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-rw-r--r--buch/chapters/110-elliptisch/images/Makefile13
-rw-r--r--buch/chapters/110-elliptisch/images/jacobiplots.pdfbin56975 -> 59737 bytes
-rw-r--r--buch/chapters/110-elliptisch/images/kegelpara.pdfbin202828 -> 203620 bytes
-rw-r--r--buch/chapters/110-elliptisch/images/lemnispara.cpp126
-rw-r--r--buch/chapters/110-elliptisch/images/lemnispara.pdfbin0 -> 28447 bytes
-rw-r--r--buch/chapters/110-elliptisch/images/lemnispara.tex90
-rw-r--r--buch/chapters/110-elliptisch/images/slcl.pdfbin28233 -> 31823 bytes
-rw-r--r--buch/chapters/110-elliptisch/images/torusschnitt.pdfbin301677 -> 302496 bytes
8 files changed, 228 insertions, 1 deletions
diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile
index c8f98cb..3094877 100644
--- a/buch/chapters/110-elliptisch/images/Makefile
+++ b/buch/chapters/110-elliptisch/images/Makefile
@@ -5,7 +5,7 @@
#
all: lemniskate.pdf ellipsenumfang.pdf unvollstaendig.pdf rechteck.pdf \
ellipse.pdf pendel.pdf jacobiplots.pdf jacobidef.pdf jacobi12.pdf \
- sncnlimit.pdf slcl.pdf torusschnitt.pdf kegelpara.pdf
+ sncnlimit.pdf slcl.pdf torusschnitt.pdf kegelpara.pdf lemnispara.pdf
lemniskate.pdf: lemniskate.tex
pdflatex lemniskate.tex
@@ -102,3 +102,14 @@ torusschnitt.jpg: torusschnitt.png Makefile
torusschnitt.pdf: torusschnitt.tex torusschnitt.jpg
pdflatex torusschnitt.tex
+lemnispara: lemnispara.cpp
+ g++ -O2 -Wall -g -o lemnispara `pkg-config --cflags gsl` \
+ lemnispara.cpp `pkg-config --libs gsl`
+
+lemnisparadata.tex: lemnispara
+ ./lemnispara
+
+lemnispara.pdf: lemnispara.tex lemnisparadata.tex
+ pdflatex lemnispara.tex
+
+ltest: lemnispara.pdf
diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.pdf b/buch/chapters/110-elliptisch/images/jacobiplots.pdf
index c11affc..fdd3d1f 100644
--- a/buch/chapters/110-elliptisch/images/jacobiplots.pdf
+++ b/buch/chapters/110-elliptisch/images/jacobiplots.pdf
Binary files differ
diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pdf b/buch/chapters/110-elliptisch/images/kegelpara.pdf
index 2f76593..2dbe39d 100644
--- a/buch/chapters/110-elliptisch/images/kegelpara.pdf
+++ b/buch/chapters/110-elliptisch/images/kegelpara.pdf
Binary files differ
diff --git a/buch/chapters/110-elliptisch/images/lemnispara.cpp b/buch/chapters/110-elliptisch/images/lemnispara.cpp
new file mode 100644
index 0000000..6f4d55d
--- /dev/null
+++ b/buch/chapters/110-elliptisch/images/lemnispara.cpp
@@ -0,0 +1,126 @@
+/*
+ * lemnispara.cpp -- Display parametrisation of the lemniskate
+ *
+ * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+ */
+#include <cstdio>
+#include <cstdlib>
+#include <cmath>
+#include <gsl/gsl_sf_elljac.h>
+#include <iostream>
+#include <fstream>
+#include <map>
+#include <string.h>
+#include <string>
+
+const static double s = sqrt(2);
+const static double k = 1 / s;
+const static double m = k * k;
+
+typedef std::pair<double, double> point_t;
+
+point_t operator*(const point_t& p, double s) {
+ return point_t(s * p.first, s * p.second);
+}
+
