add grid to images

12 files changed, 60 insertions, 20 deletions

diff --git a/buch/chapters/110-elliptisch/dglsol.tex b/buch/chapters/110-elliptisch/dglsol.tex
index 74f2f8c..3303aee 100644
--- a/buch/chapters/110-elliptisch/dglsol.tex
+++ b/buch/chapters/110-elliptisch/dglsol.tex
@@ -403,27 +403,27 @@ abgelesen werden:
 \begin{equation}
 \begin{aligned}
 \operatorname{sn}(0,k)&=0
-&
+&&\qquad&
 \operatorname{cn}(0,k)&=1
-&
+&&\qquad&
 \operatorname{dn}(0,k)&=1
 \\
 \operatorname{sn}(iK',k)&=\infty
-&
+&&\qquad&
 \operatorname{cn}(iK',k)&=\infty
-&
+&&\qquad&
 \operatorname{dn}(iK',k)&=\infty
 \\
 \operatorname{sn}(K,k)&=1
-&
+&&\qquad&
 \operatorname{cn}(K,k)&=0
-&
+&&\qquad&
 \operatorname{dn}(K,k)&=k'
 \\
 \operatorname{sn}(K+iK',k)&=\frac{1}{k}
-&
+&&\qquad&
 \operatorname{cn}(K+iK',k)&=\frac{k'}{ik}
-&
+&&\qquad&
 \operatorname{dn}(K+iK',k)&=0
 \end{aligned}
 \label{buch:elliptische:eqn:eckwerte}
diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile
index 43ca35e..7636e65 100644
--- a/buch/chapters/110-elliptisch/images/Makefile
+++ b/buch/chapters/110-elliptisch/images/Makefile
@@ -120,6 +120,11 @@ ellpolnul.pdf:	ellpolnul.tex ellcommon.tex
 ellall.pdf:	ellall.tex ellcommon.tex
 	pdflatex ellall.tex
 
-ellselection.pdf:	ellselection.tex
+rechteckpfade2.tex:	rechteck Makefile
+	./rechteck --outfile rechteckpfade2.tex --k 0.87 --vsteps=1
+ellselection.pdf:	ellselection.tex rechteckpfade2.tex
 	pdflatex ellselection.tex
 
+rechteckpfade3.tex:	rechteck
+	./rechteck --outfile rechteckpfade3.tex --k 0.70710678118654752440 \
+		--vsteps=4
diff --git a/buch/chapters/110-elliptisch/images/ellpolnul.pdf b/buch/chapters/110-elliptisch/images/ellpolnul.pdf
index 9143d2d..a60a51b 100644
--- a/buch/chapters/110-elliptisch/images/ellpolnul.pdf
+++ b/buch/chapters/110-elliptisch/images/ellpolnul.pdf
diff --git a/buch/chapters/110-elliptisch/images/ellpolnul.tex b/buch/chapters/110-elliptisch/images/ellpolnul.tex
index 16730f9..fe1d235 100644
--- a/buch/chapters/110-elliptisch/images/ellpolnul.tex
+++ b/buch/chapters/110-elliptisch/images/ellpolnul.tex
@@ -15,6 +15,15 @@
 \def\skala{1}
 \begin{tikzpicture}[>=latex,thick,scale=\skala]
 
+\input rechteckpfade3.tex
+
+\pgfmathparse{1/\xmax}
+\xdef\dx{\pgfmathresult}
+\xdef\dy{\dx}
+
+\netz{0.1pt}
+\draw[line width=0.1pt] (-1,0) -- (1,0);
+\fill[color=white,opacity=0.5] (-1,-1) rectangle (1,1);
 \draw (-1,-1) rectangle (1,1);
 \node at (-1,-1) [below left] {$0$};
 \node at (1,-1) [below right] {$K$};
diff --git a/buch/chapters/110-elliptisch/images/ellselection.pdf b/buch/chapters/110-elliptisch/images/ellselection.pdf
index bc9af35..bad342c 100644
--- a/buch/chapters/110-elliptisch/images/ellselection.pdf
+++ b/buch/chapters/110-elliptisch/images/ellselection.pdf
diff --git a/buch/chapters/110-elliptisch/images/ellselection.tex b/buch/chapters/110-elliptisch/images/ellselection.tex
index 9e822ec..0dd1e04 100644
--- a/buch/chapters/110-elliptisch/images/ellselection.tex
+++ b/buch/chapters/110-elliptisch/images/ellselection.tex
@@ -14,15 +14,22 @@
 \def\skala{1}
 \begin{tikzpicture}[>=latex,thick,scale=\skala]
 
