def testUserCreatedInteraction(self):
		O.engines=[
				ForceResetter(),
				InsertionSortCollider([Bo1_Sphere_Aabb(),Bo1_Facet_Aabb(),Bo1_Box_Aabb()],label="collider"),
				InteractionLoop(
					[Ig2_Sphere_Sphere_ScGeom(),Ig2_Facet_Sphere_ScGeom(),Ig2_Box_Sphere_ScGeom()],
					[Ip2_FrictMat_FrictMat_FrictPhys()],	#for linear model only
					[Law2_ScGeom_FrictPhys_CundallStrack(label="law")],	#for linear model only
					label="interactionLoop"
				),
				GlobalStiffnessTimeStepper(timeStepUpdateInterval=10,label="timeStepper"),
				NewtonIntegrator(label="newton")
			]
		O.bodies.append([utils.sphere((0,0,0),0.5),
			utils.sphere((2,0,0),0.5), #(0,1) no overlap , no contacts
			utils.sphere((0.9,0.9,0),0.5), #(0,2) overlapping bounds, no contacts
			utils.sphere((-0.99,0,0),0.5)]) #(0,3) overlaping + contact
		O.dt=0
		O.dynDt=False
		O.step()
		i=utils.createInteraction(0,1)
		self.assert_(i.iterBorn==1 and i.iterMadeReal==1)
		j=utils.createInteraction(0,2)
		self.assert_(j.iterBorn==1 and j.iterMadeReal==1)
		self.assertRaises(RuntimeError,lambda: utils.createInteraction(0,3))

	def testErasedAndNewlyCreatedSphere(self):
		"Bodies: The bug is described in LP:1001194. If the new body was created after deletion of previous, it has no bounding box"
		O.reset()
		id1 = O.bodies.append(utils.sphere([0.0, 0.0, 0.0],0.5))
		id2 = O.bodies.append(utils.sphere([0.0, 2.0, 0.0],0.5))
		O.engines=[
			ForceResetter(),
			InsertionSortCollider([Bo1_Sphere_Aabb()]),
			InteractionLoop(
				[Ig2_Sphere_Sphere_L3Geom()],
				[Ip2_FrictMat_FrictMat_FrictPhys()],
				[Law2_L3Geom_FrictPhys_ElPerfPl()]
			),
			NewtonIntegrator(damping=0.1,gravity=(0,0,-9.81))
		]
		O.dt=.5e-4*utils.PWaveTimeStep()
		#Before first step the bodies should not have bounds
		self.assert_(O.bodies[id1].bound==None and O.bodies[id2].bound==None)
		O.run(1, True)
		#After first step the bodies should have bounds
		self.assert_(O.bodies[id1].bound!=None and O.bodies[id2].bound!=None)
		#Add 3rd body
		id3 = O.bodies.append(utils.sphere([0.0, 4.0, 0.0],0.5))
		O.run(1, True)
		self.assert_(O.bodies[id1].bound!=None and O.bodies[id2].bound!=None and O.bodies[id3].bound!=None)
		#Remove 3rd body
		O.bodies.erase(id3)
		O.run(1, True)
		#Add 4th body
		id4 = O.bodies.append(utils.sphere([0.0, 6.0, 0.0],0.5))
		O.run(1, True)
		self.assert_(O.bodies[id1].bound!=None and O.bodies[id2].bound!=None and O.bodies[id4].bound!=None)

 def SpherePack_toSimulation(self,rot=Matrix3.Identity,**kw):
   """Append spheres directly to the simulation. In addition calling :yref:`O.bodies.append<BodyContainer.append>`,
 this method also appropriately sets periodic cell information of the simulation.
 
   >>> from yade import pack; from math import *
   >>> sp=pack.SpherePack()
 
 Create random periodic packing with 20 spheres:
 
   >>> sp.makeCloud((0,0,0),(5,5,5),rMean=.5,rRelFuzz=.5,periodic=True,num=20)
   20
 
 Virgin simulation is aperiodic:
 
   >>> O.reset()
   >>> O.periodic
   False
 
 Add generated packing to the simulation, rotated by 45° along +z
 
   >>> sp.toSimulation(rot=Quaternion((0,0,1),pi/4),color=(0,0,1))
   [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
 
 Periodic properties are transferred to the simulation correctly, including rotation (this could be avoided by explicitly passing "hSize=O.cell.hSize" as an argument):
 
