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ffd_axisymetric.py
333 lines (252 loc) · 13 KB
/
ffd_axisymetric.py
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import copy
import numpy as np
from bspline import Bspline
class Coordinates(object):
"""transforms points from Cartesian space to cylindrical space and vice versa"""
def __init__(self,points,cartesian=True):
"""cartisian flag indicates which type of coordinates are begin given"""
#cartesian: x along the length; y,z along the thickness
#cylindrical: x along the axis; r,theta along the thickness
points = np.array(points,dtype=np.float64)
if cartesian:
self.cartesian = points
X,Y,Z = points[:,0],points[:,1],points[:,2]
R = np.sqrt(Y**2+Z**2)
Theta = np.arctan2(Y,Z)
self.cylindrical = np.nan_to_num(np.vstack((X,R,Theta)).T)
else:
self.cylindrical = points
X,R,Theta = points[:,0],points[:,1],points[:,2]
Z = R*np.cos(Theta)
Y = R*np.sin(Theta)
self.cartesian = np.nan_to_num(np.vstack((X,Y,Z)).T)
class Body(object):
"""FFD class for solid bodies which only have one surface"""
def __init__(self,stl,controls,name="body", r_ref=None, x_ref=None):
"""stl must be an STL object"""
self.stl = stl
geom_points = stl.points
self.coords = Coordinates(geom_points,cartesian=True)
self.P = self.coords.cylindrical
self.P_cart = self.coords.cartesian
self.P_bar = geom_points.copy() #just initialization
if isinstance(controls,int):
X = geom_points[:,0]
x_max = np.max(X)
x_min = np.min(X)
C_x = np.linspace(x_min,x_max,controls)
C_r = np.zeros((controls,))
control_points = np.array(zip(C_x,C_r))
self.C = control_points
self.n_controls = controls
else:
self.C = controls
self.n_controls = len(controls)
self.C_bar = self.C.copy()
self.delta_C = np.zeros(self.C.shape)
self.bs = Bspline(self.C,geom_points)
self.name = name
if x_ref is not None:
self.x_mag = float(x_ref)
else:
self.x_mag = 10**np.floor(np.log10(np.average(geom_points[:,0])))
if r_ref is not None:
self.r_mag = float(r_ref)
else:
indecies = np.logical_and(abs(geom_points[:,2])<2E-6, geom_points[:,1]>0)
points = geom_points[indecies]
self.r_mag = 10**np.floor(np.log10(np.average(points[:,1]))) #grab the order of magnitude of the average
#for revolution of 2-d profile
#self.n_theta = 20
#sgrab the theta values from the points
self.Theta = self.P[:,2]
#this is too complex. shouldn't need to tile, then flatten later.
self.sin_theta = np.tile(np.sin(self.Theta),(self.n_controls,1)).T.flatten()
self.cos_theta = np.tile(np.cos(self.Theta),(self.n_controls,1)).T.flatten()
# self.sin_theta = np.tile(np.sin(self.Theta),self.n_controls)
# self.cos_theta = np.tile(np.cos(self.Theta),self.n_controls)
#calculate derivatives
#in polar coordinates
self.dP_bar_xqdC = np.array(self.x_mag*self.bs.B.flatten())
self.dP_bar_rqdC = np.array(self.r_mag*self.bs.B.flatten())
#Project Polar derivatives into revolved cartisian coordinates
self.dXqdC = self.dP_bar_xqdC.reshape(-1,self.n_controls)
self.dYqdC = (self.dP_bar_rqdC*self.sin_theta).reshape(-1,self.n_controls)
self.dZqdC = (self.dP_bar_rqdC*self.cos_theta).reshape(-1,self.n_controls)
def copy(self):
return copy.deepcopy(self)
def deform(self,delta_C):
"""returns new point locations for the given motion of the control
points"""
self.delta_C = delta_C
self.delta_C[:,0] = self.delta_C[:,0]*self.x_mag
self.C_bar = self.C+self.delta_C
