new images

65 files changed, 256 insertions, 1 deletions

diff --git a/vorlesungen/slides/7/images/Makefile b/vorlesungen/slides/7/images/Makefile
index 1b9590d..cc67c8a 100644
--- a/vorlesungen/slides/7/images/Makefile
+++ b/vorlesungen/slides/7/images/Makefile
@@ -3,10 +3,17 @@
 #
 # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
 # 
-all:	rodriguez.jpg
+all:	rodriguez.jpg 
 
 rodriguez.png:	rodriguez.pov
 	povray +A0.1 -W1920 -H1080 -Orodriguez.png rodriguez.pov
 
 rodriguez.jpg:	rodriguez.png 
 	convert -extract 1740x1070+135+10 rodriguez.png rodriguez.jpg
+
+commutator:	commutator.ini commutator.pov common.inc
+	povray +A0.1 -W1920 -H1080 -Oc/c.png commutator.ini
+jpg:
+	for f in c/c*.png; do convert $${f} c/`basename $${f} .png`.jpg; done
+
+
diff --git a/vorlesungen/slides/7/images/c/c01.jpg b/vorlesungen/slides/7/images/c/c01.jpg
new file mode 100644
index 0000000..b2dbdb2
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c01.jpg
diff --git a/vorlesungen/slides/7/images/c/c02.jpg b/vorlesungen/slides/7/images/c/c02.jpg
new file mode 100644
index 0000000..9b45ba3
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c02.jpg
diff --git a/vorlesungen/slides/7/images/c/c03.jpg b/vorlesungen/slides/7/images/c/c03.jpg
new file mode 100644
index 0000000..882be40
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c03.jpg
diff --git a/vorlesungen/slides/7/images/c/c04.jpg b/vorlesungen/slides/7/images/c/c04.jpg
new file mode 100644
index 0000000..5d26572
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c04.jpg
diff --git a/vorlesungen/slides/7/images/c/c05.jpg b/vorlesungen/slides/7/images/c/c05.jpg
new file mode 100644
index 0000000..458f565
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c05.jpg
diff --git a/vorlesungen/slides/7/images/c/c06.jpg b/vorlesungen/slides/7/images/c/c06.jpg
new file mode 100644
index 0000000..cd40cda
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c06.jpg
diff --git a/vorlesungen/slides/7/images/c/c07.jpg b/vorlesungen/slides/7/images/c/c07.jpg
new file mode 100644
index 0000000..3349795
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c07.jpg
diff --git a/vorlesungen/slides/7/images/c/c08.jpg b/vorlesungen/slides/7/images/c/c08.jpg
new file mode 100644
index 0000000..65048cf
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c08.jpg
diff --git a/vorlesungen/slides/7/images/c/c09.jpg b/vorlesungen/slides/7/images/c/c09.jpg
new file mode 100644
index 0000000..000d502
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c09.jpg
diff --git a/vorlesungen/slides/7/images/c/c10.jpg b/vorlesungen/slides/7/images/c/c10.jpg
new file mode 100644
index 0000000..064c96b
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c10.jpg
diff --git a/vorlesungen/slides/7/images/c/c11.jpg b/vorlesungen/slides/7/images/c/c11.jpg
new file mode 100644
index 0000000..c67bc5d
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c11.jpg
diff --git a/vorlesungen/slides/7/images/c/c12.jpg b/vorlesungen/slides/7/images/c/c12.jpg
new file mode 100644
index 0000000..f2174de
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c12.jpg
diff --git a/vorlesungen/slides/7/images/c/c13.jpg b/vorlesungen/slides/7/images/c/c13.jpg
new file mode 100644
index 0000000..3cb5ae6
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c13.jpg
diff --git a/vorlesungen/slides/7/images/c/c14.jpg b/vorlesungen/slides/7/images/c/c14.jpg
new file mode 100644
index 0000000..6985e4f
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c14.jpg
diff --git a/vorlesungen/slides/7/images/c/c15.jpg b/vorlesungen/slides/7/images/c/c15.jpg
new file mode 100644
index 0000000..5bb5aed
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c15.jpg
