simpliziale Approximation

1 files changed, 77 insertions, 0 deletions

diff --git a/buch/chapters/95-homologie/images/approx.m b/buch/chapters/95-homologie/images/approx.m
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+++ b/buch/chapters/95-homologie/images/approx.m
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+#
+# 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)
+