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authorAndreas Müller <andreas.mueller@ost.ch>2021-06-14 07:26:10 +0200
committerGitHub <noreply@github.com>2021-06-14 07:26:10 +0200
commit114633b43a0f1ebedbc5dfd85f75ede9841f26fd (patch)
tree18e61c7d69883a1c9b69098b7d36856abaed5c1e /vorlesungen/slides/7/images
parentDelete buch.pdf (diff)
parentFix references.bib (diff)
downloadSeminarMatrizen-114633b43a0f1ebedbc5dfd85f75ede9841f26fd.tar.gz
SeminarMatrizen-114633b43a0f1ebedbc5dfd85f75ede9841f26fd.zip
Merge branch 'master' into master
Diffstat (limited to 'vorlesungen/slides/7/images')
-rw-r--r--vorlesungen/slides/7/images/Makefile29
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-rw-r--r--vorlesungen/slides/7/images/common.inc70
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-rw-r--r--vorlesungen/slides/7/images/interpolation.pov10
-rw-r--r--vorlesungen/slides/7/images/rodriguez.jpgbin0 -> 168776 bytes
-rw-r--r--vorlesungen/slides/7/images/rodriguez.pngbin0 -> 261798 bytes
-rw-r--r--vorlesungen/slides/7/images/rodriguez.pov118
-rw-r--r--vorlesungen/slides/7/images/test.pov7
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diff --git a/vorlesungen/slides/7/images/Makefile b/vorlesungen/slides/7/images/Makefile
new file mode 100644
index 0000000..6f99bc3
--- /dev/null
+++ b/vorlesungen/slides/7/images/Makefile
@@ -0,0 +1,29 @@
+#
+# Makefile -- Illustrationen zu
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+# 
+all: rodriguez.jpg test.png
+
+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
+
+dreibein/timestamp: interpolation.m
+ octave interpolation.m
+ touch dreibein/timestamp
+
+test.png: test.pov drehung.inc dreibein/d025.inc dreibein/timestamp
+ povray +A0.1 -W1080 -H1080 -Otest.png test.pov
+
+dreibein/d025.inc: dreibein/timestamp
+
+animation:
+ povray +A0.1 -W1080 -H1080 -Ointerpolation/i.png interpolation.ini
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diff --git a/vorlesungen/slides/7/images/c/c58.jpg b/vorlesungen/slides/7/images/c/c58.jpg
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diff --git a/vorlesungen/slides/7/images/c/c60.jpg b/vorlesungen/slides/7/images/c/c60.jpg
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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
+ }
+}
+
diff --git a/vorlesungen/slides/7/images/drehung.inc b/vorlesungen/slides/7/images/drehung.inc
new file mode 100644
index 0000000..c9b4bb7
--- /dev/null
+++ b/vorlesungen/slides/7/images/drehung.inc
@@ -0,0 +1,142 @@
+//
+// common.inc
+//
+// (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#version 3.7;
+#include "colors.inc"
+
+global_settings {
+ assumed_gamma 1
+}
+
+#declare imagescale = 0.23;
+#declare O = <0, 0, 0>;
+#declare at = 0.02;
+
+camera {
+ location <8.5, 2, 6.5>
+ look_at <0, 0, 0>
+ right x * imagescale
+ up y * imagescale
+}
+
+//light_source {
+// <-14, 20, -50> color White
+// area_light <1,0,0> <0,0,1>, 10, 10