   >>> O.periodic
   True
   >>> O.cell.refSize
   Vector3(5,5,5)
   >>> O.cell.hSize
   Matrix3(3.53553,-3.53553,0, 3.53553,3.53553,0, 0,0,5)
 
 The current state (even if rotated) is taken as mechanically undeformed, i.e. with identity transformation:
 
   >>> O.cell.trsf
   Matrix3(1,0,0, 0,1,0, 0,0,1)
 
 :param Quaternion/Matrix3 rot: rotation of the packing, which will be applied on spheres and will be used to set :yref:`Cell.trsf` as well.
 :param \*\*kw: passed to :yref:`yade.utils.sphere`
 :return: list of body ids added (like :yref:`O.bodies.append<BodyContainer.append>`)
 """
   if isinstance(rot,Quaternion): rot=rot.toRotationMatrix()
   assert(isinstance(rot,Matrix3))
   if self.isPeriodic: O.periodic=True
   if self.cellSize!=Vector3.Zero and self.isPeriodic:
     O.cell.hSize=rot*Matrix3(self.cellSize[0],0,0, 0,self.cellSize[1],0, 0,0,self.cellSize[2])
     O.cell.trsf=Matrix3.Identity
   if not self.hasClumps():
     return O.bodies.append([utils.sphere(rot*c,r,**kw) for c,r in self])
   else:
     standalone,clumps=self.getClumps()
     ids=O.bodies.append([utils.sphere(rot*c,r,**kw) for c,r in self]) # append all spheres first
     clumpIds=[]
     userColor='color' in kw
     for clump in clumps:
       clumpIds.append(O.bodies.clump(clump)) # clump spheres with given ids together, creating the clump object as well
       # make all spheres within one clump a single color, unless color was specified by the user
       if not userColor:
         for i in clump[1:]: O.bodies[i].shape.color=O.bodies[clump[0]].shape.color
     return ids+clumpIds

	def setUp(self):
		O.reset()
		r1,r2,p0,p1=1,.5,Vector3.Zero,Vector3(0,0,3)
		self.idC,(self.id1,self.id2)=O.bodies.appendClumped([
			utils.sphere(p0,r1),
			utils.sphere(p1,r2)
		])

	def setUp(self):
		# common setup for all tests in this class
		O.reset()
		O.materials.append([
			FrictMat(young=1,label='materialZero'),
			ElastMat(young=100,label='materialOne')
		])
		O.bodies.append([
			utils.sphere([0,0,0],.5,material=0),
			utils.sphere([1,1,1],.5,material=0),
			utils.sphere([1,1,1],.5,material=1)
		])

	def setUp(self):
		O.reset(); O.periodic=True;
		O.cell.setBox(2.5,2.5,3)
		self.cellDist=Vector3i(0,0,10) # how many cells away we go
		self.relDist=Vector3(0,.999999999999999999,0) # rel position of the 2nd ball within the cell
		self.initVel=Vector3(0,0,5)
		O.bodies.append(utils.sphere((1,1,1),.5))
		self.initPos=Vector3([O.bodies[0].state.pos[i]+self.relDist[i]+self.cellDist[i]*O.cell.refSize[i] for i in (0,1,2)])
		O.bodies.append(utils.sphere(self.initPos,.5))
		#print O.bodies[1].state.pos
		O.bodies[1].state.vel=self.initVel
		O.engines=[NewtonIntegrator(warnNoForceReset=False)]
		O.cell.velGrad=Matrix3(0,0,0, 0,0,0, 0,0,-1)
		O.dt=0 # do not change positions with dt=0 in NewtonIntegrator, but still update velocities from velGrad

def gengeo(mntable,shift=Vector3.Zero,scale=1.0,**kw):
	""" Imports geometry from LSMGenGeo library and creates spheres.
	Since 2012 the package is available in Debian/Ubuntu and known as python-demgengeo
	http://packages.qa.debian.org/p/python-demgengeo.html

	:Parameters:
		`mntable`: mntable
			object, which creates by LSMGenGeo library, see example
		`shift`: [float,float,float]
			[X,Y,Z] parameter moves the specimen.
		`scale`: float
			factor scales the given data.
		`**kw`: (unused keyword arguments)
				is passed to :yref:`yade.utils.sphere`
	
	LSMGenGeo library allows one to create pack of spheres
	with given [Rmin:Rmax] with null stress inside the specimen.
	Can be useful for Mining Rock simulation.
	
