class Shell:
'''
A shell consists of two segments, one in the front and one behind. The base location
of the front segment has a smaller z value than that of the back segement. Thus, rays
coming from sources in the negative z range will enter the front end first.
'''
def __init__(self,
base = [0,0,0],
seglen = 30.0,
ang = 0.00643866102405, # focal length of 2m
r = 5.151
):
'''
Constructor
Parameters:
base: the center point of the wide end of the segment
seglen: the axial length of each segment
ang: angle between the shell axis and the side of the front segment
r: radius of the shell where the two segments meet
'''
self.front = Segment(base=base, seglen=seglen, ang=ang, r1=r)
backBase = [base[0], base[1], base[2]+seglen]
self.back = Segment(base=backBase, seglen=seglen, ang=3*ang, r0=r)
def getSurfaces(self):
'''
Returns a list of surfaces
'''
return [self.front,self.back]
def plot2D(self, axes, color = 'b'):
'''
Plots a 2d cross section of the shell
'''
self.front.plot2D(axes, color)
self.back.plot2D(axes, color)
# plot rays
ang = self.front.ang
r = self.back.r1
z = self.back.base[2]
d = r*tan((pi/2)-4*ang)
axes.plot((2*z,2*z+d),(r,0),'y:')
axes.plot((2*z,2*z+d),(-r,0),'y:')
def plot3D(self, axes, color = 'b'):
'''
Generates a 3d plot of the shell in the given figure
'''
self.front.plot3D(axes,color)
self.back.plot3D(axes,color)
def targetFront(self,a,b):
'''
Takes two list arguments of equal size, the elements of which range from 0 to 1.
Returns an array of points that exist on the circle defined by the wide end of
the shell.
'''
return self.front.targetFront(a,b)
def targetBack(self,a,b):
'''
Takes two list arguments of equal size, the elements of which range from 0 to 1.
Returns an array of points that exist on the circle defined by the small end of
the shell.
'''
return self.back.targetBack(a,b)
class Module:
'''
A complete foxsi module. By default, it consists of seven nested shells.
'''
def __init__(self,
base = [0,0,0],
seglen = 30.0,
focal = 200.0,
radii = [5.151,4.9,4.659,4.429,4.21,4.0,3.799],
angles = None
):
'''
Constructor
Parameters:
base: the center point of the wide end of the segment
seglen: the axial length of each segment
focal: the focal length, measured from the center of the module
radii: a list of radii, one for each shell from biggest to smallest
angles: optional parameter to overwrite the shell angles computed by constructor
'''
if angles is None:
angles = calcShellAngle(radii,focal)
elif len(radii) != len(angles):
raise ValueError('number of radii and number of angles do not match')
self.shells = []
for i,r in enumerate(radii):
self.shells.append(Shell(base=base, seglen=seglen, ang=angles[i], r=r))
# inner core (blocks rays going through center of module)
r0 = self.shells[-1].back.r0
r1 = r0 - seglen * tan(4*angles[-1])
ang = atan((r0-r1)/(2*seglen))
self.core = Segment(base=base, seglen=2*seglen, ang=ang, r0=r0)
self.coreFaces = [Circle(center=base,normal=[0,0,1],radius=r0),
Circle(center=[base[0],base[1],base[2]+2*seglen],normal=[0,0,-1],radius=r1)]
def getDims(self):
'''
Returns the module's dimensions:
[radius at wide end, radius at small end, length]
'''
front = self.shells[0].front
back = self.shells[0].back
return [front.r0, back.r1, front.seglen+back.seglen]
def getSurfaces(self):
'''
Returns a list of surfaces
'''
surfaces = []
for shell in self.shells:
surfaces.extend(shell.getSurfaces())
surfaces.append(self.core)
surfaces.extend(self.coreFaces)
return(surfaces)
def passRays(self, rays, robust = False):
'''
Takes an array of rays and passes them through the front end of
the module.