diff --git a/vorlesungen/slides/7/images/c/c16.jpg b/vorlesungen/slides/7/images/c/c16.jpg
new file mode 100644
index 0000000..cc77fa1
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c16.jpg
diff --git a/vorlesungen/slides/7/images/c/c17.jpg b/vorlesungen/slides/7/images/c/c17.jpg
new file mode 100644
index 0000000..a60e2e9
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c17.jpg
diff --git a/vorlesungen/slides/7/images/c/c18.jpg b/vorlesungen/slides/7/images/c/c18.jpg
new file mode 100644
index 0000000..1d08c29
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c18.jpg
diff --git a/vorlesungen/slides/7/images/c/c19.jpg b/vorlesungen/slides/7/images/c/c19.jpg
new file mode 100644
index 0000000..9210c60
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c19.jpg
diff --git a/vorlesungen/slides/7/images/c/c20.jpg b/vorlesungen/slides/7/images/c/c20.jpg
new file mode 100644
index 0000000..8951883
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c20.jpg
diff --git a/vorlesungen/slides/7/images/c/c21.jpg b/vorlesungen/slides/7/images/c/c21.jpg
new file mode 100644
index 0000000..5169c7e
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c21.jpg
diff --git a/vorlesungen/slides/7/images/c/c22.jpg b/vorlesungen/slides/7/images/c/c22.jpg
new file mode 100644
index 0000000..bdeb90b
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c22.jpg
diff --git a/vorlesungen/slides/7/images/c/c23.jpg b/vorlesungen/slides/7/images/c/c23.jpg
new file mode 100644
index 0000000..fa3eac7
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c23.jpg
diff --git a/vorlesungen/slides/7/images/c/c24.jpg b/vorlesungen/slides/7/images/c/c24.jpg
new file mode 100644
index 0000000..52adc13
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c24.jpg
diff --git a/vorlesungen/slides/7/images/c/c25.jpg b/vorlesungen/slides/7/images/c/c25.jpg
new file mode 100644
index 0000000..d557497
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c25.jpg
diff --git a/vorlesungen/slides/7/images/c/c26.jpg b/vorlesungen/slides/7/images/c/c26.jpg
new file mode 100644
index 0000000..f825f49
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c26.jpg
diff --git a/vorlesungen/slides/7/images/c/c27.jpg b/vorlesungen/slides/7/images/c/c27.jpg
new file mode 100644
index 0000000..0de6c3e
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c27.jpg
diff --git a/vorlesungen/slides/7/images/c/c28.jpg b/vorlesungen/slides/7/images/c/c28.jpg
new file mode 100644
index 0000000..d9f89a4
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c28.jpg
diff --git a/vorlesungen/slides/7/images/c/c29.jpg b/vorlesungen/slides/7/images/c/c29.jpg
new file mode 100644
index 0000000..937f692
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c29.jpg
diff --git a/vorlesungen/slides/7/images/c/c30.jpg b/vorlesungen/slides/7/images/c/c30.jpg
new file mode 100644
index 0000000..45901cc
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c30.jpg
diff --git a/vorlesungen/slides/7/images/c/c31.jpg b/vorlesungen/slides/7/images/c/c31.jpg
new file mode 100644
index 0000000..eb52bec
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c31.jpg
diff --git a/vorlesungen/slides/7/images/c/c32.jpg b/vorlesungen/slides/7/images/c/c32.jpg
new file mode 100644
index 0000000..a011640
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c32.jpg
diff --git a/vorlesungen/slides/7/images/c/c33.jpg b/vorlesungen/slides/7/images/c/c33.jpg
new file mode 100644
index 0000000..ecbb8bd
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c33.jpg
diff --git a/vorlesungen/slides/7/images/c/c34.jpg b/vorlesungen/slides/7/images/c/c34.jpg
new file mode 100644
index 0000000..8a624d1