	Example: :ysrc:`examples/packs/packs.py`, usage of LSMGenGeo library in :ysrc:`examples/test/genCylLSM.py`.
	
	* https://answers.launchpad.net/esys-particle/+faq/877
	* http://www.access.edu.au/lsmgengeo_python_doc/current/pythonapi/html/GenGeo-module.html
	* https://svn.esscc.uq.edu.au/svn/esys3/lsm/contrib/LSMGenGeo/"""
	try:
		from GenGeo import MNTable3D,Sphere
	except ImportError:
		from gengeo import MNTable3D,Sphere
	ret=[]
	sphereList=mntable.getSphereListFromGroup(0)
	for i in range(0, len(sphereList)):
		r=sphereList[i].Radius()
		c=sphereList[i].Centre()
		ret.append(utils.sphere([shift[0]+scale*float(c.X()),shift[1]+scale*float(c.Y()),shift[2]+scale*float(c.Z())],scale*float(r),**kw))
	return ret

def filterSpherePack(predicate, spherePack, returnSpherePack=None, **kw):
    """Using given SpherePack instance, return spheres the satisfy predicate.
	The packing will be recentered to match the predicate and warning is given if the predicate
	is larger than the packing."""
    if returnSpherePack == None:
        warnings.warn(
            'The default behavior will change; specify returnSpherePack=True for the new behavior, and False to get rid of this warning (your code will break in the future, however). The returned SpherePack object can be added to the simulation using SpherePack.toSimulation()',
            category=FutureWarning)
        returnSpherePack = False
    mn, mx = predicate.aabb()
    dimP, centP = predicate.dim(), predicate.center()
    dimS, centS = spherePack.dim(), spherePack.center()
    if dimP[0] > dimS[0] or dimP[1] > dimS[1] or dimP[2] > dimS[2]:
        warnings.warn(
            "Packing's dimension (%s) doesn't fully contain dimension of the predicate (%s)."
            % (dimS, dimP))
    spherePack.translate(centP - centS)
    if returnSpherePack:
        ret = SpherePack()
        for c, r in spherePack:
            if predicate(c, r): ret.add(c, r)
        return ret
    else:
        # return particles to be added to O.bodies
        ret = []
        for s in spherePack:
            if predicate(s[0], s[1]):
                ret += [utils.sphere(s[0], radius=s[1], **kw)]
        return ret

def regularHexa(predicate, radius, gap, **kw):
    """Return set of spheres in regular hexagonal grid, clipped inside solid given by predicate.
	Created spheres will have given radius and will be separated by gap space."""
    ret = []
    a = 2 * radius + gap
    # thanks to Nasibeh Moradi for finding bug here:
    # http://www.mail-archive.com/[email protected]/msg01424.html
    hy, hz = a * sqrt(3) / 2., a * sqrt(6) / 3.
    mn, mx = predicate.aabb()
    dim = [mx[i] - mn[i] for i in 0, 1, 2]
    if (max(dim) == float('inf')):
        raise ValueError(
            "Aabb of the predicate must not be infinite (didn't you use union | instead of intersection & for unbounded predicate such as notInNotch?"
        )
    ii, jj, kk = [
        range(0,
              int(dim[0] / a) + 1),
        range(0,
              int(dim[1] / hy) + 1),
        range(0,
              int(dim[2] / hz) + 1)
    ]
    for i, j, k in itertools.product(ii, jj, kk):
        x, y, z = mn[0] + radius + i * a, mn[1] + radius + j * hy, mn[
            2] + radius + k * hz
        if j % 2 == 0: x += a / 2. if k % 2 == 0 else -a / 2.
        if k % 2 != 0:
            x += a / 2.
            y += hy / 2.
        if predicate((x, y, z), radius):
            ret += [utils.sphere((x, y, z), radius=radius, **kw)]
    return ret

def randomPeriPack(radius,initSize,rRelFuzz=0.0,memoizeDb=None,noPrint=False):
	"""Generate periodic dense packing.

	A cell of initSize is stuffed with as many spheres as possible, then we run periodic compression with PeriIsoCompressor, just like with
	randomDensePack.

	:param radius: mean sphere radius
	:param rRelFuzz: relative fuzz of sphere radius (equal distribution); see the same param for randomDensePack.
	:param initSize: initial size of the periodic cell.