'''
#print 'Module: passing ',len(rays),' rays'
# get all module surfaces
allSurfaces = self.getSurfaces()
allSurfaces.remove(self.coreFaces[0]) # we'll test these seperately
allSurfaces.remove(self.coreFaces[1])
# create regions consisting of adjacent shells
regions = [None for shell in self.shells]
for i,shell in enumerate(self.shells):
# innermost shell
if i == len(self.shells)-1:
regions[i] = shell.getSurfaces()
regions[i].append(self.core)
else:
regions[i] = shell.getSurfaces() # outer shell (reflective side facing region)
regions[i].extend(self.shells[i+1].getSurfaces()) # nested shell (non reflective)
for ray in rays:
# skip rays that hit a core face
if ray.pos[2] < self.coreFaces[0].center[2]:
sol = self.coreFaces[0].rayIntersect(ray)
if sol is not None:
ray.pos = ray.getPoint(sol[2])
ray.bounces += 1
ray.dead = True
continue
else: ray.moveToZ(self.coreFaces[0].center[2])
elif ray.pos[2] > self.coreFaces[1].center[2]:
sol = self.coreFaces[1].rayIntersect(ray)
if sol is not None:
ray.pos = ray.getPoint(sol[2])
ray.bounces += 1
ray.dead = True
continue
else: ray.moveToZ(self.coreFaces[1].center[2])
# reset surfaces
surfaces = [s for s in allSurfaces]
firstBounce = True # used for optimization
# while ray is inside module
while True:
# find nearest ray intersection
bestDist = None
bestSol = None
bestSurf = None
for surface in surfaces:
sol = surface.rayIntersect(ray)
if sol is not None:
dist = norm(ray.getPoint(sol[2])-ray.pos)
if bestDist is None or dist < bestDist:
bestDist = dist
bestSol = sol
bestSurf = surface
# if a closest intersection was found
if bestSol is not None:
# update ray
ray.pos = ray.getPoint(bestSol[2])
ray.bounces += 1
x = reflect(ray.ori,bestSurf.getNormal(bestSol[0],bestSol[1]))
# if reflected
if x is not None:
ray.ori = x / norm(x) # update ori to unit vector reflection
# otherwise, no reflection means ray is dead
else:
ray.dead = True
break
# knowing the surface it has just hit, we can
# narrow down the number of surface to test
# remove shells the ray cannot even 'see'
if firstBounce:
firstBounce = False
for region in regions:
if bestSurf is region[0] or bestSurf is region[1]:
surfaces = [s for s in region]
break
# assuming each segment can be hit no more than once
# eliminate the surface from our list
if not robust: surfaces.remove(bestSurf)
# if no intersection, ray can exit module
else: break
def plot2D(self, axes, color = 'b'):
'''
Plots a 2d cross section of the module
'''
for shell in self.shells:
shell.plot2D(axes, color)
# plot core
self.core.plot2D(axes, color)
base = self.core.base
r0 = self.core.r0
r1 = self.core.r1
seglen = self.core.seglen
axes.plot((base[2],base[2]),(r0,-r0),'-'+color)
axes.plot((base[2]+seglen,base[2]+seglen),(r1,-r1),'-'+color)
def plot3D(self, axes, color = 'b'):
'''
Generates a 3d plot of the module in the given figure
'''
for shell in self.shells:
shell.plot3D(axes,color)
def targetFront(self,a,b):
'''
Takes two list arguments of equal size, the elements of which range from 0 to 1.
Returns an array of points that exist on the circle defined by the wide end of
the module.
'''
#must modify 'a' so that we dont return points from the core
r0 = self.shells[0].front.r0
r1 = self.core.r0
a0 = (r1/r0)**2 # the 'a' value that gives r1=sqrt(a)*r0
adiff = 1 - a0
for i in range(len(a)):
a[i] = a[i]*adiff + a0
return self.shells[0].targetFront(a,b)
def targetBack(self,a,b):
'''
Takes two list arguments of equal size, the elements of which range from 0 to 1.
Returns an array of points that exist on the circle defined by the small end of
the module.
'''
#must modify 'a' so that we dont return points from the core
r0 = self.shells[0].back.r1
r1 = self.core.r1
a0 = (r1/r0)**2 # the 'a' value that gives r1=sqrt(a)*r0
adiff = 1 - a0
for i in range(len(a)):
a[i] = a[i]*adiff + a0
return self.shells[0].targetBack(a,b)