import graph;

unitsize(3cm);

real dt = 0.04;
int n = 0;

void ship() {
	write(n);
	shipout(outprefix() + format("-%04d", n));
	++n;
}

pen fix = rgb(0.3, 0, 0.7)+linewidth(2);
pen trans = rgb(0.7, 0, 0.3)+linewidth(2);

string pilabel(real x) {
	int n = floor(2*x/pi+0.5);
	if(n % 2 == 0) {
		return "$"+(n!=2 ? format("%d", n#2) : "")+"\pi$";
	} else {
		return "$\frac{"+(n!=1 ? format("%d", n) : "")+"\pi}2$";
	}
}

xaxis(Label("$x$", EndPoint, 2*E), 0, 2*pi+0.2, LeftTicks(pilabel, n=3, Step=pi/2, NoZero), EndArrow);
yaxis(Label("$y$", EndPoint, 2*N), -1.2, 1.2, LeftTicks(n=2, Step=1), EndArrow);

path cl = box(truepoint(SW), truepoint(NE));
draw(cl, invisible);

draw(graph(cos, 0, pi), fix);
clip(cl);

for(real t = 0; t+dt/2 < 1; t += dt) {
	ship();
}

for(real t = 0; t+dt/2 < 2; t += dt) {
	save();
	draw(yscale(cos(t*pi/2))*shift(t*pi/2, 0)*graph(cos, 0, pi), trans);
	clip(cl);
	ship();
	restore();
}

save();
draw(graph(cos, pi, 2*pi), fix);
clip(cl);
for(real t = 0; t+dt/2 < 1; t += dt) {
	ship();
}
restore();

for(real t = 0; t+dt/2 < 2; t += dt) {
	save();
	draw(yscale(cos(t*pi/2))*shift(-t*pi/2, 0)*graph(cos, pi, 2*pi), trans);
	clip(cl);
	ship();
	restore();
}