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authorAndreas Müller <andreas.mueller@ost.ch>2021-04-10 22:56:28 +0200
committerAndreas Müller <andreas.mueller@ost.ch>2021-04-10 22:56:28 +0200
commite8fcbfb46f9d7badd043b9daca9659bbd45f84ee (patch)
tree0dbb86dcc2b8139d95edaa28a0b7d4694855e1eb /vorlesungen/slides/7
parentadd rodriguez image (diff)
downloadSeminarMatrizen-e8fcbfb46f9d7badd043b9daca9659bbd45f84ee.tar.gz
SeminarMatrizen-e8fcbfb46f9d7badd043b9daca9659bbd45f84ee.zip
new images
Diffstat (limited to '')
-rw-r--r--vorlesungen/slides/7/Makefile.inc1
-rw-r--r--vorlesungen/slides/7/chapter.tex1
-rw-r--r--vorlesungen/slides/7/images/Makefile9
-rw-r--r--vorlesungen/slides/7/images/c/c01.jpgbin0 -> 89652 bytes
-rw-r--r--vorlesungen/slides/7/images/c/c02.jpgbin0 -> 91977 bytes
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-rw-r--r--vorlesungen/slides/7/images/c/c60.jpgbin0 -> 142174 bytes
-rw-r--r--vorlesungen/slides/7/images/common.inc70
-rw-r--r--vorlesungen/slides/7/images/commutator.ini8
-rw-r--r--vorlesungen/slides/7/images/commutator.m111
-rw-r--r--vorlesungen/slides/7/images/commutator.pov59
-rw-r--r--vorlesungen/slides/7/kommutator.tex139
-rw-r--r--vorlesungen/slides/7/sl2.tex26
69 files changed, 423 insertions, 1 deletions
diff --git a/vorlesungen/slides/7/Makefile.inc b/vorlesungen/slides/7/Makefile.inc
index ef004ca..540b080 100644
--- a/vorlesungen/slides/7/Makefile.inc
+++ b/vorlesungen/slides/7/Makefile.inc
@@ -15,6 +15,7 @@ chapter5 = \
../slides/7/einparameter.tex \
../slides/7/ableitung.tex \
../slides/7/liealgebra.tex \
+ ../slides/7/kommutator.tex \
../slides/7/dg.tex \
../slides/7/chapter.tex
diff --git a/vorlesungen/slides/7/chapter.tex b/vorlesungen/slides/7/chapter.tex
index 44d46a6..5878164 100644
--- a/vorlesungen/slides/7/chapter.tex
+++ b/vorlesungen/slides/7/chapter.tex
@@ -14,4 +14,5 @@
\folie{7/einparameter.tex}
\folie{7/ableitung.tex}
\folie{7/liealgebra.tex}
+\folie{7/kommutator.tex}
\folie{7/dg.tex}
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
+
+
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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
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diff --git a/vorlesungen/slides/7/images/c/c55.jpg b/vorlesungen/slides/7/images/c/c55.jpg
new file mode 100644
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+++ b/vorlesungen/slides/7/images/c/c55.jpg
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diff --git a/vorlesungen/slides/7/images/c/c56.jpg b/vorlesungen/slides/7/images/c/c56.jpg
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+++ b/vorlesungen/slides/7/images/c/c56.jpg
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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
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+++ b/vorlesungen/slides/7/images/c/c57.jpg
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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
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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
Binary files differ
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
Binary files differ
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/kommutator.tex b/vorlesungen/slides/7/kommutator.tex
new file mode 100644
index 0000000..f01debe
--- /dev/null
+++ b/vorlesungen/slides/7/kommutator.tex
@@ -0,0 +1,139 @@
+%
+% template.tex -- slide template
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Kommutator in $\operatorname{SO}(3)$}
+\vspace{-20pt}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+\ifthenelse{\boolean{presentation}}{
+\only<1>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c01.jpg}};}
+\only<2>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c02.jpg}};}
+\only<3>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c03.jpg}};}
+\only<4>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c04.jpg}};}
+\only<5>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c05.jpg}};}
+\only<6>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c06.jpg}};}
+\only<7>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c07.jpg}};}
+\only<8>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c08.jpg}};}
+\only<9>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c09.jpg}};}
+\only<10>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c10.jpg}};}
+\only<11>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c11.jpg}};}
+\only<12>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c12.jpg}};}
+\only<13>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c13.jpg}};}
+\only<14>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c14.jpg}};}
+\only<15>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c15.jpg}};}
+\only<16>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c16.jpg}};}
+\only<17>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c17.jpg}};}
