def cell(o, us, ua, fm):
m = Matrix2_Identity + us + ua
d = dim
vs = [Vector2(x, y) for x, y in ((0, 0), (d, 0), (d, -d), (0, -d))]
vs = [m * v for v in vs]
vs = [Vector2(o) + v for v in vs]
(x1, y1), (x2, y2), (x3, y3), (x4, y4) = vs
paper.path(["M", o[0], o[1], "h", +1.1 * d])
paper.path(["M", o[0], o[1], "v", -1.1 * d])
paper.path(["M", x1, y1, "L", x2, y2, "L", x3, y3, "L", x4, y4,
"Z"]).normal().fill("#ddd")
#
d1, d3 = [dim * v for v in (.3, .7)]
cs = [
Vector2(x, y) for x, y in ((d1, -d1), (d3, -d1), (d3, -d3), (d1, -d3))
]
cs = [m * c for c in cs]
cs = [Vector2(o) + c for c in cs]
r = .15 * d
rr = .2 * d
a = -ua[0, 1] - fm[0, 1]
co, si = [f(a) for f in cos, sin]
for c in cs:
paper.circle(c[0], c[1], r).fill("white")
paper.path([
"M",
c[0],
c[1],
"l",
+co * rr,
+si * rr,
"M",
c[0],
c[1],
"l",
-co * rr,
-si * rr,
"M",
c[0],
c[1],
"l",
-si * rr,
+co * rr,
"M",
c[0],
c[1],
"l",
+si * rr,
-co * rr,
]).normal()
def aarrow(c, d, text=None, rev=False):
d = Vector2(d).normalized()
t = Vector2(-d[1], d[0])
v0 = c + t * r
v1 = c - t * r
if rev:
v0, v1 = v1, v0
paper.path(
["M", v0[0], v0[1], "A", r, r, 0, 0, 1 if rev else 0, v1[0],
v1[1]]).mediumThick().arrow()
ret = c + r * d
if text is not None:
papertext(ret[0], ret[1], text)
return c + r * d
def larrow(c, d, text=None):
d = Vector2(d).normalized() * a
paper.path(["M", c[0], c[1], "l", d[0], d[1]]).mediumThick().arrow()
ret = c + d
if text is not None:
papertext(ret[0], ret[1], text)
return ret
def flat(v):
return Vector2(v[0], v[1])
class EllGroup(woo.core.Preprocessor, woo.pyderived.PyWooObject):
'Simulation of group of ellipsoids moving in 2-dimensional box.'
_classTraits = None
_PAT = woo.pyderived.PyAttrTrait # less typing
_attrTraits = [
_PAT(
Vector2,
'rRange',
Vector2(.02, .04),
unit='m',
doc=
'Range (minimum and maximum) for particle radius (greatest semi-axis); if both are the same, all particles will have the same radius.'
),
_PAT(bool,
'spheres',
False,
doc='Use spherical particles instead of elliptical'),
_PAT(
float,
'semiMinRelRnd',
0,
hideIf='self.spheres',
doc=
'Minimum semi-axis length relative to particle radius; minor semi-axes are randomly selected from (:obj:`semiMinRelRnd` … 1) × greatest semi-axis. If non-positive, :obj:`semiRelFixed` is used instead.'
),
_PAT(
Vector3,
'semiRelFixed',
Vector3(1., .5, .5),
hideIf='self.spheres',
doc=
'Fixed sizes of semi-axes relative (all elements should be ≤ 1). The :math:`z`-component is the out-of-plane size which only indirectly influences contact stiffnesses. This variable is only used if semi-axes are not assigned randomly (see :obj:`semiMinRelRnd`).'
),
_PAT(Vector2,
'boxSize',
Vector2(2, 2),
unit='m',
doc='Size of the 2d domain in which particles move.'),
_PAT(
float,
'vMax',
1.,
unit='m/s',
doc=
'Maximum initial velocity of particle; assigned randomly from 0 to this value; intial angular velocity of all particles is zero.'
),
_PAT(
woo.models.ContactModelSelector,
'model',
woo.models.ContactModelSelector(name='Schwarz',
restitution=1.,
damping=0.01,
numMat=(1, 2),
matDesc=['ellipsoids', 'walls'],
mats=[
woo.dem.HertzMat(density=5000,
young=1e6,
tanPhi=0.0,
surfEnergy=4.,
alpha=.6)
]),
doc=
'Select contact model. The first material is for particles; the second, optional, material is for walls at the boundary (the first material is used if there is no second one).'
),
_PAT(
str,
'exportFmt',
"/tmp/ell2d-{tid}-",
filename=True,
doc=
"Prefix for saving :obj:`woo.dem.VtkExport` data, and :obj:`woo.pre.ell2d.ell2plot` data; formatted with ``format()`` providing :obj:`woo.core.Scene.tags` as keys."
),
_PAT(
int, 'vtkStep', 0,
"How often should :obj:`woo.dem.VtkExport` run. If non-positive, never run the export."
),
_PAT(
int, 'vtkEllLev', 1,
'Tesselation level of ellipsoids when expored as VTK meshes (see :obj:`woo.dem.VtkExport.ellLev`).'
),
_PAT(
int, 'ell2Step', 0,
"How often should :obj:`woo.pre.ell2d.ell2plot` run. If non-positive, never run that one."
),
_PAT(
float, 'dtSafety', .5,
'Safety coefficient for critical timestep; should be smaller than one.'