	:return: SpherePack object, which also contains periodicity information.
	"""
	from math import pi
	sp=_getMemoizedPacking(memoizeDb,radius,rRelFuzz,initSize[0],initSize[1],initSize[2],fullDim=Vector3(0,0,0),wantPeri=True,fillPeriodic=False,spheresInCell=-1,memoDbg=True,noPrint=noPrint)
	if sp: return sp
	O.switchScene(); O.resetThisScene()
	sp=SpherePack()
	O.periodic=True
	#O.cell.refSize=initSize
	O.cell.setBox(initSize)
	sp.makeCloud(Vector3().Zero,O.cell.refSize,radius,rRelFuzz,-1,True)
	O.engines=[ForceResetter(),InsertionSortCollider([Bo1_Sphere_Aabb()],nBins=2,verletDist=.05*radius),InteractionLoop([Ig2_Sphere_Sphere_ScGeom()],[Ip2_FrictMat_FrictMat_FrictPhys()],[Law2_ScGeom_FrictPhys_CundallStrack()]),PeriIsoCompressor(charLen=2*radius,stresses=[-100e9,-1e8],maxUnbalanced=1e-2,doneHook='O.pause();',globalUpdateInt=20,keepProportions=True),NewtonIntegrator(damping=.8)]
	O.materials.append(FrictMat(young=30e9,frictionAngle=.1,poisson=.3,density=1e3))
	for s in sp: O.bodies.append(utils.sphere(s[0],s[1]))
	O.dt=utils.PWaveTimeStep()
	O.timingEnabled=True
	O.run(); O.wait()
	ret=SpherePack()
	ret.fromSimulation()
	_memoizePacking(memoizeDb,ret,radius,rRelFuzz,wantPeri=True,fullDim=Vector3(0,0,0),noPrint=noPrint) # fullDim unused
	O.switchScene()
	return ret

	def testEraseBodiesInInteraction(self):
		O.reset()
		id1 = O.bodies.append(utils.sphere([0.5,0.5,0.0+0.095],.1))
		id2 = O.bodies.append(utils.sphere([0.5,0.5,0.0+0.250],.1))
		O.engines=[
			ForceResetter(),
			InsertionSortCollider([Bo1_Sphere_Aabb()]),
			InteractionLoop(
				[Ig2_Sphere_Sphere_L3Geom()],
				[Ip2_FrictMat_FrictMat_FrictPhys()],
				[Law2_L3Geom_FrictPhys_ElPerfPl()]
			),
			NewtonIntegrator(damping=0.1,gravity=(0,0,-9.81))
		]
		O.dt=.5e-4*utils.PWaveTimeStep()
		O.step()
		O.bodies.erase(id1)
		O.step()

def textExt(fileName,format='x_y_z_r',shift=Vector3.Zero,scale=1.0,attrs=[],**kw):
	"""Load sphere coordinates from file in specific format, returns a list of corresponding bodies; that may be inserted to the simulation with O.bodies.append().
	
	:param str filename: file name
	:param str format: the name of output format. Supported `x_y_z_r`(default), `x_y_z_r_matId`, 'x_y_z_r_attrs'
	:param [float,float,float] shift: [X,Y,Z] parameter moves the specimen.
	:param float scale: factor scales the given data.
	:param list attrs: attrs read from file if export.textExt(format='x_y_z_r_attrs') were used ('passed by refernece' style)
	:param \*\*kw: (unused keyword arguments) is passed to :yref:`yade.utils.sphere`
	:returns: list of spheres.

	Lines starting with # are skipped
	"""
	infile = open(fileName,"r")
	lines = infile.readlines()
	infile.close()
	ret=[]
	for line in lines:
		data = line.split()
		if (data[0] == "#format"):
			format=data[1]
			continue
		elif (data[0][0] == "#"): continue
		
		if (format=='x_y_z_r'):
			pos = Vector3(float(data[0]),float(data[1]),float(data[2]))
			ret.append(utils.sphere(shift+scale*pos,scale*float(data[3]),**kw))
		elif (format=='x_y_z_r_matId'):
			pos = Vector3(float(data[0]),float(data[1]),float(data[2]))
			ret.append(utils.sphere(shift+scale*pos,scale*float(data[3]),material=int(data[4]),**kw))
		
		elif (format=='id_x_y_z_r_matId'):
			pos = Vector3(float(data[1]),float(data[2]),float(data[3]))
			ret.append(utils.sphere(shift+scale*pos,scale*float(data[4]),material=int(data[5]),**kw))