delta_P = self.bs.calc(self.C_bar)
self.P_bar = self.P.copy()
self.P_bar[:,0] = delta_P[:,0]
self.P_bar[:,1] = self.P[:,1]+self.r_mag*delta_P[:,1]
#transform to cartesian coordinates
self.coords = Coordinates(self.P_bar,cartesian=False)
self.P_bar_cart = self.coords.cartesian
self.Xo = self.P_bar_cart[:,0]
self.Yo = self.P_bar_cart[:,1]
self.Zo = self.P_bar_cart[:,2]
self.stl.update_points(self.P_bar_cart)
return self.P_bar
class Shell(object):
"""FFD class for shell bodies which have two connected surfaces"""
def __init__(self, outer_stl, inner_stl, center_line_controls,
thickness_controls, name='shell', r_ref=None, x_ref=None):
self.outer_stl = outer_stl
self.inner_stl = inner_stl
outer_points = outer_stl.points
inner_points = inner_stl.points
self.n_outer = len(outer_points)
self.n_inner = len(inner_points)
self.outer_coords = Coordinates(outer_points, cartesian=True)
self.inner_coords = Coordinates(inner_points, cartesian=True)
self.Po = self.outer_coords.cylindrical
self.Pi = self.inner_coords.cylindrical
self.Po_cart = self.outer_coords.cartesian
self.Pi_cart = self.inner_coords.cartesian
#just initialization for array size
self.Po_bar = outer_points.copy()
self.Pi_bar = inner_points.copy()
self.name = name
if isinstance(center_line_controls,int):
X = outer_points[:,0]
x_max = np.max(X)
x_min = np.min(X)
C_x = np.linspace(x_min,x_max,center_line_controls)
C_r = np.zeros((center_line_controls,))
control_points = np.array(zip(C_x,C_r))
self.Cc = control_points
self.n_c_controls = center_line_controls
else:
self.Cc = center_line_controls
self.n_c_controls = len(center_line_controls)
self.Cc_bar = self.Cc.copy()
self.delta_Cc = np.zeros(self.Cc.shape)
if isinstance(thickness_controls,int):
X = inner_points[:,0]
x_max = np.max(X)
x_min = np.min(X)
C_x = np.linspace(x_min,x_max,thickness_controls)
C_r = np.zeros((thickness_controls,))
control_points = np.array(zip(C_x,C_r))
self.Ct = control_points
self.n_t_controls = thickness_controls
else:
self.Ct = thickness_controls
self.n_t_controls = len(thickness_controls)
self.Ct_bar = self.Ct.copy()
self.delta_Ct = np.zeros(self.Ct.shape)
self.bsc_o = Bspline(self.Cc,outer_points)
self.bsc_i = Bspline(self.Cc,inner_points)
self.bst_o = Bspline(self.Ct,outer_points)
self.bst_i = Bspline(self.Ct,inner_points)
self.name = name
if x_ref is not None:
self.x_mag = float(x_ref)
else:
self.x_mag = 10**np.floor(np.log10(np.average(outer_points[:,0])))
if r_ref is not None:
self.r_mag = float(r_ref)
else:
indecies = np.logical_and(abs(outer_points[:,2])<2E-6, outer_points[:,1]>0)
points = outer_points[indecies]
self.r_mag = 10**np.floor(np.log10(np.average(points[:,1]))) #grab the order of magnitude of the average
self.outer_theta = self.Po[:,2]
self.sin_outer_c_theta = np.tile(np.sin(self.outer_theta),(self.n_c_controls,1)).T.flatten()
self.cos_outer_c_theta = np.tile(np.cos(self.outer_theta),(self.n_c_controls,1)).T.flatten()
self.sin_outer_t_theta = np.tile(np.sin(self.outer_theta),(self.n_t_controls,1)).T.flatten()
self.cos_outer_t_theta = np.tile(np.cos(self.outer_theta),(self.n_t_controls,1)).T.flatten()
self.inner_theta = self.Pi[:,2]
self.sin_inner_c_theta = np.tile(np.sin(self.inner_theta),(self.n_c_controls,1)).T.flatten()
self.cos_inner_c_theta = np.tile(np.cos(self.inner_theta),(self.n_c_controls,1)).T.flatten()
