def background(self, ray):
unit_dir = ray.unit_direction()
t = 0.5 * (unit_dir.y() + 1.0) # scale y direction to [0, 1.0]
white_grad = vec3([1, 1, 1]) * t
blue_grad = vec3([0.5, 0.7, 1.0]) * (1.0 - t)
return white_grad + blue_grad # linear interpolation blue/white
def f():
a = vec3(1.0, 2.0, 3.0)
b = vec3(2.0, 1.0, 3.0)
if a.x > b.x:
c = a.dot(b)
else:
c = b.dot(a)
return c
def f(): a = vec3(1.0, 2.0, 3.0) b = vec3(2.0, 1.0, 3.0) if a.x > b.x: c = a.dot(b) else: c = b.dot(a) return c
def testirregulargfx(): o = piece2obj.piece2obj(['l']) assert len(o) == 1 assert len(o[0].gfxmesh.vertices) == 10 assert vec3(0,0,GRID) in o[0].gfxmesh.vertices assert len(o[0].gfxmesh.indices) == 14*3 # Front and back optimization. assert len(o[0].physgeoms) == 1 assert type(o[0].physgeoms[0]) == piece2obj.PhysMesh assert o[0].physgeoms[0].pos == vec3(0,0,0)
def testtinyrotated2dcube(): o = piece2obj.piece2obj(['<>']) assert len(o[0].gfxmesh.vertices) == 8 assert piece2obj.invrotq == o[0].gfxmesh.q assert vec3(0,0,0) == o[0].gfxmesh.pos assert vec3(0,GRID,GRID) in o[0].gfxmesh.vertices assert len(o[0].gfxmesh.indices) == 12*3 assert len(o[0].physgeoms) == 1 assert type(o[0].physgeoms[0]) == piece2obj.PhysBox
def give_fade_blue_down(ray): # goal color is vec3(.5, .7, 1.0) //blue # start is white(1,1,1) # r's original y val goes from -1, 1 # 1 then *.5, to go 0-1 unit_direction = vec3.unit_vector( ray.direction() ) percent = 0.5*(1.0 + unit_direction.e[1]) return vec3.lerp( vec3.vec3(in_list=[1.0, 1.0, 1.0]), vec3.vec3(in_list=[0.5, 0.7, 1.0]), percent)
def confuseMethods(a, b, c, d, e, f): va = vec3(a, b, c) vb = vec3(d, e, f) if a > b: vc = va.cross(vb) else: vc = vb.cross(va) return vc.dot(vc)
def generateScene():
world = hitableList()
# Bottom "plane"
world.add(sphere(vec3(0, -1000, 0), 1000, lambertian(vec3(0.5, 0.5, 0.5))))
# three large spheres
world.add(sphere(vec3(0, 1, 0), 1.0, dielectric(1.5)))
world.add(sphere(vec3(-4, 1, 0), 1.0, lambertian(vec3(0.4, 0.2, 0.1))))
world.add(sphere(vec3(4, 1, 0), 1.0, metal(vec3(0.7, 0.6, 0.5), 0.0)))
# numerous small spheres
i = 1
for a in range(-11, 11):
for b in range(-11, 11):
chooseMat = random.random()
center = vec3(a + 0.9 * random.random(), 0.2,
b + 0.9 * random.uniform(0, 1))
if (center - vec3(4, 0.2, 0)).length() > 0.9:
if chooseMat < 0.8:
# diffuse
albedo = vec3.random() * vec3.random()
world.add(sphere(center, 0.2, lambertian(albedo)))
elif chooseMat < 0.95:
# metal
albedo = random.uniform(.5, 1)
fuzz = random.uniform(0, .5)
world.add(sphere(center, 0.2, metal(albedo, fuzz)))
else:
# glass
world.add(sphere(center, 0.2, dielectric(1.5)))
return world
def test2dcube(): o = piece2obj.piece2obj(['X']) assert len(o) == 1 assert len(o[0].gfxmesh.vertices) == 8 assert vec3(GRID,GRID,GRID) in o[0].gfxmesh.vertices assert len(o[0].gfxmesh.indices) == 12*3 # Reduced two in the back, two in the front (and of course none in the middle). assert len(o[0].physgeoms) == 1 assert type(o[0].physgeoms[0]) == piece2obj.PhysBox assert o[0].physgeoms[0].pos == vec3(0,0,0) assert o[0].physgeoms[0].size.x == G2 assert o[0].physgeoms[0].size.y == G2 assert o[0].physgeoms[0].size.z == G2
def testasymmeticcubes():
length = 7
wide,high,deep = (['X'*length],vec3(length,1,1)), (['X']*length,vec3(1,length,1)), ('\n---\n'.join(['X']*length).split(),vec3(1,1,length))
def innercubetest(ascii,size):
o = piece2obj.piece2obj(ascii)
assert len(o) == 1
assert len(o[0].gfxmesh.vertices) == 8
assert size/2 in o[0].gfxmesh.vertices
assert len(o[0].gfxmesh.indices) == 12*3
assert len(o[0].physgeoms) == 1
assert type(o[0].physgeoms[0]) == piece2obj.PhysBox
[innercubetest(ascii,size) for ascii,size in [wide,high,deep]]
def look_at(self, eye_x, eye_y, eye_z, c_x, c_y, c_z, u_x, u_y, u_z):
f = vec3(c_x - eye_x, c_y - eye_y, c_z - eye_z).normalize()
up = vec3(u_x, u_y, u_z).normalize()
side = f.cross(up)
up = side.normalize().cross(f)
m = Matrix(
side.x, side.y, side.z, -eye_x,
up.x, up.y, up.z, -eye_y,
-f.x, -f.y, -f.z, -eye_z,
0., 0., 0., 1.)