		elif (format=='x_y_z_r_attrs'):
			pos = Vector3(float(data[0]),float(data[1]),float(data[2]))
			s = utils.sphere(shift+scale*pos,scale*float(data[3]),**kw)
			ret.append(s)
			attrs.append(data[4:])
			
		else:
			raise RuntimeError("Please, specify a correct format output!");
	return ret

def regularOrtho(predicate,radius,gap,**kw):
	"""Return set of spheres in regular orthogonal grid, clipped inside solid given by predicate.
	Created spheres will have given radius and will be separated by gap space."""
	ret=[]
	mn,mx=predicate.aabb()
	if(max([mx[i]-mn[i] for i in 0,1,2])==float('inf')): raise ValueError("Aabb of the predicate must not be infinite (didn't you use union | instead of intersection & for unbounded predicate such as notInNotch?");
	xx,yy,zz=[arange(mn[i]+radius,mx[i]-radius,2*radius+gap) for i in 0,1,2]
	for xyz in itertools.product(xx,yy,zz):
		if predicate(xyz,radius): ret+=[utils.sphere(xyz,radius=radius,**kw)]
	return ret

def textClumps(fileName,shift=Vector3.Zero,discretization=0,orientation=Quaternion((0,1,0),0.0),scale=1.0,**kw):
	"""Load clumps-members from file, insert them to the simulation.
	
	:param str filename: file name
	:param str format: the name of output format. Supported `x_y_z_r`(default), `x_y_z_r_clumpId`
	:param [float,float,float] shift: [X,Y,Z] parameter moves the specimen.
	:param float scale: factor scales the given data.
	:param \*\*kw: (unused keyword arguments) is passed to :yref:`yade.utils.sphere`
	:returns: list of spheres.

	Lines starting with # are skipped
	"""
	infile = open(fileName,"r")
	lines = infile.readlines()
	infile.close()
	ret=[]
	
	curClump=[]
	newClumpId = -1
	
	for line in lines:
		data = line.split()
		if (data[0][0] == "#"): continue
		pos = orientation*Vector3(float(data[0]),float(data[1]),float(data[2]))
	
		if (newClumpId<0 or newClumpId==int(data[4])):
			idD = curClump.append(utils.sphere(shift+scale*pos,scale*float(data[3]),**kw))
			newClumpId = int(data[4])
		else:
			newClumpId = int(data[4])
			ret.append(O.bodies.appendClumped(curClump,discretization=discretization))
			curClump=[]
			idD = curClump.append(utils.sphere(shift+scale*pos,scale*float(data[3]),**kw))
	
	if (len(curClump)<>0):
		ret.append(O.bodies.appendClumped(curClump,discretization=discretization))
	
	# Set the mask to a clump the same as the first member of it
	for i in range(len(ret)):
		O.bodies[ret[i][0]].mask = O.bodies[ret[i][1][0]].mask
	return ret

def textExt(fileName,format='x_y_z_r',shift=Vector3.Zero,scale=1.0,**kw):
	"""Load sphere coordinates from file in specific format, create spheres, insert them to the simulation.
	
	:Parameters:
		`filename`: string
		`format`:
			the name of output format. Supported `x_y_z_r`(default), `x_y_z_r_matId`
		`shift`: [float,float,float]
			[X,Y,Z] parameter moves the specimen.
		`scale`: float
			factor scales the given data.
		`**kw`: (unused keyword arguments)
				is passed to :yref:`yade.utils.sphere`
	:Returns: list of spheres.
	Lines starting with # are skipped
	"""
	infile = open(fileName,"r")
	lines = infile.readlines()
	infile.close()
	ret=[]
	for line in lines:
		data = line.split()
		if (data[0] == "#format"):
			format=data[1]
			continue
		elif (data[0][0] == "#"): continue
		
		if (format=='x_y_z_r'):
			pos = Vector3(float(data[0]),float(data[1]),float(data[2]))
			ret.append(utils.sphere(shift+scale*pos,scale*float(data[3]),**kw))
		elif (format=='x_y_z_r_matId'):
			pos = Vector3(float(data[0]),float(data[1]),float(data[2]))
			ret.append(utils.sphere(shift+scale*pos,scale*float(data[3]),material=int(data[4]),**kw))
		
