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authorAndreas Müller <andreas.mueller@ost.ch>2021-10-03 14:24:04 +0200
committerAndreas Müller <andreas.mueller@ost.ch>2021-10-03 14:24:04 +0200
commit6747b071a643ae99576bee6a996f2792232ad8ab (patch)
tree8d2110aac7d1012748ed739ebe8c36ee56886eda /vorlesungen/slides
parentnew slide (diff)
downloadSeminarSpezielleFunktionen-6747b071a643ae99576bee6a996f2792232ad8ab.tar.gz
SeminarSpezielleFunktionen-6747b071a643ae99576bee6a996f2792232ad8ab.zip
ad video complete
Diffstat (limited to '')
-rw-r--r--vorlesungen/slides/0/Makefile14
-rw-r--r--vorlesungen/slides/0/Makefile.inc1
-rw-r--r--vorlesungen/slides/0/chapter.tex1
-rw-r--r--vorlesungen/slides/0/fehler.tex19
-rw-r--r--vorlesungen/slides/0/simulation.cpp178
-rw-r--r--vorlesungen/slides/0/wassindss.tex2
6 files changed, 214 insertions, 1 deletions
diff --git a/vorlesungen/slides/0/Makefile b/vorlesungen/slides/0/Makefile
new file mode 100644
index 0000000..c650491
--- /dev/null
+++ b/vorlesungen/slides/0/Makefile
@@ -0,0 +1,14 @@
+#
+# Makefile -- build the images
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+
+simulation: simulation.cpp
+ g++ -Wall -O2 -g -o simulation `pkg-config --cflags Magick++` \
+ simulation.cpp `pkg-config --libs Magick++`
+test: simulation
+ ./simulation
+
+video: simulation
+ ./simulation --iterations=1000 test/
diff --git a/vorlesungen/slides/0/Makefile.inc b/vorlesungen/slides/0/Makefile.inc
index 06d0694..b06ef65 100644
--- a/vorlesungen/slides/0/Makefile.inc
+++ b/vorlesungen/slides/0/Makefile.inc
@@ -6,6 +6,7 @@
chapter0 = \
../slides/0/frueher.tex \
../slides/0/funktionen.tex \
+ ../slides/0/fehler.tex \
../slides/0/info.tex \
../slides/0/intro.tex \
../slides/0/wassindss.tex \
diff --git a/vorlesungen/slides/0/chapter.tex b/vorlesungen/slides/0/chapter.tex
index 278728e..f636a9f 100644
--- a/vorlesungen/slides/0/chapter.tex
+++ b/vorlesungen/slides/0/chapter.tex
@@ -6,6 +6,7 @@
\folie{0/intro.tex}
\folie{0/info.tex}
\folie{0/funktionen.tex}
+\folie{0/fehler.tex}
\folie{0/frueher.tex}
\folie{0/was.tex}
\folie{0/wassindss.tex}
diff --git a/vorlesungen/slides/0/fehler.tex b/vorlesungen/slides/0/fehler.tex
new file mode 100644
index 0000000..c765176
--- /dev/null
+++ b/vorlesungen/slides/0/fehler.tex
@@ -0,0 +1,19 @@
+%
+% fehler.tex -- slide template
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Exakte Lösungen sind genauer}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.48\textwidth}
+\end{column}
+\begin{column}{0.48\textwidth}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup
diff --git a/vorlesungen/slides/0/simulation.cpp b/vorlesungen/slides/0/simulation.cpp
new file mode 100644
index 0000000..6b1be8c
--- /dev/null
+++ b/vorlesungen/slides/0/simulation.cpp
@@ -0,0 +1,178 @@
+/*
+ * simulation.cpp
+ *
+ * (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+ */
+#include <ImageMagick-7/Magick++.h>
+#include <string>
+#include <cstdio>
+#include <cstdlib>
+#include <iostream>
+#include <cmath>
+#include <getopt.h>
+
+class v {
+ double _data[2];
+public:
+ v(double x, double y) {
+ _data[0] = x;
+ _data[1] = y;
+ }
+ v() {
+ _data[0] = 0;
+ _data[1] = 0;
+ }
+ double& operator[](int i) { return _data[i]; }
+ const double& operator[](int i) const { return _data[i]; }
+ v operator+(const v& other) const {
+ v result;
+ result[0] = _data[0] + other[0];
+ result[1] = _data[1] + other[1];
+ return result;
+ }
+ v operator-(const v& other) const {
+ v result;
+ result[0] = _data[0] - other[0];
+ result[1] = _data[1] - other[1];
+ return result;
+ }
+ v operator*(double l) const {
+ v result;
+ result[0] = l * _data[0];
+ result[1] = l * _data[1];
+ return result;
+ }
+ Magick::Coordinate coordinate() {
+ return Magick::Coordinate(_data[0], _data[1]);
+ }
+};
+
+v f(const v& x) {