return self * m
def assignMerge(s): a = vec3(3.0, 3.0, 3.0) b = vec3(5.0, 5.0, 5.0) #c = a if s else b if s: c = a else: c = b c.x = 7.0 return c.x
def rayColor(r, scene, depth):
if depth == 0:
return vec3(0, 0, 0)
hit = scene.hit(r, 0.0001, float("inf"))
if hit != None:
result = hit.mat.scatter(r, hit)
if result != None:
return rayColor(result[1], scene, depth - 1) * result[0]
t = (vec3.normalize(r.direction()).y() + 1) * 0.5
return vec3(1.0, 1.0, 1.0) * (1.0 - t) + vec3(0.5, 0.7, 1.0) * t
def assignMerge(s):
a = vec3(3.0, 3.0, 3.0)
b = vec3(5.0, 5.0, 5.0)
#c = a if s else b
if s:
c = a
else:
c = b
c.x = 7.0
return c.x
def add_point(self, x, y, z):
self.x = min(x, self.x)
self.y = min(y, self.y)
self.z = min(z, self.z)
self.xmax = max(x, self.xmax)
self.ymax = max(y, self.ymax)
self.zmax = max(z, self.zmax)
self.width = self.xmax - self.x
self.height = self.ymax - self.y
self.depth = self.zmax - self.z
self.pos = vec3(self.x, self.y, self.z)
self.size = vec3(self.width, self.height, self.depth)
self.center = self.pos + (self.size*0.5)
self.cx, self.cy, self.cz = self.center
def scatter(self, rIn, rec):
attenuation = vec3(1, 1, 1)
etaiOverEtat = (1.0 /
self.refIndex) if rec.frontFace else self.refIndex
unitDirection = vec3.normalize(rIn.direction())
cosTheta = min(vec3.dot(unitDirection * -1, rec.n), 1.0)
sinTheta = math.sqrt(1.0 - cosTheta * cosTheta)
# TIR
if etaiOverEtat * sinTheta > 1.0:
reflected = vec3.reflect(unitDirection, rec.n)
scattered = ray(rec.p, reflected)
return (attenuation, scattered)
# prop. reflection / refraction
reflectProb = dielectric.schlick(cosTheta, etaiOverEtat)
# reflection
if random.random() < reflectProb:
reflected = vec3.reflect(unitDirection, rec.n)
scattered = ray(rec.p, reflected)
return (attenuation, scattered)
# refraction
refracted = vec3.refract(unitDirection, rec.n, etaiOverEtat)
scattered = ray(rec.p, refracted)
return (attenuation, scattered)
def testsmall2dtriangle(): o = piece2obj.piece2obj(['v']) assert len(o[0].gfxmesh.vertices) == 6 assert vec3(0,GRID*2/3,GRID) in o[0].gfxmesh.vertices assert len(o[0].gfxmesh.indices) == 8*3 assert len(o[0].physgeoms) == 1 assert type(o[0].physgeoms[0]) == piece2obj.PhysMesh
def test3dcuboid(): o = piece2obj.piece2obj(['XX','XX','---','XX','XX','---','XX','XX']) assert len(o) == 1 assert len(o[0].gfxmesh.vertices) == 8 assert vec3(-G2,-G2,-1.5*G2) in o[0].gfxmesh.vertices assert len(o[0].gfxmesh.indices) == 12*3 assert len(o[0].physgeoms) == 1 assert type(o[0].physgeoms[0]) == piece2obj.PhysBox
def test():
objects = []
t = objects[0]
origin = vec3(0.5, 0.5, 0)
screen_pos = coordinate_from_pixel(5, 5)
direction = origin.direction_to(screen_pos)
t.ray_tri_intersect(origin, direction)
print(t)
def test_advanced_angle_fast(self): af = lambda v,x,y,z: round(mesh._angle_fast(v.normalize(),x,y,z), 3) self.assertEqual(af(vec3(1,1,0),1,0,0), 0.785) self.assertEqual(af(vec3(1,1,0),0,1,0), 0.785) self.assertEqual(af(vec3(1,1,0),0,0,1), 0.7) self.assertEqual(af(vec3(1,-1,0),1,0,0), 0.785) self.assertEqual(af(vec3(-1,0,-5),0,0,+1), 0.7) self.assertEqual(af(vec3(-1,0,-2),0,0,+1), 0.7) self.assertEqual(af(vec3(-1,0,-1),0,0,+1), 0.7) self.assertEqual(af(vec3(-5,0,-1),0,0,+1), 0.7)
def linearMove( self, splitLine ): "Parse a linear move gcode line and send the commands to the extruder." location = vec3() if self.oldLocation != None: location = self.oldLocation self.setFeedrate( splitLine ) setPointToSplitLine( location, splitLine ) self.moveExtruder( location ) self.oldLocation = location
def helicalMove( self, isCounterclockwise, splitLine ): "Parse a helical move gcode line and send the commands to the extruder." if self.oldLocation == None: return location = vec3().getFromVec3( self.oldLocation ) self.setFeedrate( splitLine ) setPointToSplitLine( location, splitLine ) location = location.plus( self.oldLocation ) center = vec3().getFromVec3( self.oldLocation ) indexOfR = indexOfStartingWithSecond( "R", splitLine ) if indexOfR > 0: radius = getDoubleAfterFirstLetter( splitLine[ indexOfR ] ) halfLocationMinusOld = location.minus( self.oldLocation ) halfLocationMinusOld.scale( 0.5 ) halfLocationMinusOldLength = halfLocationMinusOld.length() centerMidpointDistance = math.sqrt( radius * radius - halfLocationMinusOldLength * halfLocationMinusOldLength ) centerMinusMidpoint = getRotatedWiddershinsQuarterAroundZAxis( halfLocationMinusOld ) centerMinusMidpoint.normalize() centerMinusMidpoint.scale( centerMidpointDistance ) if isCounterclockwise: center.getFromVec3( halfLocationMinusOld.plus( centerMinusMidpoint ) ) else: center.getFromVec3( halfLocationMinusOld.minus( centerMinusMidpoint ) ) else: center.x = getDoubleForLetter( "I", splitLine ) center.y = getDoubleForLetter( "J", splitLine ) curveSection = 0.5 center = center.plus( self.oldLocation ) afterCenterSegment = location.minus( center ) beforeCenterSegment = self.oldLocation.minus( center ) afterCenterDifferenceAngle = getAngleAroundZAxisDifference( afterCenterSegment, beforeCenterSegment ) absoluteDifferenceAngle = abs( afterCenterDifferenceAngle ) steps = int( math.ceil( max( absoluteDifferenceAngle * 2.4, absoluteDifferenceAngle * beforeCenterSegment.length() / curveSection ) ) ) stepPlaneAngle = getPolar( afterCenterDifferenceAngle / steps, 1.0 ) zIncrement = ( afterCenterSegment.z - beforeCenterSegment.z ) / float( steps ) for step in range( 1, steps ): beforeCenterSegment = getRoundZAxisByPlaneAngle( stepPlaneAngle, beforeCenterSegment ) beforeCenterSegment.z += zIncrement arcPoint = center.plus( beforeCenterSegment ) self.moveExtruder( arcPoint ) self.moveExtruder( location ) self.oldLocation = location
def testbig3dprism():
o = piece2obj.piece2obj(codecs.open('big_3d_prism.txt', encoding='utf-8'))
assert len(o[0].gfxmesh.vertices) == 6
assert vec3(-GRID,-G2,-1.5*G2) in o[0].gfxmesh.vertices
assert len(o[0].gfxmesh.indices) == 8*3
assert len(o[0].physgeoms) == 5
assert type(o[0].physgeoms[0]) == piece2obj.PhysBox
assert type(o[0].physgeoms[1]) == piece2obj.PhysBox
assert type(o[0].physgeoms[2]) == piece2obj.PhysBox
assert type(o[0].physgeoms[3]) == piece2obj.PhysMesh
assert type(o[0].physgeoms[4]) == piece2obj.PhysMesh
def __init__(self, **kwargs):
self.mW = kwargs.get('mW', 1000.0)
self.w = kwargs.get('waists', (30., 30.))