		elif (format=='id_x_y_z_r_matId'):
			pos = Vector3(float(data[1]),float(data[2]),float(data[3]))
			ret.append(utils.sphere(shift+scale*pos,scale*float(data[4]),material=int(data[5]),**kw))
			
		else:
			raise RuntimeError("Please, specify a correct format output!");
	return ret

def fill_cylinder_with_spheres(sphereRadius,cylinderRadius,cylinderHeight,cylinderOrigin,cylinderSlope):
	spheresCount=0
	for h in xrange(0,int(cylinderHeight/sphereRadius/2)):
			for r in xrange(1,int(cylinderRadius/sphereRadius/2)):
				dfi = asin(0.5/r)*2
				for a in xrange(0,int(6.28/dfi)):
					x = cylinderOrigin[0]+2*r*sphereRadius*cos(dfi*a)
					y = cylinderOrigin[1]+2*r*sphereRadius*sin(dfi*a)
					z = cylinderOrigin[2]+h*2*sphereRadius
					s=utils.sphere([x,y*cos(cylinderSlope)+z*sin(cylinderSlope),z*cos(cylinderSlope)-y*sin(cylinderSlope)],sphereRadius)
					O.bodies.append(s)
					spheresCount+=1
	return spheresCount

def regularHexa(predicate,radius,gap,**kw):
	"""Return set of spheres in regular hexagonal grid, clipped inside solid given by predicate.
	Created spheres will have given radius and will be separated by gap space."""
	ret=[]
	a=2*radius+gap
	hy,hz=a*sqrt(3)/2.,a*sqrt(6)/3.
	mn,mx=predicate.aabb()
	dim=[mx[i]-mn[i] for i in 0,1,2]
	if(max(dim)==float('inf')): raise ValueError("Aabb of the predicate must not be infinite (didn't you use union | instead of intersection & for unbounded predicate such as notInNotch?");
	ii,jj,kk=[range(0,int(dim[0]/a)+1),range(0,int(dim[1]/hy)+1),range(0,int(dim[2]/hz)+1)]
	for i,j,k in itertools.product(ii,jj,kk):
		#Simple HCP-lattice packing
		#http://en.wikipedia.org/wiki/Close-packing_of_equal_spheres#Simple_hcp_lattice
		coordSph = Vector3((2*i + ((j + k) % 2 ) ),
											(sqrt(3.)*(j + 1./3.*(k % 2))),
											(2.*sqrt(6.)/3.*k))*(a/2.0) + mn
		if predicate(coordSph,radius): ret+=[utils.sphere(coordSph,radius=radius,**kw)]
	if (len(ret)==0):
		warnings.warn('No spheres are produced by regularHexa-function',category=RuntimeWarning)
	return ret

def gengeoFile(fileName="file.geo",shift=Vector3.Zero,scale=1.0,orientation=Quaternion((0,1,0),0.0),**kw):
	""" Imports geometry from LSMGenGeo .geo file and creates spheres. 
	Since 2012 the package is available in Debian/Ubuntu and known as python-demgengeo
	http://packages.qa.debian.org/p/python-demgengeo.html
	
	:Parameters:
		`filename`: string
			file which has 4 colums [x, y, z, radius].
		`shift`: Vector3
			Vector3(X,Y,Z) parameter moves the specimen.
		`scale`: float
			factor scales the given data.
		`orientation`: quaternion
			orientation of the imported geometry
		`**kw`: (unused keyword arguments)
				is passed to :yref:`yade.utils.sphere`
	:Returns: list of spheres.
	
	LSMGenGeo library allows one to create pack of spheres
	with given [Rmin:Rmax] with null stress inside the specimen.
	Can be useful for Mining Rock simulation.
	
	Example: :ysrc:`examples/packs/packs.py`, usage of LSMGenGeo library in :ysrc:`examples/test/genCylLSM.py`.
	