+static double norm(const point_t& p) {
+ return hypot(p.first, p.second);
+}
+
+static point_t normalize(const point_t& p) {
+ return p * (1/norm(p));
+}
+
+static point_t normal(const point_t& p) {
+ return std::make_pair(p.second, -p.first);
+}
+
+class lemniscate : public point_t {
+ double sn, cn, dn;
+public:
+ lemniscate(double t) {
+ gsl_sf_elljac_e(t, m, &sn, &cn, &dn);
+ first = s * cn * dn;
+ second = cn * sn;
+ }
+ point_t tangent() const {
+ return std::make_pair(-s * sn * (1.5 - sn * sn),
+ dn * (1 - 2 * sn * sn));
+ }
+ point_t unittangent() const {
+ return normalize(tangent());
+ }
+ point_t normal() const {
+ return ::normal(tangent());
+ }
+ point_t unitnormal() const {
+ return ::normal(unittangent());
+ }
+};
+
+std::ostream& operator<<(std::ostream& out, const point_t& p) {
+ char b[1024];
+ snprintf(b, sizeof(b), "({%.4f*\\dx},{%.4f*\\dy})", p.first, p.second);
+ out << b;
+ return out;
+}
+
+int main(int argc, char *argv[]) {
+ std::ofstream out("lemnisparadata.tex");
+
+ // the curve
+ double tstep = 0.01;
+ double tmax = 4.05;
+ out << "\\def\\lemnispath{ ";
+ out << lemniscate(0);
+ for (double t = tstep; t < tmax; t += tstep) {
+ out << std::endl << "\t" << "-- " << lemniscate(t);
+ }
+ out << std::endl;
+ out << "}" << std::endl;
+
+ out << "\\def\\lemnispathmore{ ";
+ out << lemniscate(tmax);
+ double tmax2 = 7.5;
+ for (double t = tmax + tstep; t < tmax2; t += tstep) {
+ out << std::endl << "\t" << "-- " << lemniscate(t);
+ }
+ out << std::endl;
+ out << "}" << std::endl;
+
+ // individual points
+ tstep = 0.2;
+ int i = 0;
+ char name[3];
+ strcpy(name, "L0");
+ for (double t = 0; t <= tmax; t += tstep) {
+ char c = 'A' + i++;
+ char buffer[128];
+ lemniscate l(t);
+ name[0] = 'L';
+ name[1] = c;
+ out << "\\coordinate (" << name << ") at ";
+ out << l << ";" << std::endl;
+ name[0] = 'T';
+ out << "\\coordinate (" << name << ") at ";
+ out << l.unittangent() << ";" << std::endl;
+ name[0] = 'N';
+ out << "\\coordinate (" << name << ") at ";
+ out << l.unitnormal() << ";" << std::endl;
+ name[0] = 'C';
+ out << "\\def\\" << name << "{ ";
+ out << "\\node[color=red] at ($(L" << c << ")+0.06*(N" << c << ")$) ";
+ out << "[rotate={";
+ double w = 180 * atan2(l.unitnormal().second,
+ l.unitnormal().first) / M_PI;
+ snprintf(buffer, sizeof(buffer), "%.1f", w);
+ out << buffer;
+ out << "-90}]";
+ snprintf(buffer, sizeof(buffer), "%.1f", t);
+ out << " {$\\scriptstyle " << buffer << "$};" << std::endl;
+ out << "}" << std::endl;
+ }
+
+ out.close();
+ return EXIT_SUCCESS;
+}
diff --git a/buch/chapters/110-elliptisch/images/lemnispara.pdf b/buch/chapters/110-elliptisch/images/lemnispara.pdf
new file mode 100644
index 0000000..b03997e
--- /dev/null
+++ b/buch/chapters/110-elliptisch/images/lemnispara.pdf
Binary files differ
diff --git a/buch/chapters/110-elliptisch/images/lemnispara.tex b/buch/chapters/110-elliptisch/images/lemnispara.tex
new file mode 100644
index 0000000..48557cf
--- /dev/null
+++ b/buch/chapters/110-elliptisch/images/lemnispara.tex
@@ -0,0 +1,90 @@
+%
