ad video complete

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}