	* https://answers.launchpad.net/esys-particle/+faq/877
	* http://www.access.edu.au/lsmgengeo_python_doc/current/pythonapi/html/GenGeo-module.html
	* https://svn.esscc.uq.edu.au/svn/esys3/lsm/contrib/LSMGenGeo/"""
	from yade.utils import sphere

	infile = open(fileName,"r")
	lines = infile.readlines()
	infile.close()

	numSpheres = int(lines[6].split()[0])
	ret=[]
	for line in lines[7:numSpheres+7]:
		data = line.split()
		pos = orientation*Vector3(float(data[0]),float(data[1]),float(data[2]))
		ret.append(utils.sphere(shift+scale*pos,scale*float(data[3]),**kw))
	return ret

	def testMatchMakerCollisions(self):
		fr = 0.5;rho=2000
		tc = 0.001; en = 0.5; et = 0.5;
		mat1 = O.materials.append(ViscElMat(frictionAngle=fr,tc=tc,en=en,et=et,density=rho))
		mat2 = O.materials.append(ViscElMat(frictionAngle=fr,tc=tc,en=en,et=et,density=rho))
		mat3 = O.materials.append(ViscElMat(frictionAngle=fr,tc=tc,en=en,et=et,density=rho))
		r1 = 0.002381
		r2 = 0.002381
		id11 = O.bodies.append(utils.sphere(center=[0,0,0],radius=r1,material=mat1,fixed=True,color=[0,0,1]))
		id12 = O.bodies.append(utils.sphere(center=[0,0,(r1+r2)],radius=r2,material=mat2,fixed=False,color=[0,0,1]))
		
		id21 = O.bodies.append(utils.sphere(center=[3*r1,0,0],radius=r1,material=mat1,fixed=True,color=[0,1,0]))
		id22 = O.bodies.append(utils.sphere(center=[3*r1,0,(r1+r2)],radius=r2,material=mat3,fixed=False,color=[0,1,0]))
		
		id31 = O.bodies.append(utils.sphere(center=[6*r1,0,0],radius=r1,material=mat2,fixed=True,color=[1,0,0]))
		id32 = O.bodies.append(utils.sphere(center=[6*r1,0,(r1+r2)],radius=r2,material=mat3,fixed=False,color=[1,0,0]))
		
		O.engines = [
			ForceResetter(),
			InsertionSortCollider([Bo1_Sphere_Aabb()],verletDist=r1*10.0),
			InteractionLoop(
				[Ig2_Sphere_Sphere_ScGeom()],
				[Ip2_ViscElMat_ViscElMat_ViscElPhys( 
					en=MatchMaker(matches=((mat1,mat2,.1),(mat1,mat3,.2),(mat2,mat3,.4))),
					et=MatchMaker(matches=((mat1,mat2,.7),(mat1,mat3,.8),(mat2,mat3,.9))),
					frictAngle=MatchMaker(matches=((mat1,mat2,.1),(mat1,mat3,.2),(mat2,mat3,.3)))
				)],
				[Law2_ScGeom_ViscElPhys_Basic()],
				),
			NewtonIntegrator(damping=0,gravity=[0,0,-9.81]),
		]
		
		O.step()
		self.assertTrue((atan(O.interactions[id11,id12].phys.tangensOfFrictionAngle)-0.1)==0)
		self.assertTrue((atan(O.interactions[id21,id22].phys.tangensOfFrictionAngle)-0.2)==0)
		self.assertTrue((atan(O.interactions[id31,id32].phys.tangensOfFrictionAngle)-0.3)==0)
		
		self.assertTrue(round(O.interactions[id11,id12].phys.cn, 3) - 0.26 == 0)
		self.assertTrue(round(O.interactions[id21,id22].phys.cn, 3) - 0.182 == 0)
		self.assertTrue(round(O.interactions[id31,id32].phys.cn, 3) - 0.104 == 0)

		self.assertTrue(round(O.interactions[id11,id12].phys.cs, 3) - 0.012== 0)
		self.assertTrue(round(O.interactions[id21,id22].phys.cs, 3) - 0.007 == 0)
		self.assertTrue(round(O.interactions[id31,id32].phys.cs, 3) - 0.003 == 0)