self.l = kwargs.get('wavelength', 1.064)
#
self.axis = kwargs.get('axis', (np.pi / 2, 0.))
self.origin = kwargs.get('origin', vec3(0, 0, 0))
# Make sure vectors are of type(vec3)
self.axisvec = vec3()
th = self.axis[0]
ph = self.axis[1]
self.axisvec.set_spherical(1, th, ph)
self.origin = vec3(self.origin)
# Calculate two orthogonal directions
# which will be used to specify the beam waists
self.orth0 = vec3( np.cos(th)*np.cos(ph) , \
np.cos(th)*np.sin(ph), -1.*np.sin(th) )
self.orth1 = vec3(-1. * np.sin(ph), np.cos(ph), 0.)
def draw_scene(self):
for i in tqdm(range(self.cam.height)):
for j in range(self.cam.width):
pixel = vec3([0, 0, 0])
for s in range(self.cam.samples_per_pixel):
u = (j + self.random()) / (self.cam.width - 1)
v = (self.cam.height - i +
self.random()) / (self.cam.height - 1)
r = self.cam.get_ray(u, v)
pixel += self.get_ray_colour(r, self.max_depth)
colour(pixel).write_colour(self.cam.samples_per_pixel)
def __init__( self,
**kwargs ):
self.mW = kwargs.get('mW',1000.0 )
self.w = kwargs.get('waists', (30.,30.) )
self.l = kwargs.get('wavelength', 1.064 )
#
self.axis = kwargs.get('axis', (np.pi/2,0.) )
self.origin = kwargs.get('origin', vec3(0,0,0) )
# Make sure vectors are of type(vec3)
self.axisvec = vec3()
th = self.axis[0]
ph = self.axis[1]
self.axisvec.set_spherical( 1, th, ph)
self.origin = vec3(self.origin)
# Calculate two orthogonal directions
# which will be used to specify the beam waists
self.orth0 = vec3( np.cos(th)*np.cos(ph) , np.cos(th)*np.sin(ph), -1.*np.sin(th) )
self.orth1 = vec3( -1.*np.sin(ph), np.cos(ph), 0. )
def pol(self):
'''This method calculates the sum over final polarizations'''
try:
kin = self.kin
kout = self.kout
kipol = self.kipol
except Exception as e:
print "k vectors have not been defined in the crystal"
print "program will stop"
print e
exit()
# unit vectors for input polarization
zvec = vec3.vec3(0.,0.,1.)
in1 = vec3.cross( zvec, kin )
in1 = in1 / abs(in1)
in2 = vec3.cross( kin, in1)
in2 = in2 / abs(in2)
# input polarization
inpol = kipol[0]*in1 + kipol[1]*in2
# unit vectors for output polarization
out1 = vec3.cross( zvec, kout )
out1 = out1 / abs(out1)
out2 = vec3.cross( kout, out1)
out2 = out2 / abs(out2)
# polarization of transition
splus = 1/np.sqrt(2.) *( vec3.vec3(1.,0.,0.) + 1j * vec3.vec3(0.,1.,0.))
sminus = 1/np.sqrt(2.) *( vec3.vec3(1.,0.,0.) - 1j * vec3.vec3(0.,1.,0.))
# sum over output polarizations
polsum = 0.
for i,pout in enumerate([out1, out2]):
term = abs( (splus * pout)*(inpol*sminus) )**2.
polsum = polsum + term
if verbose:
print "\tSum over output pol (vectors) = ", polsum
self.polsum = polsum
# also obtain this result using the angles
# with respect to the magnetic field
cosIN = kin/abs(kin) * zvec
cosOUT = kout/abs(kout) * zvec
polsumANGLE = 1./4. * (1 + cosIN**2.) * (1 + cosOUT**2.)
#print "Sum over output pol (angles) = ", polsumANGLE
# optional draw polarization vectors on bloch sphere
if False:
b = bsphere.Bloch()
origin = vec3.vec3()
b.add_arrow( -kin/abs(kin), origin, 'red')
b.add_arrow( -kin/abs(kin), -kin/abs(kin) + in1/2., 'black')
b.add_arrow( -kin/abs(kin), -kin/abs(kin) + in2/2., 'black')
b.add_arrow( origin, kout/abs(kout), 'red')
b.add_arrow( origin, out1/2., 'black')
b.add_arrow( origin, out2/2., 'black')
b.show()
return self.polsum
def test_basic_angle_fast(self): af = lambda v,x,y,z: round(mesh._angle_fast(v.normalize(),x,y,z), 3) self.assertEqual(af(vec3(1,0,0),1,0,0), 0) self.assertEqual(af(vec3(0,1,0),0,1,0), 0) self.assertEqual(af(vec3(0,0,1),0,0,1), 0) self.assertEqual(af(vec3(1,0,0),0,1,0), 0.7) self.assertEqual(af(vec3(1,0,0),0,0,1), 0.7) self.assertEqual(af(vec3(0,1,0),0,0,1), 0.7)
def methodMerge(s): v = vec3(0.0, 0.0, 0.0) if s: vs = VecSetter(5.0) else: vs = VecSetter(3.0) ## # Old analysis method chokes, as the types are unrelated. ## if s: ## vs = VecSetter5() ## else: ## vs = VecSetter3() vs.setter(v) return v.x
def get_lowest_world_point(self):
p = self._scalenode.get_world_translation() - self._scalenode.getphysmaster().get_world_translation()
lp = p[:3]
if self._shapenode.nodetype == "polyCube":
lp[0] -= self.data[0]/2
lp[1] -= self.data[2]/2
lp[2] -= self.data[1]/2
elif self._shapenode.nodetype == "polySphere":
lp[0] -= self.data[0]
lp[1] -= self.data[0]
lp[2] -= self.data[0]
else:
print("Error: (2) primitive physics shape type '%s' on node '%s' is unknown." % (shapenode.nodetype, shapenode.getFullName()))
sys.exit(22)
#print("Shape %s at %s says it has a lowest point of %s with size %s." %(self._scalenode.getName(), p, lp, self.data))
return vec3(lp[:3])
def methodMerge(s):
v = vec3(0.0, 0.0, 0.0)
if s:
vs = VecSetter(5.0)
else:
vs = VecSetter(3.0)
## # Old analysis method chokes, as the types are unrelated.
## if s:
## vs = VecSetter5()
## else:
## vs = VecSetter3()
vs.setter(v)
return v.x
def get_lowest_world_point(self):
p = self._scalenode.get_world_translation(
) - self._scalenode.getphysmaster().get_world_translation()
lp = p[:3]
if self._shapenode.nodetype == "polyCube":
lp[0] -= self.data[0] / 2
lp[1] -= self.data[2] / 2
lp[2] -= self.data[1] / 2
elif self._shapenode.nodetype == "polySphere":
lp[0] -= self.data[0]
lp[1] -= self.data[0]
lp[2] -= self.data[0]
else:
print(
"Error: (2) primitive physics shape type '%s' on node '%s' is unknown."
