# functions

maluj <- function(u)
{
	q <- cbind(0,0);
	a <- matrix(nrow=0,ncol=2);
	b <- matrix(nrow=0,ncol=2);
	for (i in 1:nrow(u)) {
		m <- rep(u[i,],each=nrow(q));
		q0 <- q-m/2;
		q1 <- q+m/2;
		m <- rep(u[i,],each=nrow(a));
		a0 <- a-m/2;
		a1 <- a+m/2;
		m <- rep(u[i,],each=nrow(b));
		b0 <- b-m/2;
		b1 <- b+m/2;
		q <- rbind(q0,q1);
		a <- rbind(a0,a1,q0);
		b <- rbind(b0,b1,q1);
	}
	r <- 0.6*sqrt(nrow(u));
	plot(0,0,xlim=c(-r,r),ylim=c(-r,r),type="n",xlab="",ylab="");
	arrows(a[,1],a[,2],b[,1],b[,2],length=0,code=3);
}

uni <- function(x) { x/sqrt(sum(x^2)); }

ortog <- function(n)
{
	u <- uni(rnorm(n));
	v <- uni(rnorm(n));
	cbind(uni(u+v),uni(u-v));
}

krychle <- function(n,ind=NULL)
{
	if (is.null(ind)) {
		maluj(ortog(n));
	} else {
		ind2 <- sprintf("%02d",as.integer(ind));
		jmeno <- paste("dim",n,"i",ind2,".png",sep="");
		png(file=jmeno);
		maluj(ortog(n));
		dev.off();
	}
}