),
]
def __init__(self, **kw):
woo.core.Preprocessor.__init__(self)
self.wooPyInit(self.__class__, woo.core.Preprocessor, **kw)
def __call__(self):
import woo
woo.master.usesApi = 10102
# preprocessor builds the simulation when called
pre = self # more readable
S = woo.core.Scene(fields=[woo.dem.DemField()], pre=self.deepcopy())
# material definitions
ellMat = pre.model.mats[0]
wallMat = (pre.model.mats[1] if len(pre.model.mats) > 1 else ellMat)
ZZ = pre.rRange[1] * 3
# only generate spheres randomly in 2d box
S.engines = [
woo.dem.BoxInlet2d(
axis=2,
box=((0, 0, ZZ), (pre.boxSize[0], pre.boxSize[1], ZZ)),
materials=[ellMat],
generator=woo.dem.MinMaxSphereGenerator(dRange=2 * pre.rRange),
massRate=0),
woo.dem.InsertionSortCollider([woo.dem.Bo1_Sphere_Aabb()])
]
S.one()
posRad = [(p.pos, p.shape.radius) for p in S.dem.par]
# clear the dem field
S.fields = [woo.dem.DemField()]
import random
def rndOri2d():
q = Quaternion((0, 0, 1), 2 * math.pi * random.random())
q.normalize()
return q
S.energy['kin0'] = 0
for pos, rad in posRad:
if not pre.spheres:
if pre.semiMinRelRnd > 0:
semiAxes = [
random.uniform(pre.semiMinRelRnd, 1) * rad
for i in (0, 1, 2)
]
else:
semiAxes = Vector3(pre.semiRelFixed) * rad
p = woo.utils.ellipsoid(center=pos,
semiAxes=semiAxes,
ori=rndOri2d(),
mat=ellMat)
else:
p = woo.utils.sphere(center=pos, radius=rad, mat=ellMat)
p.vel = rndOri2d() * Vector3(pre.vMax * random.random(), 0, 0)
S.energy['kin0'] -= p.Ek
p.blocked = 'zXY'
S.dem.par.add(p)
#for coord,axis,sense in [(0,0,+1),(pre.boxSize[0],0,-1),(0,1,+1),(pre.boxSize[1],1,-1)]:
# S.dem.par.add(woo.utils.wall(coord,axis=axis,sense=sense,mat=wallMat,visible=False))
S.dem.par.add([
woo.dem.Wall.make(0, axis=0, mat=wallMat, visible=True),
woo.dem.Wall.make(0, axis=1, mat=wallMat, visible=True)
])
S.periodic = True
S.cell.setBox((pre.boxSize[0], pre.boxSize[1], 2 * ZZ))
S.engines = woo.dem.DemField.minimalEngines(
model=pre.model, dynDtPeriod=10
) + [
# trace particles and color by z-angVel
woo.dem.Tracer(num=100,
compress=4,
compSkip=1,
glSmooth=True,
glWidth=2,
scalar=woo.dem.Tracer.scalarAngVel,
vecAxis=2,
stepPeriod=40,
minDist=pre.rRange[0]),
woo.core.PyRunner(
100,
'S.plot.addData(i=S.step,t=S.time,total=S.energy.total(),relErr=(S.energy.relErr() if S.step>100 else 0),**S.energy)'
),
woo.dem.VtkExport(stepPeriod=pre.vtkStep,
out=pre.exportFmt,
ellLev=pre.vtkEllLev,
dead=(pre.vtkStep <= 0)),
woo.core.PyRunner(
pre.ell2Step,
'import woo.pre.ell2d; mx=woo.pre.ell2d.ell2plot(out="%s-%05d.png"%(S.expandTags(S.pre.exportFmt),engine.nDone),S=S,colorRange=(0,S.lab.maxEll2Color),bbox=((0,0),S.pre.boxSize)); S.lab.maxEll2Color=max(mx,S.lab.maxEll2Color)',
dead=(pre.ell2Step <= 0)),
woo.dem.WeirdTriaxControl(goal=(-0, -0, 0),
stressMask=0,
maxStrainRate=(.1, .1, 0),
mass=1.,
label='triax'),
]
S.lab.leapfrog.kinSplit = True
S.dtSafety = pre.dtSafety
S.trackEnergy = True
S.uiBuild = 'import woo.pre.ell2d; woo.pre.ell2d.ellGroupUiBuild(S,area)'
S.lab.maxEll2Color = 0. # max |angVel| for the start when plotting
S.plot.plots = {'i': ('total', '**S.energy'), ' t': ('relErr')}
S.plot.data = {
'i': [nan],
'total': [nan],
'relErr': [nan]
} # to make plot displayable from the very start
try:
import woo.gl
S.gl.renderer = woo.gl.Renderer(iniUp=(0, 1, 0),
iniViewDir=(0, 0, -1),
grid=4)
except ImportError:
pass
return S
def flat(v): return Vector2(v[0],v[1]) for p in S.dem.par:
def __init__(self, c, r):
self.center = Vector2(c)
self.radius = r
self.extra = {}
def arrow(p, d, l):
d = l * Vector2(d).normalized()
d = p + d
line(p, d).mediumThick().arrow()
y += dy
paper.path(["M", x, y, "h", l]).normal().dotted().stroke('red')
y += dy
paper.path(["M", x, y, "h", l]).normal().arrow().stroke('red')
#
paper.sphere(200, 100, 50, "#440")
#
paper.save()
######################################################################
######################################################################
# periodic packing
######################################################################
w, h = 520, 500
d = 200
trans = Vector2(165, 350)
ps = (
Vector2(0, 0),
Vector2(d, 0),
Vector2(d, -d),
Vector2(0, -d),
)
cs1 = (
Vector2(35, -50),
Vector2(135, -65),
Vector2(150, -165),
Vector2(50, -150),
)
kss = (
((1, 0), (0, -1), (1, -1)),
((-1, 0), (0, -1)),