% (shapenode.nodetype, shapenode.getFullName()))
sys.exit(22)
#print("Shape %s at %s says it has a lowest point of %s with size %s." %(self._scalenode.getName(), p, lp, self.data))
return vec3(lp[:3])
def Barycentric(p, a, b, c):
# Vector v0 = b - a
v0 = b - a
# Vector v1 = c - a
v1 = c - a
# Vector v2 = p - a
v2 = p - a
d00 = v0.dot(v0)
d01 = v0.dot(v1)
d11 = v1.dot(v1)
d20 = v2.dot(v0)
d21 = v2.dot(v1)
denom = d00 * d11 - d01 * d01
v = (d11 * d20 - d01 * d21) / denom
w = (d00 * d21 - d01 * d20) / denom
u = 1.0 - v - w
return vec3(u, v, w)
def Bands( self, X, Y, Z, **kwargs):
NBand = kwargs.get('NBand',0.)
# Make 1d array with distances
R_unit = vec3( X[-1]-X[0], Y[-1]-Y[0], Z[-1]-Z[0] ); R_unit = R_unit / abs(R_unit)
# Below we get the signed distance from the origin
self.R = X*R_unit[0]+Y*R_unit[1]+Z*R_unit[2]
self.V0_ = self.V0(X,Y,Z)
self.Bottom_ = self.Bottom(X,Y,Z)
self.LatticeMod_ = self.Bottom_ + np.amin(self.V0_,axis=0)*\
np.power( np.cos( 2.*np.pi*self.R / self.l / self.scale ), 2)
bands = bands3dvec( self.V0_, NBand=0 )
excband = bands3dvec( self.V0_, NBand=1 )
# The zero of energy for this problem is exactly at the center
# of the lowest band. This comes from the t_{ii} matrix element
# which is generally neglected in the Hamiltonian.
self.Ezero = (bands[1]+bands[0])/2. + self.Bottom_
self.Ezero0 = self.Ezero.min()
# The threshold for evaporation can ge obtaind from
# the bottom of the band going far along one beam
self.evapTH = bands3dvec( self.V0( 100., 0., 0. ), NBand=0 )[0] + self.Bottom(100.,0.,0.)
# Tunneling, onsite interactions, and localMu for phase diagram
self.tunneling = (bands[1]-bands[0])/12.
self.onsite = Onsite( self.V0_, a_s=self.a_s, lattice_spacing= self.l/2. )
self.onsite_t = self.onsite / self.tunneling
# Offset the chemical potential for use in the phase diagram
self.globalMuZ = self.Ezero0 + self.globalMu
self.localMu_t = ( self.globalMuZ - self.Ezero )/ self.tunneling
# Obtain the thermodynamic quantities
density = self.fHdens( self.onsite_t, self.localMu_t )
doublons = self.fHdoub( self.onsite_t, self.localMu_t )
entropy = self.fHentr( self.onsite_t, self.localMu_t )
# Higher zorder puts stuff in front
return [
{'y':(bands[0] + self.Bottom_, self.Ezero ), 'color':'blue', 'lw':2., \
'fill':True, 'fillcolor':'blue', 'fillalpha':0.75,'zorder':10, 'label':'$\mathrm{band\ lower\ half}$'},
{'y':(self.Ezero + self.onsite, bands[1] + self.Bottom_+self.onsite), 'color':'purple', 'lw':2., \
'fill':True, 'fillcolor':'plum', 'fillalpha':0.75,'zorder':10, 'label':'$\mathrm{band\ upper\ half}+U$'},
{'y':(excband[0] + self.Bottom_, excband[1] + self.Bottom_ ), 'color':'red', 'lw':2., \
'fill':True, 'fillcolor':'pink', 'fillalpha':0.75,'zorder':10, 'label':'$\mathrm{exc\ band}$'},
{'y':np.ones_like(X)*self.globalMuZ, 'color':'limegreen','lw':2,'zorder':1.9, 'label':'$\mu_{0}$'},
{'y':np.ones_like(X)*self.evapTH, 'color':'#FF6F00', 'lw':2,'zorder':1.9, 'label':'$\mathrm{evap\ th.}$'},
{'y':self.Bottom_,'color':'gray', 'lw':0.5,'alpha':0.5},
{'y':self.LatticeMod_,'color':'gray', 'lw':1.5,'alpha':0.5,'label':r'$\mathrm{lattice\ potential\ \ }\lambda\times10$'},
{'y':density, 'color':'blue', 'lw':1.75, 'axis':2, 'label':'$n$'},
{'y':doublons, 'color':'red', 'lw':1.75, 'axis':2, 'label':'$d$'},
{'y':entropy, 'color':'black', 'lw':1.75, 'axis':2, 'label':'$s$'},
{'y':density-2*doublons, 'color':'green', 'lw':1.75, 'axis':2, 'label':'$n-2d$'},
#{'y':self.localMu_t, 'color':'cyan', 'lw':1.75, 'axis':2, 'label':r'$\mu$'},
{'figprop':True,'figsuptitle':self.figlabel, 'foottext':self.foottext}
]
def kinchamber( phi ):
k = vec3.vec3()
the_ = np.pi/2
phi_ = np.pi/2. + np.pi* phi/180.
k.set_spherical( 2.*np.pi/l671, the_, phi_ )
return k
def kinsph(theta, phi):
k = vec3.vec3()
the_ = np.pi/2 - ( np.pi*theta/180. - np.pi/2.)
phi_ = np.pi/2. + np.pi* phi/180.
k.set_spherical( 2.*np.pi/l671, the_, phi_ )
return k
def __init__(self):
self.lower_left_corner = vec3.vec3([-2.0, -1.0, -1.0])
self.horizontal = vec3.vec3([4.0, 0.0, 0.0])
self.vertical = vec3.vec3([0.0, 2.0, 0.0])
self.origin = vec3.vec3([0.0, 0.0, 0.0])
import scipy
l671 = 671.
l1064 = 1064.