+% lemnispara.tex -- parametrization of the lemniscate
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math,calc}
+\begin{document}
+\def\skala{1}
+
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+\def\dx{4}
+\def\dy{4}
+\input{lemnisparadata.tex}
+
+% add image content here
+\draw[color=red!20,line width=1.4pt] \lemnispathmore;
+\draw[color=red,line width=1.4pt] \lemnispath;
+
+\draw[->] ({-1.6*\dx},0) -- ({1.6*\dx},0) coordinate[label={$X$}];
+\draw[->] (0,{-0.7*\dy}) -- (0,{0.7*\dy}) coordinate[label={right:$Y$}];
+\draw ({1.5*\dx},-0.05) -- ({1.5*\dx},0.05);
+\draw ({\dx},-0.05) -- ({\dx},0.05);
+\draw ({0.5*\dx},-0.05) -- ({0.5*\dx},0.05);
+\draw ({-0.5*\dx},-0.05) -- ({-0.5*\dx},0.05);
+\draw ({-\dx},-0.05) -- ({-\dx},0.05);
+\draw ({-1.5*\dx},-0.05) -- ({-1.5*\dx},0.05);
+\draw (-0.05,{0.5*\dy}) -- (0.05,{0.5*\dy});
+\draw (-0.05,{-0.5*\dy}) -- (0.05,{-0.5*\dy});
+
+\node at ({\dx},0) [above] {$1$};
+\node at ({-\dx},0) [above] {$-1$};
+\node at ({-0.5*\dx},0) [above] {$-\frac12$};
+\node at ({0.5*\dx},0) [above] {$\frac12$};
+\node at (0,{0.5*\dy}) [left] {$\frac12$};
+\node at (0,{-0.5*\dy}) [left] {$-\frac12$};
+
+\def\s{0.02}
+
+\draw[color=red] ($(LA)-\s*(NA)$) -- ($(LA)+\s*(NA)$);
+\draw[color=red] ($(LB)-\s*(NB)$) -- ($(LB)+\s*(NB)$);
+\draw[color=red] ($(LC)-\s*(NC)$) -- ($(LC)+\s*(NC)$);
+\draw[color=red] ($(LD)-\s*(ND)$) -- ($(LD)+\s*(ND)$);
+\draw[color=red] ($(LE)-\s*(NE)$) -- ($(LE)+\s*(NE)$);
+\draw[color=red] ($(LF)-\s*(NF)$) -- ($(LF)+\s*(NF)$);
+\draw[color=red] ($(LG)-\s*(NG)$) -- ($(LG)+\s*(NG)$);
+\draw[color=red] ($(LH)-\s*(NH)$) -- ($(LH)+\s*(NH)$);
+\draw[color=red] ($(LI)-\s*(NI)$) -- ($(LI)+\s*(NI)$);
+\draw[color=red] ($(LJ)-\s*(NJ)$) -- ($(LJ)+\s*(NJ)$);
+\draw[color=red] ($(LK)-\s*(NK)$) -- ($(LK)+\s*(NK)$);
+\draw[color=red] ($(LL)-\s*(NL)$) -- ($(LL)+\s*(NL)$);
+\draw[color=red] ($(LM)-\s*(NM)$) -- ($(LM)+\s*(NM)$);
+\draw[color=red] ($(LN)-\s*(NN)$) -- ($(LN)+\s*(NN)$);
+\draw[color=red] ($(LO)-\s*(NO)$) -- ($(LO)+\s*(NO)$);
+\draw[color=red] ($(LP)-\s*(NP)$) -- ($(LP)+\s*(NP)$);
+\draw[color=red] ($(LQ)-\s*(NQ)$) -- ($(LQ)+\s*(NQ)$);
+\draw[color=red] ($(LR)-\s*(NR)$) -- ($(LR)+\s*(NR)$);
+\draw[color=red] ($(LS)-\s*(NS)$) -- ($(LS)+\s*(NS)$);
+\draw[color=red] ($(LT)-\s*(NT)$) -- ($(LT)+\s*(NT)$);
+\draw[color=red] ($(LU)-\s*(NU)$) -- ($(LU)+\s*(NU)$);
+
+\CB
+\CC
+\CD
+\CE
+\CF
+\CG
+\CH
+\CI
+\CJ
+\CK
+\CL
+\CM
+\CN
+\CO
+\CP
+\CQ
+\CR
+\CS
+\CT
+\CU
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/110-elliptisch/images/slcl.pdf b/buch/chapters/110-elliptisch/images/slcl.pdf
index c15051b..71645e3 100644
--- a/buch/chapters/110-elliptisch/images/slcl.pdf
+++ b/buch/chapters/110-elliptisch/images/slcl.pdf
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diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pdf b/buch/chapters/110-elliptisch/images/torusschnitt.pdf
index 11bd353..fde5268 100644
--- a/buch/chapters/110-elliptisch/images/torusschnitt.pdf
+++ b/buch/chapters/110-elliptisch/images/torusschnitt.pdf
Binary files differ