+// adaptive 1
+// jitter
+//}
+
+light_source {
+ <41, 20, 10> 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, 1.0 * 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 r = 1.0;
+
+arrow(< -r-0.2, 0.0, 0 >, < r+0.2, 0.0, 0.0 >, at, Gray)
+arrow(< 0.0, 0.0, -r-0.2>, < 0.0, 0.0, r+0.2 >, at, Gray)
+arrow(< 0.0, -r-0.2, 0 >, < 0.0, r+0.2, 0.0 >, at, Gray)
+
+#declare farbeX = rgb<1.0,0.2,0.6>;
+#declare farbeY = rgb<0.0,0.8,0.4>;
+#declare farbeZ = rgb<0.4,0.6,1.0>;
+
+#declare farbex = rgb<1.0,0.0,0.0>;
+#declare farbey = rgb<0.0,0.6,0.0>;
+#declare farbez = rgb<0.0,0.0,1.0>;
+
+#macro quadrant(X, Y, Z)
+ intersection {
+ sphere { O, 0.5 }
+ plane { -X, 0 }
+ plane { -Y, 0 }
+ plane { -Z, 0 }
+ pigment {
+ color rgb<1.0,0.6,0.2>
+ }
+ finish {
+ specular 0.95
+ metallic
+ }
+ }
+ arrow(O, X, 1.1*at, farbex)
+ arrow(O, Y, 1.1*at, farbey)
+ arrow(O, Z, 1.1*at, farbez)
+#end
+
+#macro drehung(X, Y, Z)
+// intersection {
+// sphere { O, 0.5 }
+// plane { -X, 0 }
+// plane { -Y, 0 }
+// plane { -Z, 0 }
+// pigment {
+// color Gray
+// }
+// finish {
+// specular 0.95
+// metallic
+// }
+// }
+ arrow(O, 1.1*X, 0.9*at, farbeX)
+ arrow(O, 1.1*Y, 0.9*at, farbeY)
+ arrow(O, 1.1*Z, 0.9*at, farbeZ)
+#end
+
+#macro achse(H)
+ cylinder { H, -H, at
+ pigment {
+ color rgb<0.6,0.4,0.2>
+ }
+ finish {
+ specular 0.95
+ metallic
+ }
+ }
+ cylinder { 0.003 * H, -0.003 * H, 1
+ pigment {
+ color rgbt<0.6,0.4,0.2,0.5>
+ }
+ finish {
+ specular 0.95
+ metallic
+ }
+ }
+#end
diff --git a/vorlesungen/slides/7/images/interpolation.ini b/vorlesungen/slides/7/images/interpolation.ini
new file mode 100644
index 0000000..f07c079
--- /dev/null
+++ b/vorlesungen/slides/7/images/interpolation.ini
@@ -0,0 +1,8 @@
+Input_File_Name=interpolation.pov
+Initial_Frame=0
+Final_Frame=50
+Initial_Clock=0
+Final_Clock=50
+Cyclic_Animation=off
+Pause_when_Done=off
+
diff --git a/vorlesungen/slides/7/images/interpolation.m b/vorlesungen/slides/7/images/interpolation.m
new file mode 100644
index 0000000..31554e8
--- /dev/null
+++ b/vorlesungen/slides/7/images/interpolation.m
@@ -0,0 +1,54 @@
+#
+# interpolation.m
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+global N;
+N = 50;
+global A;
+global B;
+
+A = (pi / 2) * [
+ 0, 0, 0;
+ 0, 0, -1;
+ 0, 1, 0
+];
+g0 = expm(A)
+
+B = (pi / 2) * [
+ 0, 0, 1;
+ 0, 0, 0;
+ -1, 0, 0
+];
+g1 = expm(B)
+
+function retval = g(t)
+ global A;
+ global B;
+ retval = expm((1-t)*A+t*B);
+endfunction
+
+function dreibein(fn, M, funktion)
+ fprintf(fn, "%s(<%.4f,%.4f,%.4f>, <%.4f,%.4f,%.4f>, <%.4f,%.4f,%.4f>)\n",
+ funktion,
+ M(1,1), M(3,1), M(2,1),
+ M(1,2), M(3,2), M(2,2),
+ M(1,3), M(3,3), M(2,3));
+endfunction
+
+G = g1 * inverse(g0);
+[V, lambda] = eig(G);
+H = real(V(:,3));
+
+D = logm(g1*inverse(g0));
+
+for i = (0:N)
+ filename = sprintf("dreibein/d%03d.inc", i);
+ fn = fopen(filename, "w");
+ t = i/N;
+ dreibein(fn, g(t), "quadrant");
+ dreibein(fn, expm(t*D)*g0, "drehung");