# Coordinate system:
# input Bragg light for HHH propagates almost along +Y
# +Z is up
# Q vector for bragg scattering HHH
# Remember that for AFM there is a doubling of the unit cell, so the
# lattice spacing is lambda instead of lambda/2
Q = 2*np.pi/l1064 * vec3.vec3( -1., -1., 1.)
Qunit = Q/abs(Q)
# Calculate angle for HHH Bragg conditiion
# with respect to Q vector
braggTH = np.arccos( abs(Q) / 2. / (2.*np.pi/l671) )
print "HHH Bragg angle wrt Q = ", braggTH * 180. / np.pi
# Calculate angle for HHH Bragg condition
# with respect to y axis, when coming from
# under lattice beam 2.
from scipy.optimize import fsolve
def cond(x):
return np.sin(x)-np.cos(x) + 3./2. * l671 / l1064
braggTH2 = fsolve(cond, 0.)
print "HHH Bragg angle wrt -y axis = ", braggTH2 * 180. / np.pi
def project_to_stereomap(p, r, w, h):
sphere_center = vec3([w // 2, h // 2, r])
v = p - sphere_center
s = r * (v / abs(v))
return np.array(s[:2])
sample_count = 1
cam = camera.camera()
with open('testPPM.ppm', 'w') as image_file:
width = 200
height = 100
# fWidth = float(width)
# fHeight = float(height)
print_count=4000
image_file.write("P3\n{w} {h}\n255\n".format(w=width, h=height))
for i in range((height-1), -1,-1):
for j in range(width):
col = vec3.vec3(in_list=[0.0, 0.0, 0.0])
for s in range(sample_count):
# x_percent = (j + random()) / width
# y_percent = (i + random()) / height
x_percent = j / width
y_percent = i / height
r = cam.get_ray(x_percent = x_percent, y_percent = y_percent)
col += color(ray = r)
col.idiv_float(sample_count)
if (print_count > 0):
print_count-=1
print("{red} {green} {blue}\n".format(red=col[0], green=col[1], blue=col[2]))
def _normalize(ns): def xyzchunks(l): for i in range(0, len(l), 3): yield l[i:i+3] ns2 = [list(vec3(x,y,z).normalize()) for x,y,z in xyzchunks(ns)] return list(item for iter_ in ns2 for item in iter_)
def testcrds(): assert piece2obj.crd2diamondcrd(vec3(1,2,0)) == vec3(0,0,0) assert piece2obj.crd2diamondcrd(vec3(2,0,0)) == vec3(1,0,0) assert piece2obj.crd2diamondcrd(vec3(3,2,0)) == vec3(1,1,0) assert piece2obj.crd2diamondcrd(vec3(4,5,0)) == vec3(0,4,0) assert piece2obj.crd2diamondcrd(vec3(5,5,0)) == vec3(1,4,0) assert piece2obj.crd2diamondcrd(vec3(2,1,2)) == vec3(1,1,2) assert piece2obj.crd2diamondcrd(vec3(3,2,2)) == vec3(1,1,2) assert piece2obj.diamondcrd2crds(vec3(1,4,0)) == [vec3(5,5,0),vec3(6,4,0)] assert piece2obj.diamondcrd2crds(vec3(0,4,0)) == [vec3(4,5,0),vec3(5,6,0)] assert piece2obj.diamondcrd2crds(vec3(1,0,2)) == [vec3(1,1,2),vec3(2,0,2)] assert piece2obj.diamondcrd2crds(vec3(1,1,2)) == [vec3(2,1,2),vec3(3,2,2)]
def plotLine(self, **kwargs):
gs = kwargs.get('gs',None)
figGS = kwargs.get('figGS',None)
func = kwargs.get('func',None)
origin = kwargs.get('origin', vec3(0.,0.,0.))
direc = kwargs.get('direc', (np.pi/2, 0.))
lims = kwargs.get('lims', (-80.,80.))
extents = kwargs.get('extents',None)
npoints = kwargs.get('npoints', 320)
if func is None:
func = self.evalpotential
if extents is not None:
lims = (-extents, extents)
# Prepare set of points for plot
t = np.linspace( lims[0], lims[1], npoints )
unit = vec3()
th = direc[0]
ph = direc[1]
unit.set_spherical(1, th, ph)
# Convert vec3s to ndarray
unit = np.array(unit)
origin = np.array(origin)
#
XYZ = origin + np.outer(t, unit)
X = XYZ[:,0]
Y = XYZ[:,1]
Z = XYZ[:,2]
if gs is None:
# Prepare figure
fig = plt.figure(figsize=(9,4.5))
gs = matplotlib.gridspec.GridSpec( 1,2, wspace=0.2)
ax0 = fig.add_subplot( gs[0,0], projection='3d')
ax1 = fig.add_subplot( gs[0,1])
else:
gsSub0 = matplotlib.gridspec.GridSpecFromSubplotSpec( 2,2, subplot_spec=gs,\
width_ratios=[1,1.6], height_ratios=[1,1],\
wspace=0.25)
ax0 = figGS.add_subplot( gsSub0[0,0], projection='3d')
ax1 = figGS.add_subplot( gsSub0[0:2,1] )
ax2 = figGS.add_subplot( gsSub0[1,0] )
ax1.set_xlim( lims[0],lims[1])
ax2.set_xlim( lims[0]/2.,lims[1]/2.)
