#! /bin/awk -f
#
# 2004 Steven Gustafson smg@cs.nott.ac.uk
#
# Description: awk script to generate lattice points, placing a
# 1 after the x,y pair to indicate that a node is present at that location.
#
# Inputs: Output from list2lattice.awk program 
# Additionally: must make sure DEPTH is set correctly below.
# Outputs: input into dfs.awk

BEGIN{RS= "\n"}; BEGIN{FS= " "}
{
array[NR]=$1
}

END{

	DEPTH=10 # maximum depth of tree 

	PI=3.14269

	points=0 # number of points at this depth
	x=0
	y=0
	angle=0 # 360/points, our angle

	nodes=0

	#calculate up to DEPTH 
	for(depth=0;depth<=DEPTH;depth++)
	{
		points = 2 ** depth #each depth has 2^d points
		angle = (2*PI)/points
	
		#i is our radius 
		for(p=1;p<=points;p=p+2)
		{
			if(!(depth==1 && p==1))
			{		
				x = depth * sin(p*(angle));
				y = depth * cos(p*(angle));
			
				if (nodes >= NR)	
					print -x, y, "0"	
				else 	
					print -x, y, array[++nodes]	
			}			
		}
	}	
}