#include <math.h>
#include <stdio.h>

static __inline__ double func(double t, double a, double b)
{
	return pow((pow(a, -2.0) - pow(b, -2.0)) * pow(cos(t), 2.0) + pow(b, -2.0), -0.5);
}

/*
 * Simpson's Method - approximate the area under a curve using n intervals
 * and parabolic curves.
 */
double simp(double a, double b, int n, double A, double B)
{
	double c, d, s;
	int i;
	c = (b - a) / n;
	d = c / 3;
	s = func(a, A, B);
	for (i = 1; i <= (n - 1); i += 2)
		s += 4.0 * func(a + i * c, A, B);
	for (i = 2; i <= (n - 2); i += 2)
		s += 2.0 * func(a + i * c, A, B);
	s += func(b, A, B);
	s *= d;
	return s;
}

/*
 * Approximate an integral using Riemann sums on n sub-intervals.
 * Simple but slow, but who cares given the speed of modern computers!
 */
double sums(double a, double b, int n, double A, double B)
{
	double h, sum;
	int i;

	/* Start with nothing */
	sum = 0.0;

	/* Width of a sub-interval */
	h = (b - a) / n;

	/* Mid=point of 1st sub-interval */
	a += h / 2.0;

	for (i = 0; i < n; i++) {
		/* Area = width * height */
		sum += h * func(a, A, B);

		/* Mid-point of next sub-interval */
		a += h;
	}
	return sum;
}

int main(int argc, char *argv[])
{
	double a, b, i, g;
	double x, y, r, w, t, l;

	if (argc < 3)
		return 1;

	/* Radius */
	sscanf(argv[1], "%lf", &a);

	/* Height = 70.7% of radius */
	b = a * M_SQRT1_2;

	/* Gores */
	sscanf(argv[2], "%lf", &g);

	/* Plot 1000 points */
	i = M_PI_2 / 1000;

	/* Summary */
	fprintf(stderr, "a=%f b=%f g=%f\n", a, b, g);

	l = 0.0;

	for (t = 0.0; t <= M_PI_2; t += i) {
		x =  pow(pow(a, -2.0) + pow(tan(t) / b, 2.0), -0.5);
		y = x * tan(x);
		w = 2.0 * M_PI * x / g;
		l += sums(t ? t - i: 0.0, t, 1000, a, b);
		printf("%.8f %.8f\n", l, w / 2.0);
		printf("%.8f %.8f\n", l, -w / 2.0);
	}

	return 0;
}