ax2.grid()
ax2.set_xlabel('$\mu\mathrm{m}$', fontsize=14)
ax0.plot(X, Y, Z, c='blue', lw=3)
ax0.set_xlabel('X')
ax0.set_ylabel('Y')
ax0.set_zlabel('Z')
lmin = min([ ax0.get_xlim()[0], ax0.get_ylim()[0], ax0.get_zlim()[0] ] )
lmax = max([ ax0.get_xlim()[1], ax0.get_ylim()[1], ax0.get_zlim()[1] ] )
ax0.set_xlim( lmin, lmax )
ax0.set_ylim( lmin, lmax )
ax0.set_zlim( lmin, lmax )
LMIN = np.ones_like(X)*lmin
LMAX = np.ones_like(X)*lmax
ax0.plot(X, Y, LMIN, c='gray', lw=2,alpha=0.3)
ax0.plot(LMIN, Y, Z, c='gray', lw=2,alpha=0.3)
ax0.plot(X, LMAX, Z, c='gray', lw=2,alpha=0.3)
ax0.set_yticklabels([])
ax0.set_xticklabels([])
ax0.set_zticklabels([])
ax0.text2D(0.05, 0.87, kwargs.get('ax0label',None),transform=ax0.transAxes)
# Evaluate function at points and make plot
EVAL = func(X,Y,Z, **kwargs)
# EVAL can be of various types, handled below
Emin =[]; Emax=[]
if isinstance(EVAL,list):
for p in EVAL:
if isinstance(p,dict):
if 'y' in p.keys():
whichax = p.get('axis',1)
axp = ax2 if whichax ==2 else ax1
porder = p.get('zorder',2)
labelstr = p.get('label',None)
fill = p.get('fill', False)
if fill:
ydat = p.get('y',None)
if ydat is not None:
axp.plot(t,ydat[0],
lw=p.get('lw',2.),\
color=p.get('color','black'),\
alpha=p.get('fillalpha',0.5),\
zorder=porder,\
label=labelstr
)
axp.fill_between( t, ydat[0], ydat[1],\
lw=p.get('lw',2.),\
color=p.get('color','black'),\
facecolor=p.get('fillcolor','gray'),\
alpha=p.get('fillalpha',0.5),\
zorder=porder
)
Emin.append( min( ydat[0].min(), ydat[1].min() ))
Emax.append( max( ydat[0].max(), ydat[1].max() ))
else:
ydat = p.get('y',None)
if ydat is not None:
axp.plot( t, ydat,\
lw=p.get('lw',2.),\
color=p.get('color','black'),\
alpha=p.get('alpha',1.0),\
zorder=porder,\
label=labelstr
)
Emin.append( ydat.min() )
Emax.append( ydat.max() )
elif 'figprop' in p.keys():
figsuptitle = p.get('figsuptitle', None)
figGS.suptitle(figsuptitle, y=kwargs.get('suptitleY',1.0),fontsize=14)
figGS.text(0.5,kwargs.get('foottextY',1.0),p.get('foottext',None),fontsize=14,
ha='center')
else:
ax1.plot(t,p); Emin.append(p.min()); Emax.append(p.max())
elif len(EVAL.shape) > 1 :
for i,E in enumerate(EVAL):
ax1.plot(t,E); Emin.append(E.min()); Emax.append(E.max())
else:
ax1.plot( t, EVAL); Emin.append(E.min()), Emax.append(E.max())
Emin = min(Emin); Emax=max(Emax)
dE = Emax-Emin
ax1.grid()
ax1.set_xlabel('$\mu\mathrm{m}$', fontsize=14)
ax1.set_ylabel( self.unitlabel, rotation=0, fontsize=14, labelpad=-5 )
# Finalize figure
if gs is None:
gs.tight_layout(fig, rect=[0.,0.,1.0,1.0])
return Emin-0.05*dE, Emax+0.05*dE, ax1
else:
ax2.xaxis.set_major_locator( matplotlib.ticker.MultipleLocator(20) )
ax2.xaxis.set_minor_locator( matplotlib.ticker.MultipleLocator(10) )
return Emin-0.05*dE, Emax+0.05*dE, ax1, ax2
else:
# glass
world.add(sphere(center, 0.2, dielectric(1.5)))
return world
width = 200
aspectRatio = 16 / 9
height = int(width / aspectRatio)
image = width * height * [None]
maxDepth = 10
sampleCount = 1
lookFrom = vec3(13, 2, 3)
lookAt = vec3(0, 0, 0)
vUp = vec3(0, 1, 0)
distToFocus = 10
aperture = 0 # 0.1
fovy = 20
myCamera = camera(lookFrom, lookAt, vUp, fovy, aspectRatio, aperture,
distToFocus)
scene = generateScene()
i = 0
for y in range(height):
print("Berechne Zeile", y)
for x in range(width):
c = vec3(0, 0, 0)
def doDot():
v0 = vec3(1.0, 2.0, 3.0)
v1 = vec3(2.0, 1.0, 3.0)
return v0.dot(v1)
def surfcut_points(**kwargs):
"""
Defines an surface cut through the potential geometry. Parameters are given
as keyword arguments (kwargs).
All distances are in microns.
Parameters
----------
npoints : number of points along the cut
extents : a way of specifying the limits for a cut that is symmetric
about the cut origin. the limits will be
lims = (-extents, extents)
lims : used only if extents = None. limits are specified using
a tuple ( min, max )
direc : tuple, two elements. polar coordinates for the direcdtion
of the cut
origin : tuple, three elements. cartesian coordinates for the origin
of the cut
ax0 : optional axes where the reference surface for the surface
cut can be plotted
Returns
-------
T0, T1 : arrays which parameterizes the position on the cut surface
X, Y, Z : each of X,Y,Z is an array with the same shape as T0 and T1.
They correspond to the cartesian coordinates of all the
points on the cut surface.
Notes
----
Examples
--------
"""
npoints = kwargs.get('npoints', 240)
origin = kwargs.get('origin', vec3(0., 0., 0.))
normal = kwargs.get('normal', (np.pi / 2., 0.))
lims0 = kwargs.get('lims0', (-50., 50.))
lims1 = kwargs.get('lims1', (-50., 50.))
extents = kwargs.get('extents', None)
if extents is not None:
lims0 = (-extents, extents)
lims1 = (-extents, extents)
# Make the unit vectors that define the plane
unit = vec3()
th = normal[0]
ph = normal[1]
unit.set_spherical(1, th, ph)
orth0 = vec3(-1. * np.sin(ph), np.cos(ph), 0.)
orth1 = cross(unit, orth0)
t0 = np.linspace(lims0[0], lims0[1], npoints)
t1 = np.linspace(lims1[0], lims1[1], npoints)
# Obtain points on which function will be evaluated
T0, T1 = np.meshgrid(t0, t1)
X = origin[0] + T0 * orth0[0] + T1 * orth1[0]
Y = origin[1] + T0 * orth0[1] + T1 * orth1[1]
Z = origin[2] + T0 * orth0[2] + T1 * orth1[2]
# If given an axes it will plot the reference surface to help visusalize
# the surface cut
# Note that the axes needs to be created with a 3d projection.
# For example:
# fig = plt.figure( figsize=(4.,4.) )
# gs = matplotlib.gridspec.GridSpec( 1,1 )
# ax0 = fig.add_subplot( gs[0,0], projection='3d' )
ax0 = kwargs.get('ax0', None)
if ax0 is not None:
# Plot the reference surface
ax0.plot_surface(X,
Y,
Z,
rstride=8,
cstride=8,
alpha=0.3,
linewidth=0.)