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c34.jpg
diff --git a/vorlesungen/slides/7/images/c/c35.jpg b/vorlesungen/slides/7/images/c/c35.jpg
new file mode 100644
index 0000000..33765a1
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+++ b/vorlesungen/slides/7/images/c/c35.jpg
diff --git a/vorlesungen/slides/7/images/c/c36.jpg b/vorlesungen/slides/7/images/c/c36.jpg
new file mode 100644
index 0000000..e38a448
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c36.jpg
diff --git a/vorlesungen/slides/7/images/c/c37.jpg b/vorlesungen/slides/7/images/c/c37.jpg
new file mode 100644
index 0000000..9f823f4
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c37.jpg
diff --git a/vorlesungen/slides/7/images/c/c38.jpg b/vorlesungen/slides/7/images/c/c38.jpg
new file mode 100644
index 0000000..19c96fc
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c38.jpg
diff --git a/vorlesungen/slides/7/images/c/c39.jpg b/vorlesungen/slides/7/images/c/c39.jpg
new file mode 100644
index 0000000..c00482b
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c39.jpg
diff --git a/vorlesungen/slides/7/images/c/c40.jpg b/vorlesungen/slides/7/images/c/c40.jpg
new file mode 100644
index 0000000..de9fca4
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c40.jpg
diff --git a/vorlesungen/slides/7/images/c/c41.jpg b/vorlesungen/slides/7/images/c/c41.jpg
new file mode 100644
index 0000000..1b8a3d1
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c41.jpg
diff --git a/vorlesungen/slides/7/images/c/c42.jpg b/vorlesungen/slides/7/images/c/c42.jpg
new file mode 100644
index 0000000..6d4e5bc
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c42.jpg
diff --git a/vorlesungen/slides/7/images/c/c43.jpg b/vorlesungen/slides/7/images/c/c43.jpg
new file mode 100644
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--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c43.jpg
diff --git a/vorlesungen/slides/7/images/c/c44.jpg b/vorlesungen/slides/7/images/c/c44.jpg
new file mode 100644
index 0000000..0fe56f6
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c44.jpg
diff --git a/vorlesungen/slides/7/images/c/c45.jpg b/vorlesungen/slides/7/images/c/c45.jpg
new file mode 100644
index 0000000..9196ad3
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c45.jpg
diff --git a/vorlesungen/slides/7/images/c/c46.jpg b/vorlesungen/slides/7/images/c/c46.jpg
new file mode 100644
index 0000000..a4f5823
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c46.jpg
diff --git a/vorlesungen/slides/7/images/c/c47.jpg b/vorlesungen/slides/7/images/c/c47.jpg
new file mode 100644
index 0000000..18474dd
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+++ b/vorlesungen/slides/7/images/c/c47.jpg
diff --git a/vorlesungen/slides/7/images/c/c48.jpg b/vorlesungen/slides/7/images/c/c48.jpg
new file mode 100644
index 0000000..d839014
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c48.jpg
diff --git a/vorlesungen/slides/7/images/c/c49.jpg b/vorlesungen/slides/7/images/c/c49.jpg
new file mode 100644
index 0000000..3cb5cb0
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+++ b/vorlesungen/slides/7/images/c/c49.jpg
diff --git a/vorlesungen/slides/7/images/c/c50.jpg b/vorlesungen/slides/7/images/c/c50.jpg
new file mode 100644
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+++ b/vorlesungen/slides/7/images/c/c50.jpg
diff --git a/vorlesungen/slides/7/images/c/c51.jpg b/vorlesungen/slides/7/images/c/c51.jpg
new file mode 100644
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+++ b/vorlesungen/slides/7/images/c/c51.jpg
diff --git a/vorlesungen/slides/7/images/c/c52.jpg b/vorlesungen/slides/7/images/c/c52.jpg
new file mode 100644
