diff options
Diffstat (limited to '')
| -rw-r--r-- | vorlesungen/slides/7/images/Makefile | 38 | ||||
| -rw-r--r-- | vorlesungen/slides/7/images/common.inc | 140 | ||||
| -rw-r--r-- | vorlesungen/slides/7/images/commutator.ini | 16 | ||||
| -rw-r--r-- | vorlesungen/slides/7/images/commutator.m | 222 | ||||
| -rw-r--r-- | vorlesungen/slides/7/images/commutator.pov | 118 | ||||
| -rw-r--r-- | vorlesungen/slides/7/images/rodriguez.pov | 236 |
6 files changed, 385 insertions, 385 deletions
diff --git a/vorlesungen/slides/7/images/Makefile b/vorlesungen/slides/7/images/Makefile index cc67c8a..9de1c34 100644 --- a/vorlesungen/slides/7/images/Makefile +++ b/vorlesungen/slides/7/images/Makefile @@ -1,19 +1,19 @@ -# -# Makefile -- Illustrationen zu -# -# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule -# -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 - - +#
+# Makefile -- Illustrationen zu
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+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/common.inc b/vorlesungen/slides/7/images/common.inc index 0e27c9a..b028956 100644 --- a/vorlesungen/slides/7/images/common.inc +++ b/vorlesungen/slides/7/images/common.inc @@ -1,70 +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) - +//
+// 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 index 8c2211e..44a5ac5 100644 --- a/vorlesungen/slides/7/images/commutator.ini +++ b/vorlesungen/slides/7/images/commutator.ini @@ -1,8 +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 - +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 index 5a448db..3f5ea17 100644 --- a/vorlesungen/slides/7/images/commutator.m +++ b/vorlesungen/slides/7/images/commutator.m @@ -1,111 +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 +#
+# 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 index 9ae11b9..8229a06 100644 --- a/vorlesungen/slides/7/images/commutator.pov +++ b/vorlesungen/slides/7/images/commutator.pov @@ -1,59 +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 - } -} - +//
+// 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/rodriguez.pov b/vorlesungen/slides/7/images/rodriguez.pov index 07aec19..62306f8 100644 --- a/vorlesungen/slides/7/images/rodriguez.pov +++ b/vorlesungen/slides/7/images/rodriguez.pov @@ -1,118 +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) +//
+// 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)
|