# === Python v. 3.1 ===
"""
Investigating T,E,K modules with Extended Precision

by Kirby Urner
4D Solutions
Nov 29, 2009

Blog post about:
http://controlroom.blogspot.com/2009/11/back-in-saddle.html
"""

from decimal import Decimal, getcontext
getcontext().prec = 31

# whole numbers
d1,d2,d3,d4,d5,d6 = [Decimal(i) for i in range(1,7)]

# fractions
dthird = d1/d3
dhalf = d1/d2

# surds
droot2 = d2.sqrt()
droot5 = d5.sqrt()

# constants
# http://www.rwgrayprojects.com/synergetics/s09/figs/f86210.html
syn3 = d3/pow(droot2, d3)  # tetravolume:cubevolume
phi = (d1 + droot5)/d2  # golden ratio

# 7.5 to 5.0 vol change = 3rd root 2/3 linear change
scalefactor = pow(d2/d3, d1/d3) 

def tvolume(h):
   # http://www.rwgrayprojects.com/synergetics/s09/figs/f86411a.html
   # http://www.rwgrayprojects.com/synergetics/s09/figs/f86411b.html
   AC, BC, OC = ((h/d2) * (droot5 - d1), (h/d2) * (d3 - droot5), h)
   base = dhalf * (AC * OC)
   return dthird * base * BC

# T module (1/120th of volume 5 rhombic triacontahedron)
h = (phi/droot2) * scalefactor
tvol = tvolume(h)

print(h)
print("T Module")
print("T in tetravolumes: ", tvol * syn3)
print("Rh Triacontrahedron: ", 120 * tvol * syn3)

# E module (1/120th of rhombic triacontahedron with radius 1)
h = d1
evol = tvolume(h)

print("E Module")
print("E in tetravolumes: ", evol * syn3)
print("Rh Triacontrahedron: ", 120 * evol * syn3)

# K module (1/120th of volume 7.5 rhombic triacontahedron)
h = phi/droot2
kvol = tvolume(h)

print("K Module")
print("K in tetravolumes: ", kvol * syn3)
print("Rh Triacontrahedron: ", 120 * kvol * syn3)

from turtle import Screen, Turtle
from random import randint
from math import sqrt

def planeNet(h = 500.0):              
   # http://www.rwgrayprojects.com/synergetics/s09/figs/f86411a.html
   # http://www.rwgrayprojects.com/synergetics/s09/figs/f86411b.html
   s = Screen(); s.setup(560,560); s.title("Plane Net for T-module")
   s.tracer(True)

   writer = Turtle(visible=True, shape="turtle")
   writer.penup(); writer.goto(-245, -245); writer.pendown()
   writer.color("Black","")

   for i in range(4):
      # square of edge h
      writer.forward(h); writer.left(90)

   writer.left(31.717); writer.forward(sqrt( (5 - sqrt(5))/2) * h)
   writer.left(2 * 58.283); writer.forward(sqrt(5-2*sqrt(5)) * h)
   writer.left(31.717 + 69.095)
   writer.forward(sqrt((9 - 3*sqrt(5))/2) * h)

def optional():   # bonus feature
   planeNet()
   
optional()