+\only<18>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c18.jpg}};}
+\only<19>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c19.jpg}};}
+\only<20>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c20.jpg}};}
+\only<21>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c21.jpg}};}
+\only<22>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c22.jpg}};}
+\only<23>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c23.jpg}};}
+\only<24>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c24.jpg}};}
+\only<25>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c25.jpg}};}
+\only<26>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c26.jpg}};}
+\only<27>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c27.jpg}};}
+\only<28>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c28.jpg}};}
+\only<29>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c29.jpg}};}
+\only<30>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c30.jpg}};}
+\only<31>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c31.jpg}};}
+\only<32>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c32.jpg}};}
+\only<33>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c33.jpg}};}
+\only<34>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c34.jpg}};}
+\only<35>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c35.jpg}};}
+\only<36>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c36.jpg}};}
+\only<37>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c37.jpg}};}
+\only<38>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c38.jpg}};}
+\only<39>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c39.jpg}};}
+\only<40>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c40.jpg}};}
+\only<41>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c41.jpg}};}
+\only<42>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c42.jpg}};}
+\only<43>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c43.jpg}};}
+\only<44>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c44.jpg}};}
+\only<45>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c45.jpg}};}
+\only<46>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c46.jpg}};}
+\only<47>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c47.jpg}};}
+\only<48>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c48.jpg}};}
+\only<49>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c49.jpg}};}
+\only<50>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c50.jpg}};}
+\only<51>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c51.jpg}};}
+\only<52>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c52.jpg}};}
+\only<53>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c53.jpg}};}
+\only<54>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c54.jpg}};}
+\only<55>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c55.jpg}};}
+\only<56>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c56.jpg}};}
+\only<57>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c57.jpg}};}
+\only<58>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c58.jpg}};}
+\only<59>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c59.jpg}};}
+\only<60>{\node at (0,0) {
+\includegraphics[width=\textwidth]{../slides/7/images/c/c60.jpg}};}
+}{}
+\end{tikzpicture}
+\end{center}
+\end{frame}
+\egroup
diff --git a/vorlesungen/slides/7/sl2.tex b/vorlesungen/slides/7/sl2.tex
index 3480460..a65b4f6 100644
--- a/vorlesungen/slides/7/sl2.tex
+++ b/vorlesungen/slides/7/sl2.tex
@@ -50,6 +50,7 @@ c&d
\foreach \y in {-2,...,2}{
\draw[color=blue,line width=0.3pt] (-3,\y) -- (3,\y);
}
+ \ifthenelse{\boolean{presentation}}{
\foreach \d in {4,...,10}{
\only<\d>{
\pgfmathparse{1+(\d-4)/10}
@@ -66,6 +67,7 @@ c&d
}
}
}
+ }{}
\uncover<11->{
\xdef\t{1.6}
\fill[color=red!40,opacity=0.5]
@@ -105,6 +107,7 @@ c&d
\foreach \y in {-2,...,2}{
\draw[color=blue,line width=0.3pt] (-3,\y) -- (3,\y);
}
+ \ifthenelse{\boolean{presentation}}{
\foreach \d in {11,...,17}{
\only<\d>{
\pgfmathparse{(\d-11)/10}
@@ -128,6 +131,7 @@ c&d
}
}
}
+ }{}
\uncover<18->{
\xdef\t{0.6}
\fill[color=red!40,opacity=0.5]
@@ -174,6 +178,7 @@ c&d
\foreach \y in {-2,...,2}{
\draw[color=blue,line width=0.3pt] (-3,\y) -- (3,\y);
}
+ \ifthenelse{\boolean{presentation}}{
\foreach \d in {18,...,24}{
\only<\d>{
\pgfmathparse{(\d-18)/10}
@@ -197,6 +202,27 @@ c&d
}
}
}
+ }{}
+ \uncover<25->{
+ \xdef\t{0.6}
+ \fill[color=red!40,opacity=0.5]
+ (-1,{\t*(-1)-1})
+ --
+ (1,{\t*1-1})
+ --
+ (1,{\t*1+1})
+ --
+ (-1,{\t*(-1)+1})
+ -- cycle;
+ \foreach \x in {-3,...,3}{
+ \draw[color=red,line width=0.3pt]
+ (\x,{\x*\t-3}) -- (\x,{\x*\t+3});
+ }
+ \foreach \y in {-3,...,3}{
+ \draw[color=red,line width=0.3pt]
+ (-3,{-3*\t+\y}) -- (3,{3*\t+\y});
+ }
+ }
\end{scope}
\draw[->] (-2.1,0) -- (2.3,0) coordinate[label={$x$}];
\draw[->] (0,-2.1) -- (0,2.3) coordinate[label={right:$y$}];