def ComputeSpringForce(Nodes,Spring_Eq,K,time):
"""
ComputeSpringForce(x,y,Spring_Eq,K,time)
Finds the inward force exerted by the two springs pulling on each node.
Uses Hooke's Law and assumes two springs pull on each node.
:param Nodes: structure containing nodes
:type Nodes: struct
:param Spring_Eq: array of spring equilibrium values.
:type Spring_Eq: np.array
:param K: array of K values.
:type K: np.array
:returns: updated node structure.
.. note::
K values typically change with age.
"""
theta,foo = dm.cart2pol(Nodes['x'][time], Nodes['y'][time])
distance = CircularDist(Nodes['x'][time], Nodes['y'][time])
F_s1 = -K * (Spring_Eq - distance)
F_s2 = np.r_[F_s1[-1], F_s1[0:-1]]
F_S = F_s1 + F_s2
Nodes['f_sx'],Nodes['f_sy'] = dm.pol2cart(theta, F_S)
return Nodes
def CheckNodes(Nodes,time):
"""
Make sure that the nodes do not cross over or move in towards the center.
:param Nodes: node structure
:param time: time in the integration algorithm
:returns: Nodes updated node structure.
"""
# Conditionals constraining the motion of nodes
Nodes['theta'][time+1,:], Nodes['r'][time+1,:] = dm.cart2pol(Nodes['x'][time], Nodes['y'][time])
# Ensure that no nodes move inwards
a = np.nonzero(Nodes['r'][time+1,:] - Nodes['r'][time,:]<0)[0]
Nodes['i'][time+1,:],n = dm.MatlabSort(Nodes['theta'][time+1,:])
if time > 1:
# Ensure that no nodes cross over
c = np.nonzero([Nodes['i'][time+1,:] - Nodes['i_initial']!=0])[0]
else:
a = np.array([])
c = np.array([])
if len(a) > 0 and len(c) > 0:
Nodes['r'][time+1,a] = Nodes['r'][time,a]
d = Nodes['i'][time+1,c]
Nodes['theta'][time+1,d] = Nodes['theta'][time,d]
Nodes['x'],Nodes['y'] = dm.pol2cart(Nodes['theta'][time+1,:], Nodes['r'][time+1,:])
elif np.sum(c)>0:
d = Nodes['i'][time+1,c]
Nodes['theta'][time+1,d] = Nodes['theta'][time,d]
Nodes['x'],Nodes['y'] = dm.pol2cart(Nodes['theta'][time+1,:], Nodes['r'][time+1,:])
elif np.sum(a)>0:
Nodes['r'][time+1,a]= Nodes['r'][time,a]
Nodes['x'][time],Nodes['y'][time] = dm.pol2cart(Nodes['theta'][time+1,:], Nodes['r'][time+1,:])
return Nodes
def GenerateNodes(NumberofNodes=36,age=6,Pressure=0.002,LengthofTime=12,INTSTEP=0.01):
"""
Creates a structure of nodes based on the input parameters.
:param NumberofNodes: the number of nodes desired.
:type NumberofNodes: int
:param age: age at the start of the simulation, in years.
:type age: float
:param Pressure: intraocular pressure.
:type Pressure: float
:param LengthofTime: duration of the simulation, in years.
:type LengthofTime: int
:param INTSTEP: integration step, in fraction of a year.
:type INTSTEP: float
:returns: structure of nodes
.. note::
Initial node acceleration is still a free parameter.
"""
AGE = np.linspace(age,age + LengthofTime,LengthofTime/INTSTEP)
# Parameters of emmetropic eye from 2004 paper:
Child_Eye_Length = EyeLength(age) # in mm
initial_node_acc = NodeRate(age,INTSTEP)
Radius = Child_Eye_Length/2.0
F_Px_initial = np.ones((NumberofNodes)) * Pressure * 0.5
F_Py_initial = np.ones((NumberofNodes)) * Pressure * 0.5
# memory for x positions:
x = np.zeros(( (LengthofTime / INTSTEP) + 1, NumberofNodes))
y = np.zeros(( (LengthofTime / INTSTEP) + 1, NumberofNodes))
# set the start location of each of the nodes.
location = np.linspace(0, 2 * np.pi - (2 * np.pi / NumberofNodes), NumberofNodes)
x[0,:] = np.cos(location) # 16mm typical size @ birth.
y[0,:] = np.sin(location)
Pressure = Pressure/NumberofNodes
THETA, R = dm.cart2pol(x[0,:],y[0,:])
I_initial, foo = dm.MatlabSort(THETA)
I_initial = I_initial[np.newaxis,:]
Initial_Area = np.sum((R**2) * np.pi / len(R))
# Preallocate memory
# Memory for checks:
r = np.zeros(((LengthofTime/INTSTEP)+1, NumberofNodes))
theta = np.zeros(((LengthofTime/INTSTEP)+1, NumberofNodes))
I = np.zeros(((LengthofTime/INTSTEP)+1, NumberofNodes))
# Memory for velocities.
xDOT,yDOT = dm.pol2cart(THETA,initial_node_acc * 4)
xDOT = np.ones((NumberofNodes)) * xDOT
yDOT = np.ones((NumberofNodes)) * yDOT
# Memory for force.
xx = np.zeros((NumberofNodes))
yy = np.zeros((NumberofNodes))
# Memory for eye length.
ModelEyeLength = np.zeros((LengthofTime / INTSTEP,1))
Nodes = {'x': x,
'y': y,
'radius': Radius,
'f_px_initial': F_Px_initial,
'f_py_initial': F_Py_initial,
'f_px': [],
'f_py': [],
'node_accel': initial_node_acc,
'pressure': Pressure,
'xDOT': xDOT,
'yDOT': yDOT,
'xx': xx,
'yy': yy,
'initial_area': Initial_Area,
'i_initial': I_initial[0],
'r': r,
'theta': theta,
'i': I,
'modeleyelength': ModelEyeLength,
'age': AGE
}
return Nodes
