From 0344a846c083c11e9ed93ddc5898dd55c6dd1022 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Wed, 20 Apr 2022 10:30:56 +0200
Subject: lemniscate sine stuff

---
 buch/chapters/110-elliptisch/images/slcl.cpp | 128 +++++++++++++++++++++++++++
 1 file changed, 128 insertions(+)
 create mode 100644 buch/chapters/110-elliptisch/images/slcl.cpp

(limited to 'buch/chapters/110-elliptisch/images/slcl.cpp')

diff --git a/buch/chapters/110-elliptisch/images/slcl.cpp b/buch/chapters/110-elliptisch/images/slcl.cpp
new file mode 100644
index 0000000..8584e94
--- /dev/null
+++ b/buch/chapters/110-elliptisch/images/slcl.cpp
@@ -0,0 +1,128 @@
+/*
+ * slcl.cpp
+ *
+ * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+ */
+#include <cstdlib>
+#include <cstdio>
+#include <cmath>
+#include <iostream>
+#include <fstream>
+#include <sstream>
+#include <getopt.h>
+#include <vector>
+#include <gsl/gsl_sf_elljac.h>
+
+namespace slcl {
+
+static struct option	longopts[] {
+{ "outfile",	required_argument,	NULL,	'o' },
+{ "a",		required_argument,	NULL,	'a' },
+{ "b",		required_argument,	NULL,	'b' },
+{ "steps",	required_argument,	NULL,	'n' },
+{ NULL,		0,			NULL,	 0  }
+};
+
+class plot {
+	typedef std::pair<double, double>	point_t;
+	typedef std::vector<point_t>	curve_t;
+	curve_t	_sl;
+	curve_t	_cl;
+	double	_a;
+	double	_b;
+	int	_steps;
+public:
+	double 	a() const { return _a; }
+	double 	b() const { return _b; }
+	int	steps() const { return _steps; }
+public:
+	plot(double a, double b, int steps) : _a(a), _b(b), _steps(steps) {
+		double	l = sqrt(2);
+		double	k = 1 / l;
+		double	m = k * k;
+		double	h = (b - a) / steps;
+		for (int i = 0; i <= steps; i++) {
+			double	x = a + h * i;
+			double	sn, cn, dn;
+			gsl_sf_elljac_e(x, m, &sn, &cn, &dn);
+			_sl.push_back(std::make_pair(l * x, k * sn / dn));
+			_cl.push_back(std::make_pair(l * x, cn));
+		}
+	}
+private:
+	std::string	point(const point_t p) const {
+		char	buffer[128];
+		snprintf(buffer, sizeof(buffer), "({%.4f*\\dx},{%.4f*\\dy})",
+			p.first, p.second);
+		return std::string(buffer);
+	}
+	std::string	path(const curve_t& curve) const {
+		std::ostringstream	out;
+		auto i = curve.begin();
+		out << point(*(i++));
+		do {
+			out << std::endl << "   -- " << point(*(i++));
+		} while (i != curve.end());
+		out.flush();
+		return out.str();
+	}
+public:
+	std::string	slpath() const {
+		return path(_sl);
+	}
+	std::string	clpath() const {
+		return path(_cl);
+	}
+};
+
+/**
+ * \brief Main function for the slcl program
+ */
+int	main(int argc, char *argv[]) {
+	int	longindex;
+	int	c;
+	double	a = 0;
+	double	b = 10;
+	int	steps = 100;
+	std::ostream	*out = &std::cout;
+	while (EOF != (c = getopt_long(argc, argv, "a:b:o:n:",
+		longopts, &longindex)))
+		switch (c) {
+		case 'a':
+			a = std::stod(optarg);
+			break;
+		case 'b':
+			b = std::stod(optarg) / sqrt(2);
+			break;
+		case 'n':
+			steps = std::stol(optarg);
+			break;
+		case 'o':
+			out = new std::ofstream(optarg);
+			break;
+		}
+
+	plot	p(a, b, steps);
+	(*out) << "\\def\\slpath{ " << p.slpath();
+	(*out) << std::endl << " }" << std::endl;
+	(*out) << "\\def\\clpath{ " << p.clpath();
+	(*out) << std::endl << " }" << std::endl;
+
+	out->flush();
+	//out->close();
+	return EXIT_SUCCESS;
+}
+
+} // namespace slcl
+
+int	main(int argc, char *argv[]) {
+	try {
+		return slcl::main(argc, argv);
+	} catch (const std::exception& e) {
+		std::cerr << "terminated by exception: " << e.what();
+		std::cerr << std::endl;
+	} catch (...) {
+		std::cerr << "terminated by unknown exception" << std::endl;
+	}
+	return EXIT_FAILURE;
+}
-- 
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