+\input{rechteckpfade2.tex}
+
 \def\l{0.45}
 \pgfmathparse{\l*72/2.54}
 \xdef\L{\pgfmathresult}
 
+\pgfmathparse{4.1/\xmax}
+\xdef\dx{\pgfmathresult}
+\xdef\dy{\dx}
+
 \def\sx{4.1}
 \pgfmathparse{\sx*72/2.54}
 \xdef\Sx{\pgfmathresult}
 
-\def\sy{3.2}
+\pgfmathparse{\dx*\ymax}
+\xdef\sy{\pgfmathresult}
 \pgfmathparse{\sy*72/2.54}
 \xdef\Sy{\pgfmathresult}
 
@@ -36,8 +43,10 @@
 \pgfmathparse{\sy/2}
 \xdef\rechtsy{\pgfmathresult}
 
-\fill[color=red!20] ({-\sx},0) rectangle (\sx,\sy);
-\fill[color=blue!20] ({-\sx},{-\sy}) rectangle (\sx,0);
+\hintergrund
+\netz{0.7pt}
+\fill[color=red!14,opacity=0.7] ({-\sx},0) rectangle (\sx,\sy);
+\fill[color=blue!14,opacity=0.7] ({-\sx},{-\sy}) rectangle (\sx,0);
 \fill[color=yellow!40,opacity=0.5] (0,0) rectangle (\sx,\sy);
 
 \draw (-\sx,-\sy) rectangle (\sx,\sy);
diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.pdf b/buch/chapters/110-elliptisch/images/jacobiplots.pdf
index 59aea81..3ac9fe5 100644
--- a/buch/chapters/110-elliptisch/images/jacobiplots.pdf
+++ b/buch/chapters/110-elliptisch/images/jacobiplots.pdf
diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pdf b/buch/chapters/110-elliptisch/images/kegelpara.pdf
index 59f9f50..0d6f63d 100644
--- a/buch/chapters/110-elliptisch/images/kegelpara.pdf
+++ b/buch/chapters/110-elliptisch/images/kegelpara.pdf
diff --git a/buch/chapters/110-elliptisch/images/rechteck.cpp b/buch/chapters/110-elliptisch/images/rechteck.cpp
index c65ae0f..b5ad0ec 100644
--- a/buch/chapters/110-elliptisch/images/rechteck.cpp
+++ b/buch/chapters/110-elliptisch/images/rechteck.cpp
@@ -163,7 +163,7 @@ curvetracer::curve_t	curvetracer::trace(const std::complex<double>& startz,
 		} catch (const toomanyiterations& x) {
 			std::cerr << "iterations exceeded after ";
 			std::cerr << result.size();
-			std::cerr << " points";
+			std::cerr << " points" << std::endl;
 			maxsteps = 0;
 		}
 	}
@@ -230,7 +230,7 @@ void	curvedrawer::operator()(const curvetracer::curve_t& curve) {
 	double	first = true;
 	for (auto z : curve) {
 		if (first) {
-			*_out << "\\draw[color=" << _color << "] ";
+			*_out << "\\draw[color=" << _color << ",line width=#1] ";
 			first = false;
 		} else {
 			*_out << std::endl << "    -- ";
@@ -244,6 +244,7 @@ static struct option	longopts[] = {
 { "outfile",	required_argument,	NULL,	'o' },
 { "k",		required_argument,	NULL,	'k' },
 { "deltax",	required_argument,	NULL,	'd' },
+{ "vsteps",	required_argument,	NULL,	'v' },
 { NULL,		0,			NULL,	 0  }
 };
 
@@ -252,7 +253,8 @@ static struct option	longopts[] = {
  */
 int	main(int argc, char *argv[]) {
 	double	k = 0.625;
-	double	deltax = 0.2;
+	double	Deltax = 0.2;
+	int	vsteps = 4;
 
 	int	c;
 	int	longindex;
@@ -261,7 +263,7 @@ int	main(int argc, char *argv[]) {
 		&longindex)))
 		switch (c) {
 		case 'd':
-			deltax = std::stod(optarg);
+			Deltax = std::stod(optarg);
 			break;
 		case 'o':
 			outfilename = std::string(optarg);
@@ -269,6 +271,9 @@ int	main(int argc, char *argv[]) {
 		case 'k':
 			k = std::stod(optarg);
 			break;
+		case 'v':
+			vsteps = std::stoi(optarg);
+			break;
 		}
 
 	double	kprime = integrand::kprime(k);
@@ -293,15 +298,21 @@ int	main(int argc, char *argv[]) {
 	curvetracer	ct(f);
 
