diff options
Diffstat (limited to '')
| -rw-r--r-- | vorlesungen/slides/0/Makefile | 14 | ||||
| -rw-r--r-- | vorlesungen/slides/0/Makefile.inc | 1 | ||||
| -rw-r--r-- | vorlesungen/slides/0/chapter.tex | 1 | ||||
| -rw-r--r-- | vorlesungen/slides/0/fehler.tex | 19 | ||||
| -rw-r--r-- | vorlesungen/slides/0/simulation.cpp | 178 | ||||
| -rw-r--r-- | vorlesungen/slides/0/wassindss.tex | 2 |
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} |