+ v result;
+ result[0] = -x[1];
+ result[1] = x[0];
+ return result;
+}
+
+v rkstep(const v& x, double h) {
+ v k1 = f(x);
+ v k2 = f(x + k1 * (h/2));
+ v k3 = f(x + k2 * (h/2));
+ v k4 = f(x + k3 * h);
+ return x + (k1 + k2 * 2 + k3 * 2 + k4) * (h/6);
+}
+
+v rotation(const v& x0, int steps) {
+ double h = 2 * M_PI / steps;
+ v x = x0;
+ for (int i = 0; i < steps; i++) {
+ x = rkstep(x, h);
+ }
+ return x;
+}
+
+v rotations(const v& x0, int rot, int steps) {
+ v x = x0;
+ for (int i = 0; i < rot; i++) {
+ x = rotation(x, steps);
+ }
+ return x;
+}
+
+struct option longoptions[] = {
+{ "width", required_argument, NULL, 'w' },
+{ "height", required_argument, NULL, 'h' },
+{ "scale", required_argument, NULL, 'S' },
+{ "steps", required_argument, NULL, 's' },
+{ "rotations", required_argument, NULL, 'r' },
+{ "iterations", required_argument, NULL, 'i' },
+{ NULL, 0, NULL, 0 }
+};
+
+int main(int argc, char *argv[]) {
+ Magick::InitializeMagick(*argv);
+ int width = 1920;
+ int height = 1080;
+ double scale = 500;
+ int steps = 80;
+ int nrotations = 40000;
+ int iterations = 200;
+ int c;
+ int longindex;
+ std::string outputpath;
+ while (EOF != (c = getopt_long(argc, argv, "w:h:S:s:r:i:", longoptions, &longindex)))
+ switch (c) {
+ case 'w':
+ width = std::stoi(optarg);
+ break;
+ case 'h':
+ height = std::stoi(optarg);
+ break;
+ case 'S':
+ scale = std::stod(optarg);
+ break;
+ case 's':
+ steps = std::stoi(optarg);
+ break;
+ case 'r':
+ nrotations = std::stoi(optarg);
+ break;
+ case 'i':
+ iterations = std::stoi(optarg);
+ break;
+ }
+
+ if (optind < argc) {
+ outputpath = std::string(argv[optind++]);
+ }
+
+ Magick::Geometry geometry(width, height);
+ std::string backgroundcolorspec("white");
+ std::string axescolorspec("black");
+ std::string curvecolorspec("red");
+ Magick::ColorRGB background(backgroundcolorspec);
+ Magick::ColorRGB axescolor(axescolorspec);
+ Magick::ColorRGB curvecolor(curvecolorspec);
+ Magick::ColorRGB transparent("transparent");
+
+ Magick::Image image(geometry, background);
+ image.strokeColor(axescolor);
+
+ // draw axes
+ std::vector<Magick::Drawable> objects_to_draw;
+ objects_to_draw.push_back(Magick::DrawableStrokeWidth(5));
+ objects_to_draw.push_back(Magick::DrawableLine(0,540, 1919, 540));
+ objects_to_draw.push_back(Magick::DrawableLine(960,0,960,1079));
+ image.draw(objects_to_draw);
+
+ // compute rotations and errors an plot the errors
+ v x0(1,0);
+ v x = x0;
+ v offset(980, 540);
+ image.strokeColor(curvecolor);
+ Magick::CoordinateList path;
+ path.push_back((x - x0 + offset).coordinate());
+ for (int n = 0; n < iterations; n++) {
+ //v from = (x - x0) * 100;
+ x = rotations(x, nrotations, steps);
+ v to = (x - x0) * scale + offset;
+ std::cout << "(" << to[0] << "," << to[1] << ")" << std::endl;
+ path.push_back(to.coordinate());
+ std::vector<Magick::Drawable> segments;
+ segments.push_back(Magick::DrawableFillColor(transparent));
+ segments.push_back(Magick::DrawableStrokeWidth(5));
+ segments.push_back(Magick::DrawablePolyline(path));
+ image.draw(segments);
+
+ // write the image if the output path is set
+ if (outputpath.size() > 0) {
+ char buffer[1024];
+ snprintf(buffer, sizeof(buffer), "%s%05d.jpg",
+ outputpath.c_str(), n);
+ image.write(buffer);
+ }
+ }
+
+ // write the image
+ image.write("test.jpg");
+}
diff --git a/vorlesungen/slides/0/wassindss.tex b/vorlesungen/slides/0/wassindss.tex
index 047cb9d..0ed3452 100644
--- a/vorlesungen/slides/0/wassindss.tex
+++ b/vorlesungen/slides/0/wassindss.tex
@@ -22,7 +22,7 @@ Softwarebibliotheken implementieren {\em spezielle Funktionen}
\item<4->
Problemlösung und Verwendung von {\em speziellen Funktionen}
sind
-besonders effizent/genau
+besonders effizient/genau
\end{itemize}
\end{column}
\begin{column}{0.48\textwidth}