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+++ b/vorlesungen/slides/7/images/c/c52.jpg
diff --git a/vorlesungen/slides/7/images/c/c53.jpg b/vorlesungen/slides/7/images/c/c53.jpg
new file mode 100644
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+++ b/vorlesungen/slides/7/images/c/c53.jpg
diff --git a/vorlesungen/slides/7/images/c/c54.jpg b/vorlesungen/slides/7/images/c/c54.jpg
new file mode 100644
index 0000000..0ffbac2
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c54.jpg
diff --git a/vorlesungen/slides/7/images/c/c55.jpg b/vorlesungen/slides/7/images/c/c55.jpg
new file mode 100644
index 0000000..5f75419
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c55.jpg
diff --git a/vorlesungen/slides/7/images/c/c56.jpg b/vorlesungen/slides/7/images/c/c56.jpg
new file mode 100644
index 0000000..5c0f9ae
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c56.jpg
diff --git a/vorlesungen/slides/7/images/c/c57.jpg b/vorlesungen/slides/7/images/c/c57.jpg
new file mode 100644
index 0000000..9b61179
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c57.jpg
diff --git a/vorlesungen/slides/7/images/c/c58.jpg b/vorlesungen/slides/7/images/c/c58.jpg
new file mode 100644
index 0000000..81d2173
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c58.jpg
diff --git a/vorlesungen/slides/7/images/c/c59.jpg b/vorlesungen/slides/7/images/c/c59.jpg
new file mode 100644
index 0000000..0ae9bac
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c59.jpg
diff --git a/vorlesungen/slides/7/images/c/c60.jpg b/vorlesungen/slides/7/images/c/c60.jpg
new file mode 100644
index 0000000..2bc77e7
--- /dev/null
+++ b/vorlesungen/slides/7/images/c/c60.jpg
diff --git a/vorlesungen/slides/7/images/common.inc b/vorlesungen/slides/7/images/common.inc
new file mode 100644
index 0000000..0e27c9a
--- /dev/null
+++ b/vorlesungen/slides/7/images/common.inc
@@ -0,0 +1,70 @@
+//
+// common.inc
+//
+// (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#version 3.7;
+#include "colors.inc"
+
+global_settings {
+	assumed_gamma 1
+}
+
+#declare imagescale = 0.025;
+#declare O = <0, 0, 0>;
+#declare at = 0.015;
+
+camera {
+	location <18, 15, -50>
+	look_at <0.0, 0.5, 0>
+	right 16/9 * x * imagescale
+	up y * imagescale
+}
+
+light_source {
+	<-40, 30, -50> color White
+	area_light <1,0,0> <0,0,1>, 10, 10
+	adaptive 1
+	jitter
+}
+
+sky_sphere {
+	pigment {
+		color rgb<1,1,1>
+	}
+}
+
+#macro arrow(from, to, arrowthickness, c)
+#declare arrowdirection = vnormalize(to - from);
+#declare arrowlength = vlength(to - from);
+union { 
+	sphere {
+		from, 1.1 * arrowthickness
+	}
+	cylinder {
+		from,
+		from + (arrowlength - 5 * arrowthickness) * arrowdirection,
+		arrowthickness
+	}
+	cone {  
+		from + (arrowlength - 5 * arrowthickness) * arrowdirection,
+		2 * arrowthickness,
+		to,
+		0
+	}
+	pigment {
+		color c
+	}
+	finish {
+		specular 0.9
+		metallic
+	}
+}
+#end
+
+#declare l = 1.2;
+
+arrow(< -l,  0,  0 >, < l, 0, 0 >, at, White)
+arrow(<  0,  0, -l >, < 0, 0, l >, at, White)
+arrow(<  0, -l,  0 >, < 0, l, 0 >, at, White)
+
diff --git a/vorlesungen/slides/7/images/commutator.ini b/vorlesungen/slides/7/images/commutator.ini
new file mode 100644
index 0000000..8c2211e
--- /dev/null
+++ b/vorlesungen/slides/7/images/commutator.ini
@@ -0,0 +1,8 @@
+Input_File_Name=commutator.pov
+Initial_Frame=1
+Final_Frame=60
+Initial_Clock=1
+Final_Clock=60
+Cyclic_Animation=off
+Pause_when_Done=off
+
diff --git a/vorlesungen/slides/7/images/commutator.m b/vorlesungen/slides/7/images/commutator.m
new file mode 100644
index 0000000..5a448db
--- /dev/null
+++ b/vorlesungen/slides/7/images/commutator.m
@@ -0,0 +1,111 @@
+#
+# commutator.m