+ fprintf(fn, "achse(<%.4f,%.4f,%.4f>)\n", H(1,1), H(3,1), H(2,1));
+ fclose(fn);
+endfor
+
diff --git a/vorlesungen/slides/7/images/interpolation.pov b/vorlesungen/slides/7/images/interpolation.pov
new file mode 100644
index 0000000..71e0257
--- /dev/null
+++ b/vorlesungen/slides/7/images/interpolation.pov
@@ -0,0 +1,10 @@
+//
+// commutator.pov
+//
+// (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#include "drehung.inc"
+
+#declare filename = concat("dreibein/d", str(clock, -3, 0), ".inc");
+#include filename
+
diff --git a/vorlesungen/slides/7/images/rodriguez.jpg b/vorlesungen/slides/7/images/rodriguez.jpg
new file mode 100644
index 0000000..5c49700
--- /dev/null
+++ b/vorlesungen/slides/7/images/rodriguez.jpg
Binary files differ
diff --git a/vorlesungen/slides/7/images/rodriguez.png b/vorlesungen/slides/7/images/rodriguez.png
new file mode 100644
index 0000000..6d9e9e4
--- /dev/null
+++ b/vorlesungen/slides/7/images/rodriguez.png
Binary files differ
diff --git a/vorlesungen/slides/7/images/rodriguez.pov b/vorlesungen/slides/7/images/rodriguez.pov
new file mode 100644
index 0000000..07aec19
--- /dev/null
+++ b/vorlesungen/slides/7/images/rodriguez.pov
@@ -0,0 +1,118 @@
+//
+// rodriguez.pov
+//
+// (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#version 3.7;
+#include "colors.inc"
+
+global_settings {
+ assumed_gamma 1
+}
+
+#declare imagescale = 0.020;
+#declare O = <0, 0, 0>;
+#declare at = 0.015;
+
+camera {
+ location <8, 15, -50>
+ look_at <0.1, 0.475, 0>
+ right 16/9 * x * imagescale
+ up y * imagescale
+}
+
+light_source {
+ <-4, 20, -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 K = vnormalize(<0.2,1,0.1>);
+#declare X = vnormalize(<1.1,1,-1.2>);
+#declare O = <0,0,0>;
+
+#declare r = vlength(vcross(K, X)) / vlength(K);
+
+#declare l = 1.0;
+
+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)
+
+arrow(O, X, at, Red)
+arrow(O, K, at, Blue)
+
+#macro punkt(H,phi)
+ ((H-vdot(K,H)*K)*cos(phi) + vcross(K,H)*sin(phi) + vdot(K,X)*K)
+#end
+
+cone { vdot(K, X) * K, r, O, 0
+ pigment {
+ color rgbt<0.6,0.6,0.6,0.5>
+ }
+ finish {
+ specular 0.9
+ metallic
+ }
+}
+
+
+union {
+ #declare phistep = pi / 100;
+ #declare phi = 0;
+ #while (phi < 2 * pi - phistep/2)
+ sphere { punkt(K, phi), at/2 }
+ cylinder {
+ punkt(X, phi),
+ punkt(X, phi + phistep),
+ at/2
+ }
+ #declare phi = phi + phistep;
+ #end
+ pigment {
+ color Orange
+ }
+ finish {
+ specular 0.9
+ metallic
+ }
+}
+
+arrow(vdot(K,X)*K, punkt(X, 0), at, Yellow)
+#declare Darkgreen = rgb<0,0.5,0>;
+arrow(vdot(K,X)*K, punkt(X, pi/2), at, Darkgreen)
diff --git a/vorlesungen/slides/7/images/test.pov b/vorlesungen/slides/7/images/test.pov
new file mode 100644
index 0000000..5707be1
--- /dev/null
+++ b/vorlesungen/slides/7/images/test.pov
@@ -0,0 +1,7 @@
+//
+// test.pov
+//
+// (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#include "drehung.inc"
+#include "dreibein/d025.inc"