	def testKinematicEngines(self):
		'Engines: kinematic engines'
		tolerance = 1e-5
		rotIndex=1.0
		angVelTemp = pi/rotIndex
		O.reset()
		id_fixed_transl = O.bodies.append(utils.sphere((0.0,0.0,0.0),1.0,fixed=True))
		id_nonfixed_transl = O.bodies.append(utils.sphere((0.0,5.0,0.0),1.0,fixed=False))
		id_fixed_rot = O.bodies.append(utils.sphere((0.0,10.0,10.0),1.0,fixed=True))
		id_nonfixed_rot = O.bodies.append(utils.sphere((0.0,15.0,10.0),1.0,fixed=False))
		id_fixed_helix = O.bodies.append(utils.sphere((0.0,20.0,10.0),1.0,fixed=True))
		id_nonfixed_helix = O.bodies.append(utils.sphere((0.0,25.0,10.0),1.0,fixed=False))
		O.engines=[
			TranslationEngine(velocity = 1.0, translationAxis = [1.0,0,0], ids = [id_fixed_transl]),
			TranslationEngine(velocity = 1.0, translationAxis = [1.0,0,0], ids = [id_nonfixed_transl]),
			RotationEngine(angularVelocity = pi/angVelTemp, rotationAxis = [0.0,1.0,0.0], rotateAroundZero = True, zeroPoint = [0.0,0.0,0.0], ids = [id_fixed_rot]),
			RotationEngine(angularVelocity = pi/angVelTemp, rotationAxis = [0.0,1.0,0.0], rotateAroundZero = True, zeroPoint = [0.0,5.0,0.0], ids = [id_nonfixed_rot]),
			HelixEngine(angularVelocity = pi/angVelTemp, rotationAxis = [0.0,1.0,0.0], linearVelocity = 1.0, zeroPoint = [0.0,0.0,0.0], ids = [id_fixed_helix]),
			HelixEngine(angularVelocity = pi/angVelTemp, rotationAxis = [0.0,1.0,0.0], linearVelocity = 1.0, zeroPoint = [0.0,5.0,0.0], ids = [id_nonfixed_helix]),
			ForceResetter(),
			NewtonIntegrator()
		]
		O.dt = 1.0
		for i in range(0,2):
			O.step()
			self.assertTrue(abs(O.bodies[id_fixed_transl].state.pos[0] - O.iter) < tolerance)												#Check translation of fixed bodies
			self.assertTrue(abs(O.bodies[id_nonfixed_transl].state.pos[0] - O.iter) < tolerance)										#Check translation of nonfixed bodies
			
			self.assertTrue(abs(O.bodies[id_fixed_rot].state.pos[0]-10.0*sin(pi/angVelTemp*O.iter))<tolerance)			#Check rotation of fixed bodies X
			self.assertTrue(abs(O.bodies[id_fixed_rot].state.pos[2]-10.0*cos(pi/angVelTemp*O.iter))<tolerance)			#Check rotation of fixed bodies Y
			self.assertTrue(abs(O.bodies[id_fixed_rot].state.ori.toAxisAngle()[1]-Quaternion(Vector3(0.0,1.0,0.0),pi/angVelTemp*O.iter).toAxisAngle()[1])<tolerance)		#Check rotation of fixed bodies, angle
			
			self.assertTrue(abs(O.bodies[id_nonfixed_rot].state.pos[0] - 10*sin(pi/angVelTemp*O.iter))<tolerance)		#Check rotation of nonfixed bodies X
			self.assertTrue(abs(O.bodies[id_nonfixed_rot].state.pos[2] - 10*cos(pi/angVelTemp*O.iter))<tolerance)		#Check rotation of nonfixed bodies Y
			self.assertTrue(abs(O.bodies[id_nonfixed_rot].state.ori.toAxisAngle()[1]-Quaternion(Vector3(0.0,1.0,0.0),pi/angVelTemp*O.iter).toAxisAngle()[1])<tolerance)		#Check rotation of nonfixed bodies, angle
						
			self.assertTrue(abs(O.bodies[id_fixed_helix].state.pos[0] - 10*sin(pi/angVelTemp*O.iter))<tolerance)		#Check helixEngine of fixed bodies X
			self.assertTrue(abs(O.bodies[id_fixed_helix].state.pos[2] - 10*cos(pi/angVelTemp*O.iter))<tolerance)		#Check helixEngine of fixed bodies Y
			self.assertTrue(abs(O.bodies[id_fixed_helix].state.pos[1]-20.0 - O.iter)<tolerance)		#Check helixEngine of fixed bodies Z
			
			self.assertTrue(abs(O.bodies[id_nonfixed_helix].state.pos[0] - 10*sin(pi/angVelTemp*O.iter))<tolerance)		#Check helixEngine of nonfixed bodies X
			self.assertTrue(abs(O.bodies[id_nonfixed_helix].state.pos[2] - 10*cos(pi/angVelTemp*O.iter))<tolerance)		#Check helixEngine of nonfixed bodies Y
			self.assertTrue(abs(O.bodies[id_nonfixed_helix].state.pos[1]-25.0 - O.iter)<tolerance)		#Check helixEngine of nonfixed bodies Z