def test_e_module(self):
e0 = D
e1 = rt2(3) * PHI**-1
e2 = rt2((5 - root5) / 2)
e3 = (3 - root5) / 2
e4 = rt2(5 - 2 * root5)
e5 = 1 / PHI
tet = Tetrahedron(e0, e1, e2, e3, e4, e5)
self.assertTrue(1 / 23 > tet.ivm_volume() / 8 > 1 / 24, "Wrong E-mod")
def test_equilateral(self):
t = Triangle((0, 0), (10, 0), (5, 5 * rt2(3)))
t.in_radians = False
self.assertAlmostEqual(t.ABC, 60)
self.assertAlmostEqual(t.BAC, 60)
self.assertAlmostEqual(t.ACB, 60)
self.assertTrue(t.is_equiangular)
def area(self):
"""
Heron's formula
"""
s = (self.a + self.b + self.c) / 2
return rt2(s * (s - self.a) * (s - self.b) *
(s - self.c)) # Heron's formula
def xyz_area(self):
"""
Heron's Formula, without the 1/4
"""
a,b,c = self.a, self.b, self.c
xyzarea = rt2((a+b+c)* (-a+b+c) * (a-b+c) * (a+b-c))
return xyzarea
def volumes():
book = TetraBook()
book.radians = False
print("ALT IVM XYZ Long Short AngleL AngleS")
for vol in [rt2(x) / rt2_8 for x in range(0, 10)]:
book.ivm_volume = vol
xyzvol = (1 / 3) * xyz_base * book.altitude
# fancy volume formula jibes with simple (1/3 base * height)
try:
assert abs(book.xyz_volume - xyzvol) < 0.0001
except AssertionError:
print("Error: ", "{:7.5f} {:7.5f}".format(book.xyz_volume,
xyzvol))
print("{:7.5f} {:7.5f} {:7.5f} {:7.5f} {:7.5f} {:9.5f} {:9.5f}".format(
book.altitude, book.ivm_volume, book.xyz_volume, book.long_edge,
book.short_edge, book.angle_l, book.angle_s))
def test_ivm(self):
t = Triangle((-1, 0), (1, 0), (0, rt2(3))) # book cover
self.assertAlmostEqual(t.ivm_area, 1.0)
def ivm_area(self):
return self.area / rt2(3)
"""
Euler volume, modified by Gerald de Jong
http://www.grunch.net/synergetics/quadvols.html
Kirby Urner (c) MIT License
See:
http://mathforum.org/kb/thread.jspa?threadID=2836546
for explanation of quadrays, used for some unit tests
"""
from math import sqrt as rt2
from qrays import Qvector, Vector
import sys
S3 = pow(9 / 8, 0.5)
root2 = rt2(2)
root5 = rt2(5)
class Tetrahedron:
"""
Takes six edges of tetrahedron with faces
(a,b,d)(b,c,e)(c,a,f)(d,e,f) -- returns volume
if ivm and xyz
"""
def __init__(self, a, b, c, d, e, f):
# a,b,c,d,e,f = [Decimal(i) for i in (a,b,c,d,e,f)]
self.a, self.a2 = a, a**2
self.b, self.b2 = b, b**2
self.c, self.c2 = c, c**2
self.d, self.d2 = d, d**2
def c(self):
Ax, Ay = self._Axy
Bx, By = self._Bxy
return rt2((Ax - Bx)**2 + (Ay - By)**2)
def test_area_martian3(self):
qx = Vector((D,0,0)).quadray()
qy = Vector((R,rt2(3)/2,0)).quadray()
result = qx.area(qy)
self.assertAlmostEqual(result, 1, 7)
def ivm_area(self):
ivmarea = self.xyz_area() * 1/rt2(3)
return ivmarea
def _short(self):
return rt2(6 - (rt2(12) * rt2(3 - self._altitude**2)))
def _long(self):
return rt2(6 + (rt2(12) * rt2(3 - self._altitude**2)))
def short_edge(self, value):
self._short_edge = value
self._long_edge = rt2(long_diag**2 - self._short_edge**2)
self._altitude = self.xyz_volume * rt2_3
def a(self):
Bx, By = self._Bxy
Cx, Cy = self._Cxy
return rt2((Bx - Cx)**2 + (By - Cy)**2)
def b(self):
Ax, Ay = self._Axy
Cx, Cy = self._Cxy
return rt2((Ax - Cx)**2 + (Ay - Cy)**2)
def test_area_earthling2(self):
vx = Vector((2,0,0))
vy = Vector((1,rt2(3),0))
result = vx.area(vy)
self.assertAlmostEqual(result, 2*rt2(3))
Kirby Urner (c) MIT License
See:
http://mathforum.org/kb/thread.jspa?threadID=2836546
for explanation of quadrays, used for some unit tests
"""
from math import sqrt as rt2
from qrays import Qvector, Vector
import sys
R = 0.5
D = 1.0
S3 = pow(9 / 8, 0.5)
root2 = rt2(2)
root3 = rt2(3)
root5 = rt2(5)
root6 = rt2(6)
PHI = (1 + root5) / 2.0
class Tetrahedron:
"""
Takes six edges of tetrahedron with faces
(a,b,d)(b,c,e)(c,a,f)(d,e,f) -- returns volume
if ivm and xyz
"""
def __init__(self, a, b, c, d, e, f):
# a,b,c,d,e,f = [Decimal(i) for i in (a,b,c,d,e,f)]
self.a, self.a2 = a, a**2
def test_xyz_area3(self):
tri = Triangle(D, D, D)
self.assertEqual(tri.xyz_area(), rt2(3))
"Amod",
"Bmod",
"Smod3",
"Smod",
"smod3"], dtype=np.unicode),
name="Shapes")
zeros = pd.Series(np.zeros((21,)), dtype=np.float64)
volumes_table = pd.DataFrame({"Volumes" : zeros,
"Comments": pd.Series(['']*21,
dtype=np.unicode)
})
volumes_table.index = shapes
#%%
φ = (rt2(5)+1)/2 # golden ratio
S3 = rt2(9/8) # not to be confused with Smod
Smod = (φ **-5)/2 # home base Smod
smod3 = Smod * φ**-3 # small s, phi down
Smod3 = Smod * φ**3 # capital s, phi up
Smod6 = Smod3 * φ**3 # phi up yet again
cubocta = 20
SuperRT = S3 * cubocta
Octa = 4
Emod3 = SuperRT / 120 # Emod phi up
Emod = (rt2(2)/8) * (φ ** -3) # home base Emod
emod3 = Emod * φ ** -3 # Emod phi down
# -*- coding: utf-8 -*-
"""
Created on Fri Feb 17 21:41:28 2017
@author: kurner
"""
from math import sqrt as rt2, asin, sin, pi, degrees, radians
from tetravolume import Tetrahedron
# CONSTANTS
phi = (1 + rt2(5)) / 2
rt2_3 = rt2(3)
long_diag = 2 * rt2_3 # cover tip to cover tip, diagonal of rhomb
rt2_8 = rt2(8)
rt2_9 = rt2(9) # = 3
rt2_6 = rt2(6) # cover tip to page tip, page vertical
Syn3 = rt2(9 / 8) # synergetics constant (to 3rd power)
xyz_base = rt2_3
class TetraBook:
radians = True
def __init__(self, L=long_diag):
self.long_edge = L
@property
def long_edge(self):
return self._long_edge
