"""
Page 94 3v Icosa Alternate
"The Dome Builder's Handbook"
John Prenis, 1973

Kirby messing around with Trevor at
Fine Grind, see blog:
http://mybizmo.blogspot.com/2008/11/geeking-out.html

"""

from rbf import Icosa
import math

o = Icosa()
o.volume = 0
o.radius = o.vertices['X1'].mag
newo = (1/o.radius) * o
newradius = newo.vertices['X1'].mag

print "New Icosa radius = ", newradius

X1U1 = newo.vertices['U1'] - newo.vertices['X1']
X1Q1 = newo.vertices['Q1'] - newo.vertices['X1']

u = (1./3) * X1U1
a1 = newo.vertices['X1'] + u

print "flat a1 radius = ", a1.mag
aradius = a1.mag
a1sph = (1/aradius) * a1
print "Spherical a1 = ", a1sph.mag

u = (1./3) * X1Q1
a2 = newo.vertices['X1'] + u
a2sph = (1/aradius) * a2
print "Spherical a2 = ", a2sph.mag

A = newo.vertices['X1'] - a1sph
print "A length = ", A.mag

B = a1sph - a2sph
print "B length = ", B.mag

a3 = (1/3.) * (newo.vertices['X1'] + newo.vertices['U1'] + newo.vertices['Q1'])

a3radius = a3.mag
a3sph = (1/a3radius) * a3

C = a1sph - a3sph

print "C length = ", C.mag

e1 = a1sph - newo.vertices['X1']
e2 = a2sph - newo.vertices['X1']

e3 = a3sph - a1sph
e4 = a3sph - a2sph

print e1.mag
print e2.mag

print "Angle AA = ", math.degrees(e1.diff_angle(e2))
print "Angle CC = ", math.degrees(e3.diff_angle(e4)) 

"""
Figure the other angles using the fact that
they're isoceles and angles add to 180
"""