ax0.set_xlabel('X')
ax0.set_ylabel('Y')
ax0.set_zlabel('Z')
lmin = min([ax0.get_xlim()[0], ax0.get_ylim()[0], ax0.get_zlim()[0]])
lmax = max([ax0.get_xlim()[1], ax0.get_ylim()[1], ax0.get_zlim()[1]])
ax0.set_xlim(lmin, lmax)
ax0.set_ylim(lmin, lmax)
ax0.set_zlim(lmin, lmax)
ax0.set_yticklabels([])
ax0.set_xticklabels([])
ax0.set_zticklabels([])
# If given an axes and a potential it will plot the surface cut of the
# potential
ax1 = kwargs.get('ax1', None)
pot = kwargs.get('potential', None)
if (ax1 is not None) and (pot is not None):
# Evaluate function at points and plot
EVAL = pot.evalpotential(X, Y, Z)
im = ax1.pcolormesh(T0, T1, EVAL, cmap=plt.get_cmap('jet'))
# cmaps: rainbow, jet
plt.axes(ax1)
cbar = plt.colorbar(im)
cbar.set_label(pot.unitlabel, rotation=0) #self.unitlabel
return T0, T1, X, Y, Z
def creategfxobject(vertices,indices): initgfxmesh(quat(1,0,0,0),vec3(0,0,0),vertices,indices) createobject()
def testAttrMerge(s):
v = vec3(0.0, 0.0, 0.0)
if s: v.x = 1.0
return v.x
def coordinate_from_pixel(x, y):
coor = vec3((x / dimension), (y / dimension), 1)
return coor
def plotCross(self,
axes = None,
func = None,
origin = vec3(0.,0.,0.),
normal = (np.pi/2, 0),
lims0 = (-50,50),
lims1 = (-50,50),
extents = None,
npoints = 240 ):
if func is None:
func = self.evalpotential
if extents is not None:
lims0 = (-extents, extents)
lims1 = (-extents, extents)
# Make the unit vectors that define the plane
unit = vec3()
th = normal[0]
ph = normal[1]
unit.set_spherical( 1, th, ph)
#orth1 = -1.*vec3( np.cos(th)*np.cos(ph) , np.cos(th)*np.sin(ph), -1.*np.sin(th) )
orth0 = vec3( -1.*np.sin(ph), np.cos(ph), 0. )
orth1 = cross(unit,orth0)
t0 = np.linspace( lims0[0], lims0[1], npoints )
t1 = np.linspace( lims1[0], lims1[1], npoints )
# Obtain points on which function will be evaluated
T0,T1 = np.meshgrid(t0,t1)
X = origin[0] + T0*orth0[0] + T1*orth1[0]
Y = origin[1] + T0*orth0[1] + T1*orth1[1]
Z = origin[2] + T0*orth0[2] + T1*orth1[2]
if axes is None:
# Prepare figure
fig = plt.figure(figsize=(9,4.5))
gs = matplotlib.gridspec.GridSpec( 1,2, wspace=0.2)
ax0 = fig.add_subplot( gs[0,0], projection='3d')
ax1 = fig.add_subplot( gs[0,1])
else:
ax0 = axes[0]
ax1 = axes[1]
# Plot the reference surface
ax0.plot_surface(X, Y, Z, rstride=8, cstride=8, alpha=0.3, linewidth=0.)
ax0.set_xlabel('X')
ax0.set_ylabel('Y')
ax0.set_zlabel('Z')
lmin = min([ ax0.get_xlim()[0], ax0.get_ylim()[0], ax0.get_zlim()[0] ] )
lmax = max([ ax0.get_xlim()[1], ax0.get_ylim()[1], ax0.get_zlim()[1] ] )
ax0.set_xlim( lmin, lmax )
ax0.set_ylim( lmin, lmax )
ax0.set_zlim( lmin, lmax )
ax0.set_yticklabels([])
ax0.set_xticklabels([])
ax0.set_zticklabels([])
# Evaluate function at points and plot
EVAL = func(X,Y,Z)
T1_1d = np.ravel(T1)
EVAL_1d = np.ravel(EVAL)
im =ax1.pcolormesh(T0, T1, EVAL, cmap = plt.get_cmap('jet')) # cmaps: rainbow, jet
plt.axes( ax1)
cbar = plt.colorbar(im)
cbar.set_label(self.unitlabel, rotation=0 )#self.unitlabel
if axes is None:
# Finalize figure
gs.tight_layout(fig, rect=[0.,0.,1.0,1.0])
return EVAL.min(), EVAL.max(), im
def doDotHalf(a, b, c):
v0 = vec3(a, b, c)
v1 = vec3(2.0, 1.0, 3.0)
return v0.dot(v1)
def __init__(self, **kwargs):
"""Simple cubic lattice potential """
# Initialize lattice part
axes= [ (np.pi/2,0.), (np.pi/2, np.pi/2), (0,0) ]
self.l = kwargs.get('wavelength', 1.064)
self.m = kwargs.get('mass', 6.)
self.w = kwargs.get('waists', ((47.,47.), (47.,47.), (47.,47.)) )
self.r = kwargs.get('retro', (1.,1.,1.) )
self.a = kwargs.get('alpha', (1.,1.,1.) )
self.scale = kwargs.get('scale', 10.)
self.Er0 = Erecoil(self.l, self.m)
if 'allIR' in kwargs.keys():
self.Er = [kwargs.get('allIR', 7.0 )]*3
else:
self.Er = kwargs.get('Er', (7.0, 7.0, 7.0) )
lattbeams = [ LatticeBeam( axis=axes[i], Er=self.Er[i], wavelength=self.l, scale=self.scale,\
waists=self.w[i], retro=self.r[i], alpha=self.a[i] ) for i in range(3) ]
potential.__init__(self, lattbeams, units=('$E_{R}$', 1/self.Er0) )
self.GRw = kwargs.get('green_waists', ((40.,40.), (40.,40.), (40.,40.)) )
if 'allGR' in kwargs.keys():
self.GREr = [kwargs.get('allGR', 4.0 )]*3
else:
self.GREr = kwargs.get('green_Er', (4.0, 4.0, 4.0) )
self.GRl = kwargs.get('green_wavelength', 0.532)
# Express the power requiered for each GR beam, given the Er compensation value
# in units of the lattice recoil, and given the GR beam waists
GRmW = [ 1000.* self.GREr[i]* self.Er0/np.abs(U2uK(self.GRl)*2/np.pi) \
* self.GRw[i][0]*self.GRw[i][1] for i in range(3)]
self.greenbeams = [ GaussBeam( axis=axes[i], mW=GRmW[i], waists=self.GRw[i], wavelength=self.GRl) for i in range(3) ]
# Initialize quantities that will be used for the phase diagram
#
self.T = kwargs.get('Temperature', 1.6 )
self.fHdens = getHTSEInterp( self.T, name="density")
self.fHdoub = getHTSEInterp( self.T, name="doublons")
self.fHentr = getHTSEInterp( self.T, name="entropy" )
self.a_s = kwargs.get('a_s',300.)
