Source code for woo.tests.volumetric

# encoding: utf-8
# 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 *

[docs]class TestVolumetric(unittest.TestCase): 'Volumetric properties'
[docs] 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'
[docs] 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)
[docs] 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)
[docs] 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)