/usr/lib/python2.7/dist-packages/woo/tests/volumetric.py is in python-woo 1.0+dfsg1-2.
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# 2013 © Václav Šmilauer <eu@doxos.eu>
import unittest
from minieigen import *
import woo._customConverters
import woo.core
import woo.dem
import woo.fem
import woo.utils
import math
from math import sqrt
from woo.dem import *
class TestVolumetric(unittest.TestCase):
'Volumetric properties'
def testTetraCanon(self):
'Tetra: mass, centrer, inertia of canonical tetrahedron'
# analytical result:
# covariance matrix of canonical tetrahedron -- see
# http://pyffi.sourceforge.net/apidocs/pyffi.utils.inertia-pysrc.html
# http://number-none.com/blow/inertia/bb_inertia.doc
Ca=(1/120.)*Matrix3(2,1,1, 1,2,1, 1,1,2)
Ia=Matrix3.Identity*Ca.trace()-Ca
# numerical result:
A,B,C,D=[Vector3(0,0,0),Vector3(1,0,0),Vector3(0,1,0),Vector3(0,0,1)]
In=woo.comp.tetraInertia(A,B,C,D)
for ix in [(0,0),(0,1),(0,2),(1,0),(1,1),(1,2),(2,0),(2,1),(2,2)]:
self.assertAlmostEqual(Ia[ix],In[ix],delta=1e-9)
# volume
Va=(A-D).dot((B-D).cross(C-D))/6.
Vn=woo.comp.tetraVolume(A,B,C,D)
self.assertAlmostEqual(Va,Vn,delta=1e-9)
#def testTetraGeneric(self):
# 'Tetra: mass, center, inertia of generic tetrahedron'
def testTriCanon(self):
'Triangle: area, inertia of canonical triangle'
# http://en.wikipedia.org/wiki/Inertia_tensor_of_triangle#Covariance_of_a_canonical_triangle
# inertia
Ca=(1/24.)*Matrix3(2,1,0, 1,2,0, 0,0,0)
Ia=Matrix3.Identity*Ca.trace()-Ca
A,B,C=(0,0,0),(1,0,0),(0,1,0)
In=woo.comp.triangleInertia(A,B,C)
for ix in [(0,0),(0,1),(0,2),(1,0),(1,1),(1,2),(2,0),(2,1),(2,2)]:
self.assertAlmostEqual(Ia[ix],In[ix],delta=1e-9)
# area
Aa=.5
An=woo.comp.triangleArea(A,B,C)
self.assertAlmostEqual(Aa,An,delta=1e-9)
def testTetraUnit(self):
'Tetra: principal axes of unit tetrahedron'
vv=[Vector3(1,0,-1/sqrt(2)),Vector3(-1,0,-1/sqrt(2)),Vector3(0,1,1/sqrt(2)),Vector3(0,-1,1/sqrt(2))]
a=2
V=a**3/(6*(sqrt(2)))
Ia=V*a**2/20 # analytical moment of inertia for all axes
# print
for q in [Quaternion.Identity,Quaternion((0,1,0),1),Quaternion((.5,.5,0),3)]:
q.normalize()
vvR=[q*v for v in vv] # add some rotation
#print vvR
#print 'vertices',vvR
#print 'rotation',q
#print 'volume',woo.comp.tetraVolume(*vvR)
#print 'inertia',woo.comp.tetraInertia(*vvR)
p,o,ii=woo.comp.computePrincipalAxes(woo.comp.tetraVolume(*vvR),Vector3.Zero,woo.comp.tetraInertia(*vvR))
for i in 0,1,2: self.assertAlmostEqual(ii[i],Ia,delta=1e-6)
#print q,p,o,ii
## FIXME: always gives unit orientation?!
# check that we yield back the original, aligned with global axes
for i in 0,1,2:
# should yield (some) global axis
ax=o.conjugate()*q*Vector3.Unit(i)
e=Vector3.Unit(i)
#print 'ax',ax
#print 'e',e
#for j in 0,1,2:
# self.assertAlmostEqual(ax[i],e[i],delta=1e-9)
def testTetraGeneric(self):
'Tetra: inertia and principal axes of generic tetrahedron'
# example from
# https://books.google.com/books?id=2b8-79CuIkAC&pg=PA185
vvG=Vector3(0,0,0),Vector3(.2,0,0),Vector3(0,.4,0),Vector3(0,0,.6)
vvC=[vG-.25*(sum(vvG,Vector3.Zero)) for vG in vvG]
dens=60./abs(woo.comp.tetraVolume(*vvC))
# inertia tensor
In=dens*woo.comp.tetraInertia(*vvC)
# book value
Ib=Matrix3(1.17,.06,.09, .06,.9,.18, .09,.18,.45)
for i in (0,1,2):
for j in (0,1,2):
self.assertAlmostEqual(In[i,j],Ib[i,j],delta=1e-9)
# principal axes
pn,on,ii=woo.comp.computePrincipalAxes(abs(woo.comp.tetraVolume(*vvC)),Vector3.Zero,In)
# book values: principal inertia
ib=(1.20592,.93268,.38140)
for i in 0,1,2: self.assertAlmostEqual(ib[i],ii[2-i],delta=1e-4) # book orders decreasing, we order increasing
# book values: principal axes (limited precision)
eeb=[Vector3(.9392,.2908,.1811),Vector3(-.3322,.9023,.2746),Vector3(-.0836,-.3181,.9444)]
# comparison (axes may be arbitrarily ordered and reverse-oriented)
# check dot-product of basis vectors with each other:
# must be perpendicular or parallel, therefore all elements must be (approx) -1,0,1
mm=Matrix3(*eeb)*Matrix3(on*Vector3.UnitX,on*Vector3.UnitY,on*Vector3.UnitZ).transpose()
for i in 0,1,2:
for j in 0,1,2:
if abs(mm[i,j])<.5: self.assertAlmostEqual(mm[i,j],0,delta=1e-3)
else: self.assertAlmostEqual(abs(mm[i,j]),1,delta=1e-3)
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