#
# Make a cut line along 111 to calculate integrals of the
# thermodynamic quantities
direc111 = (np.arctan(np.sqrt(2)), np.pi/4)
unit = vec3(); th = direc111[0]; ph = direc111[1]
unit.set_spherical(1, th, ph); unitArr = np.array(unit)
t = np.linspace( -80, 80, 320 )
XYZ = np.outer( t, unitArr)
self.X111 = XYZ[:,0]
self.Y111 = XYZ[:,1]
self.Z111 = XYZ[:,2]
# Below we get the signed distance from the origin
self.r111 = self.X111*unit[0] + self.Y111*unit[1] + self.Z111*unit[2]
# Go ahead and calculate all relevant quantities along the 111
# direction
self.V0_111 = self.V0(self.X111,self.Y111,self.Z111)
self.Bottom_111 = self.Bottom(self.X111,self.Y111,self.Z111)
self.bands_111 = bands3dvec( self.V0_111, NBand=0 )
self.Ezero_111 = (self.bands_111[1]+self.bands_111[0])/2. + self.Bottom_111
self.Ezero0_111 = self.Ezero_111.min()
self.tunneling_111 = (self.bands_111[1]-self.bands_111[0])/12.
self.onsite_t_111 = Onsite( self.V0_111, a_s=self.a_s, lattice_spacing= self.l/2. ) / self.tunneling_111
self.verbose = kwargs.get('verbose', False)
# Initialize global chemical potential and atom number
# globalMu can be given directly or can be specified via the
# number of atoms. If the Natoms is specified we calculate
# the required gMu using this function:
muBrent = kwargs.get('muBrent', (0., 5.))
if muBrent is None: muBrent = (0., 5.)
if 'Natoms' in kwargs.keys():
self.Number = kwargs.get('Natoms', 3e5)
fN = lambda x : self.getNumber(x)- self.Number
if self.verbose:
print "Searching for globalMu => N=%.0f, "% self.Number,
self.globalMu, brentResults = optimize.brentq(fN, muBrent[0], muBrent[1], xtol=1e-2, rtol=2e4, full_output=True)
if self.verbose:
print "gMu=%.3f, " % brentResults.root,
print "n_iter=%d, " % brentResults.iterations,
print "n eval=%d, " % brentResults.function_calls,
print "conv?=", brentResults.converged
else :
# globalMu is given in Er, and is measured from the value
# of Ezero at the center of the potential
# When using it in the phase diagram it has to be changed to
# units of the tunneling
self.globalMu = kwargs.get('globalMu', 0.15)
# After the chemical potential is established the local chemical
# potential along 111 can be defined. It is used for column density
# plots and for calculating other thermodynamic quantities
gMuZero = self.Ezero0_111 + self.globalMu
self.localMu_t_111= (gMuZero - self.Ezero_111) / self.tunneling_111
# Obtain trap integrated values of the thermodynamic quantities
self.Number = self.getNumber( self.globalMu )
self.NumberD = self.getNumberD()
self.Entropy = self.getEntropy()
# MAKE FIGURE LABELS
# V Lattice
if len(np.unique(self.Er))==1:
VLlabel = '$V_{L}=%.2f$' % self.Er[0]
else:
VLlabel = '$V_{Lx}=%.1f, V_{Ly}=%.1f, V_{Lz}=%.1f$' % self.Er
# V Green
if len(np.unique(self.GREr))==1:
VGlabel = '$V_{G}=%.2f$' % self.GREr[0]
else:
VGlabel = '$V_{Gx}=%.1f, V_{Gy}=%.1f, V_{Gz}=%.1f$' % self.GREr
# Scattering length
aslabel = '$a_{s}=%.0f$' % self.a_s
# U/t label
Utlabel = '$U/t=%.1f$' % self.onsite_t_111.max()
# Temperature label
Tlabel = '$T/t=%.1f$' % self.T
self.figlabel = ', '.join([VLlabel, VGlabel, aslabel, Utlabel, Tlabel])
Nlabel = r'$N=%.2f\times 10^{5}$' % (self.Number/1e5)
Dlabel = r'$D=%.3f$' % ( self.NumberD / self.Number )
Slabel = r'$S/N=%.2f$' % ( self.Entropy / self.Number )
self.foottext = ', '.join([Nlabel, Dlabel, Slabel])
def doDotFull(a, b, c, d, e, f):
v0 = vec3(a, b, c)
v1 = vec3(d, e, f)
return v0.dot(v1)
def vecSwitch(s):
if s:
return vec3(11.0, 11.0, 11.0)
else:
return vec3(7.0, 7.0, 7.0)
def linecut_points(**kwargs):
"""
Defines an line cut through the potential geometry. Parameters are given
as keyword arguments (kwargs).
All distances are in microns.
Parameters
----------
npoints : number of points along the cut
extents : a way of specifying the limits for a cut that is symmetric
about the cut origin. the limits will be
lims = (-extents, extents)
lims : used only if extents = None. limits are specified using
a tuple ( min, max )
direc : tuple, two elements. polar coordinates for the direcdtion
of the cut
origing : tuple, three elements. cartesian coordinates for the origin
of the cut
Returns
-------
t : array which parameterizes the distance along the cut
X, Y, Z : each of X,Y,Z is an array with the same shape as t.
They correspond to the cartesian coordinates of all the
points along the cut
Notes
----
Examples
--------
"""
npoints = kwargs.get('npoints', 320)
extents = kwargs.get('extents', None)
lims = kwargs.get('lims', (-80., 80.))
direc = kwargs.get('direc', (np.pi / 2, 0.))
origin = kwargs.get('origin', vec3(0., 0., 0.))
if extents is not None:
lims = (-extents, extents)
# Prepare set of points for plot
t = np.linspace(lims[0], lims[1], npoints)
unit = vec3()
th = direc[0]
ph = direc[1]
unit.set_spherical(1, th, ph)
# Convert vec3s to ndarray
unit = np.array(unit)
origin = np.array(origin)
#
XYZ = origin + np.outer(t, unit)
X = XYZ[:, 0]
Y = XYZ[:, 1]
Z = XYZ[:, 2]
return t, X, Y, Z, lims
def vecAttrSwitch(s):
a = vec3(11.0, 11.0, 11.0)
b = vec3(7.0, 7.0, 7.0)
v = vec3(0.0, 0.0, 0.0)
attrMunge(s, v, a, b)
return v
def confusedSite(b): if b: return vec3(7.0, 7.0, 7.0) else: return vec3(11.0, 11.0, 11.0)