from math import pi,acos,asin,sin,e
from PADS.CirclePack import flower,acxyz
from SVG import SVG,colors
import sys

G = {0: [1,4,8,3,11,5,9],
     1: [0,9,10,2,6,4],
     2: [1,10,3,8,7,6],
     3: [0,8,2,10,11],
     4: [0,1,6,5,8],
     5: [0,11,8,4,6,9],
     6: [1,2,7,10,9,5,4],
     7: [2,8,11,10,6],
     8: [0,4,5,11,7,2,3],
     9: [0,5,6,10,1],
     10: [1,9,6,7,11,3,2],
     11: [0,3,10,7,8,5]}

internal = range(1,12)

tolerance = 1+10e-12    # how accurately to approximate things
radii = {i:1 for i in G}

# The main iteration for finding the correct set of radii
lastChange = 2
while lastChange > tolerance:
    lastChange = 1
    for k in internal:
        theta = flower(radii,k,G[k])
        hat = radii[k]/(1/sin(theta/(2*len(G[k])))-1)
        newrad = hat * (1/(sin(pi/len(G[k]))) - 1)
        kc = max(newrad/radii[k],radii[k]/newrad)
        lastChange = max(lastChange,kc)
        radii[k] = newrad

placements = {0:0, 1:radii[0]+radii[1]}
def place(p,q,r):
    theta = acxyz(radii[p],radii[q],radii[r])
    offset = (placements[q]-placements[p])/(radii[q]+radii[p])
    offset *= e**(-1j*theta)
    return placements[p] + offset*(radii[r]+radii[p])

for p,q,r in [[1,0,4],[1,4,6],[1,6,2],[6,4,5],[6,5,9],[2,6,7],[7,6,10],[2,7,8],[8,7,11],[11,10,3]]:
    placements[r] = place(p,q,r)

Y = place(9,5,0)
X = place(11,3,0)-Y

svg = SVG(480+360j,sys.stdout)
scale = 32
reps = 4

mid = (placements[1]+placements[2])/2+X+2*Y
ctr = 240+180j
def enscale(p):
    return (p-mid)*scale+ctr

def encircle(i):
    for j in range(reps):
        for k in range(reps):
            svg.circle(enscale(placements[i]+j*X+k*Y),radii[i]*scale)

svg.group(stroke=colors.black)
svg.group(fill=colors.blue)
for i in [0,6,8,10]:
    encircle(i)
svg.ungroup()
svg.group(fill=colors.yellow)
for i in [1,2,5,11]:
    encircle(i)
svg.ungroup()
svg.group(fill=colors.red)
for i in [3,4,7,9]:
    encircle(i)
svg.ungroup()
svg.ungroup()
svg.close()