 	// fill
+	(*cdp->out()) << "\\def\\hintergrund{" << std::endl;
 	(*cdp->out()) << "\\fill[color=red!10] ({" << (-xmax) << "*\\dx},0) "
 		<< "rectangle ({" << xmax << "*\\dx},{" << ymax << "*\\dy});"
 		<< std::endl;
 	(*cdp->out()) << "\\fill[color=blue!10] ({" << (-xmax) << "*\\dx},{"
 		<< (-ymax) << "*\\dy}) rectangle ({" << xmax << "*\\dx},0);"
 		<< std::endl;
+	(*cdp->out()) << "}" << std::endl;
+
+	// macro for grid
+	(*cdp->out()) << "\\def\\netz#1{" << std::endl;
 
 	// "circles"
 	std::complex<double>	dir(0.01, 0);
+	double	deltax = Deltax;
 	for (double im = deltax; im < 3; im += deltax) {
 		std::complex<double>	startz(0, im);
 		std::complex<double>	startw = ct.startpoint(startz);
@@ -316,9 +327,9 @@ int	main(int argc, char *argv[]) {
 	}
 
 	// imaginary axis
-	(*cdp->out()) << "\\draw[color=red] (0,0) -- (0,{" << ymax
+	(*cdp->out()) << "\\draw[color=red,line width=#1] (0,0) -- (0,{" << ymax
 		<< "*\\dy});" << std::endl;
-	(*cdp->out()) << "\\draw[color=blue] (0,0) -- (0,{" << (-ymax)
+	(*cdp->out()) << "\\draw[color=blue,line width=#1] (0,0) -- (0,{" << (-ymax)
 		<< "*\\dy});" << std::endl;
 
 	// arguments between 0 and 1
@@ -353,7 +364,8 @@ int	main(int argc, char *argv[]) {
 
 	// arguments between 1 and 1/k
 	{
-		for (double x0 = 1 + deltax; x0 < 1/k; x0 += deltax) {
+		deltax = (1/k - 1) / vsteps;
+		for (double x0 = 1 + deltax; x0 < 1/k + 0.00001; x0 += deltax) {
 			double	y0 = sqrt(1-1/(x0*x0))/kprime;
 			//std::cout << "y0 = " << y0 << std::endl;
 			double	y = gsl_sf_ellint_F(asin(y0), kprime,
@@ -389,8 +401,9 @@ int	main(int argc, char *argv[]) {
 
 	// arguments larger than 1/k
 	{
+		deltax = Deltax;
 		dir = std::complex<double>(0, 0.01);
-		double	x0 = 1;
+		double	x0 = 1/k;
 		while (x0 <= 1/k + 0.0001) { x0 += deltax; }
 		for (; x0 < 4; x0 += deltax) {
 			std::complex<double>	startz(x0);
@@ -407,6 +420,8 @@ int	main(int argc, char *argv[]) {
 		}
 	}
 
+	(*cdp->out()) << "}" << std::endl;
+
 	// border
 	(*cdp->out()) << "\\def\\xmax{" << xmax << "}" << std::endl;
 	(*cdp->out()) << "\\def\\ymax{" << ymax << "}" << std::endl;
diff --git a/buch/chapters/110-elliptisch/images/rechteck.pdf b/buch/chapters/110-elliptisch/images/rechteck.pdf
index 6209897..46f2376 100644
--- a/buch/chapters/110-elliptisch/images/rechteck.pdf
+++ b/buch/chapters/110-elliptisch/images/rechteck.pdf
diff --git a/buch/chapters/110-elliptisch/images/rechteck.tex b/buch/chapters/110-elliptisch/images/rechteck.tex
index 622a9e9..12535ba 100644
--- a/buch/chapters/110-elliptisch/images/rechteck.tex
+++ b/buch/chapters/110-elliptisch/images/rechteck.tex
@@ -18,6 +18,8 @@
 \def\dy{3}
 
 \input{rechteckpfade.tex}
+\hintergrund
+\netz{0.7pt}
 
 \begin{scope}
 	\clip ({-\xmax*\dx},{-\ymax*\dy}) rectangle ({\xmax*\dx},{\ymax*\dy});
diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pdf b/buch/chapters/110-elliptisch/images/torusschnitt.pdf
index 61293f3..2948e76 100644
--- a/buch/chapters/110-elliptisch/images/torusschnitt.pdf
+++ b/buch/chapters/110-elliptisch/images/torusschnitt.pdf