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+
+X = [
+	0, 0,  0;
+	0, 0, -1;
+	0, 1,  0
+];
+
+Y = [
+	 0, 0, 1;
+	 0, 0, 0;
+	-1, 0, 0
+];
+
+Z = [
+	0, -1, 0;
+	1,  0, 0;
+	0,  0, 0
+];
+
+function retval = Dx(alpha)
+	retval = [
+		1, 0,           0         ;
+		0, cos(alpha), -sin(alpha);
+		0, sin(alpha),  cos(alpha)
+	];
+end
+
+function retval = Dy(beta)
+	retval = [
+		 cos(beta), 0, sin(beta);
+		 0,         1, 0        ;
+		-sin(beta), 0, cos(beta)
+	];
+end
+
+t = 0.9;
+P = Dx(t) * Dy(t)
+Q = Dy(t) * Dx(t)
+P - Q
+(P - Q) * [0;0;1]
+
+function	retval = kurven(filename, t)
+	retval = -1;
+	N = 20;
+	fn = fopen(filename, "w");
+	fprintf(fn, "//\n");
+	fprintf(fn, "// %s\n", filename);
+	fprintf(fn, "//\n");
+	fprintf(fn, "#macro XYkurve()\n");
+	for i = (0:N-1)
+		v1 = Dx(t * i / N) * [0;0;1];
+		v2 = Dx(t * (i+1) / N) * [0;0;1];
+		fprintf(fn, "sphere { <%.4f,%.4f,%.4f>, at }\n",
+			v1(1,1), v1(3,1), v1(2,1));
+		fprintf(fn, "cylinder { <%.4f,%.4f,%.4f>, <%.4f, %.4f, %.4f>, at }\n",
+			v1(1,1), v1(3,1), v1(2,1), v2(1,1), v2(3,1), v2(2,1));
+	end
+	for i = (0:N-1)
+		v1 = Dx(t) * Dy(t * i / N) * [0;0;1];
+		v2 = Dx(t) * Dy(t * (i+1) / N) * [0;0;1];
+		fprintf(fn, "sphere { <%.4f,%.4f,%.4f>, at }\n",
+			v1(1,1), v1(3,1), v1(2,1));
+		fprintf(fn, "cylinder { <%.4f,%.4f,%.4f>, <%.4f, %.4f, %.4f>, at }\n",
+			v1(1,1), v1(3,1), v1(2,1), v2(1,1), v2(3,1), v2(2,1));
+	end
+	fprintf(fn, "sphere { <%.4f,%.4f,%.4f>, at }\n",
+		v2(1,1), v2(3,1), v2(2,1));
+	fprintf(fn, "#end\n");
+	fprintf(fn, "#declare finalXY = <%.4f, %.4f, %.4f>;\n",
+		v2(1,1), v2(3,1), v2(2,1));
+	fprintf(fn, "#macro YXkurve()\n");
+	for i = (0:N-1)
+		v1 = Dy(t * i / N) * [0;0;1];
+		v2 = Dy(t * (i+1) / N) * [0;0;1];
+		fprintf(fn, "sphere { <%.4f,%.4f,%.4f>, at }\n",
+			v1(1,1), v1(3,1), v1(2,1));
+		fprintf(fn, "cylinder { <%.4f,%.4f,%.4f>, <%.4f, %.4f, %.4f>, at }\n",
+			v1(1,1), v1(3,1), v1(2,1), v2(1,1), v2(3,1), v2(2,1));
+	end
+	for i = (0:N-1)
+		v1 = Dy(t) * Dx(t * i / N) * [0;0;1];
+		v2 = Dy(t) * Dx(t * (i+1) / N) * [0;0;1];
+		fprintf(fn, "sphere { <%.4f,%.4f,%.4f>, at }\n",
+			v1(1,1), v1(3,1), v1(2,1));
+		fprintf(fn, "cylinder { <%.4f,%.4f,%.4f>, <%.4f, %.4f, %.4f>, at }\n",
+			v1(1,1), v1(3,1), v1(2,1), v2(1,1), v2(3,1), v2(2,1));
+	end
+	fprintf(fn, "sphere { <%.4f,%.4f,%.4f>, at }\n",
+		v2(1,1), v2(3,1), v2(2,1));
+	fprintf(fn, "#end\n");
+	fprintf(fn, "#declare finalYX = <%.4f, %.4f, %.4f>;\n",
+		v2(1,1), v2(3,1), v2(2,1));
+
+	fclose(fn);
+	retval = 0;
+end
+
+function	retval = kurve(i)
+	n = pi / 180;
+	filename = sprintf("f/%04d.inc", i);
+	kurven(filename, n * i);
+end
+
+for i = (1:60)
+	kurve(i);
+end
diff --git a/vorlesungen/slides/7/images/commutator.pov b/vorlesungen/slides/7/images/commutator.pov
new file mode 100644
index 0000000..9ae11b9
--- /dev/null
+++ b/vorlesungen/slides/7/images/commutator.pov
@@ -0,0 +1,59 @@
+//
+// commutator.pov
+//
+// (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#include "common.inc"
+
+sphere { O, 0.99
+	pigment {
+		color rgbt<1,1,1,0.5>
+	}
+	finish {
+		specular 0.9
+		metallic
+	}
+}
+
+#declare filename = concat("f/", str(clock, -4, 0), ".inc");
+
+#include filename
+
+#declare n1 = vcross(<0,1,0>, finalXY);
+#declare n2 = vcross(<0,1,0>, finalYX);
+
+intersection {
+	sphere { O, 1 }
+	plane { -n1, 0 }
+	plane { n2, 0 }
+	pigment {
+		color rgb<0,0.4,0.1>
+	}
+	finish {
+		specular 0.9
+		metallic
+	}
+}
+
+union {
+        XYkurve()
+        pigment {
+                color Red
+        }
+	finish {
+		specular 0.9
+		metallic
+	}
+}
+
+union {
+        YXkurve()
+        pigment {
+                color Blue
+        }
+	finish {
+		specular 0.9
+		metallic
+	}
+}
+