 +0200
committerAndreas Müller <andreas.mueller@ost.ch>2021-08-24 17:21:53 +0200
commit13304c02851094180b714d71451f279966fb582f (patch)
tree13950212fb6623bf948c2fcabb6ee88ca6e459ee /buch/chapters/95-homologie/images
parentsymmetry fix (diff)
downloadSeminarMatrizen-13304c02851094180b714d71451f279966fb582f.tar.gz
SeminarMatrizen-13304c02851094180b714d71451f279966fb582f.zip
simpliziale Approximation
Diffstat (limited to '')
-rw-r--r--buch/chapters/95-homologie/images/Makefile9
-rw-r--r--buch/chapters/95-homologie/images/approx.m77
-rw-r--r--buch/chapters/95-homologie/images/approximation.pdfbin0 -> 32134 bytes
-rw-r--r--buch/chapters/95-homologie/images/approximation.tex69
-rw-r--r--buch/chapters/95-homologie/images/homoboundaries.pdfbin17163 -> 17362 bytes
-rw-r--r--buch/chapters/95-homologie/images/homoboundaries.tex3
-rw-r--r--buch/chapters/95-homologie/images/homoclasses.pdfbin11647 -> 11791 bytes
-rw-r--r--buch/chapters/95-homologie/images/homoclasses.tex17
-rw-r--r--buch/chapters/95-homologie/images/homocycles.pdfbin16779 -> 17039 bytes
-rw-r--r--buch/chapters/95-homologie/images/homocycles.tex15
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
new file mode 100644
index 0000000..8bdd2e7
--- /dev/null
+++ b/buch/chapters/95-homologie/images/approximation.pdf
Binary files differ
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
index 644f334..fb94ec8 100644
--- a/buch/chapters/95-homologie/images/homoboundaries.pdf
+++ b/buch/chapters/95-homologie/images/homoboundaries.pdf
Binary files differ
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
index 217ae75..fbbaedd 100644
--- a/buch/chapters/95-homologie/images/homoclasses.pdf
+++ b/buch/chapters/95-homologie/images/homoclasses.pdf
Binary files differ
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
index 075bb65..b68519e 100644
--- a/buch/chapters/95-homologie/images/homocycles.pdf
+++ b/buch/chapters/95-homologie/images/homocycles.pdf
Binary files differ
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}