self.sin_inner_t_theta = np.tile(np.sin(self.inner_theta),(self.n_t_controls,1)).T.flatten()
self.cos_inner_t_theta = np.tile(np.cos(self.inner_theta),(self.n_t_controls,1)).T.flatten()
#calculate derivatives
#in polar coordinates
self.dPo_bar_xqdCc = np.array(self.x_mag*self.bsc_o.B.flatten())
self.dPo_bar_rqdCc = np.array(self.r_mag*self.bsc_o.B.flatten())
self.dPi_bar_xqdCc = np.array(self.x_mag*self.bsc_i.B.flatten())
self.dPi_bar_rqdCc = np.array(self.r_mag*self.bsc_i.B.flatten())
self.dPo_bar_rqdCt = np.array(self.r_mag*self.bst_o.B.flatten())
self.dPi_bar_rqdCt = -1*np.array(self.r_mag*self.bst_i.B.flatten())
#Project Polar derivatives into revolved cartisian coordinates
self.dXoqdCc = self.dPo_bar_xqdCc.reshape(-1,self.n_c_controls)
self.dYoqdCc = (self.dPo_bar_rqdCc*self.sin_outer_c_theta).reshape(-1,self.n_c_controls)
self.dZoqdCc = (self.dPo_bar_rqdCc*self.cos_outer_c_theta).reshape(-1,self.n_c_controls)
self.dXiqdCc = self.dPi_bar_xqdCc.reshape(-1,self.n_c_controls)
self.dYiqdCc = (self.dPi_bar_rqdCc*self.sin_inner_c_theta).reshape(-1,self.n_c_controls)
self.dZiqdCc = (self.dPi_bar_rqdCc*self.cos_inner_c_theta).reshape(-1,self.n_c_controls)
self.dYoqdCt = (self.dPo_bar_rqdCt*self.sin_outer_t_theta).reshape(-1,self.n_t_controls)
self.dZoqdCt = (self.dPo_bar_rqdCt*self.cos_outer_t_theta).reshape(-1,self.n_t_controls)
self.dYiqdCt = (self.dPi_bar_rqdCt*self.sin_inner_t_theta).reshape(-1,self.n_t_controls)
self.dZiqdCt = (self.dPi_bar_rqdCt*self.cos_inner_t_theta).reshape(-1,self.n_t_controls)
def copy(self):
return copy.deepcopy(self)
def plot_geom(self,ax,initial_color='g',ffd_color='k'):
if initial_color:
ax.scatter(self.Po[:,0],self.Po[:,1],c=initial_color,s=50,label="%s initial geom"%self.name)
ax.scatter(self.Pi[:,0],self.Pi[:,1],c=initial_color,s=50)
ax.plot(self.Po[:,0],self.Po[:,1],c=initial_color)
ax.plot(self.Pi[:,0],self.Pi[:,1],c=initial_color)
if ffd_color:
ax.scatter(self.Po_bar[:,0],self.Po_bar[:,1],c=ffd_color,s=50,label="%s ffd geom"%self.name)
ax.scatter(self.Pi_bar[:,0],self.Pi_bar[:,1],c=ffd_color,s=50)
ax.plot(self.Po_bar[:,0],self.Po_bar[:,1],c=ffd_color)
ax.plot(self.Pi_bar[:,0],self.Pi_bar[:,1],c=ffd_color)
def plot_centerline_spline(self,ax,point_color='r',line_color='b'):
ax.scatter(self.Cc_bar[:,0],self.Cc_bar[:,1],c=point_color,s=50,label="%s Centerline Control Points"%self.name)
map_points = self.bsc_o(np.linspace(0,1,100))
ax.plot(map_points[:,0],map_points[:,1],label="Centerline b-spline Curve",c=line_color)
def plot_thickness_spline(self,ax,point_color='r',line_color='b'):
ax.scatter(self.Ct_bar[:,0],self.Ct_bar[:,1],c=point_color,s=50,label="%s Thickness Control Points"%self.name)
map_points = self.bst_o(np.linspace(0,1,100))
ax.plot(map_points[:,0],map_points[:,1],label="Thickness b-spline Curve",c=line_color)
def deform(self,delta_Cc,delta_Ct):
"""returns new point locations for the given motion of the control
points for center-line and thickness"""
self.delta_Cc = delta_Cc
self.delta_Cc[:,0]*=self.x_mag
self.Cc_bar = self.Cc+self.delta_Cc
delta_Pc_o = self.bsc_o.calc(self.Cc_bar)
delta_Pc_i = self.bsc_i.calc(self.Cc_bar)
self.delta_Ct = delta_Ct
self.Ct_bar = self.Ct+self.delta_Ct
delta_Pt_o = self.bst_o.calc(self.Ct_bar)
delta_Pt_i = self.bst_i.calc(self.Ct_bar)
self.Po_bar = self.Po.copy()
self.Pi_bar = self.Pi.copy()
self.Po_bar[:,0] = delta_Pc_o[:,0]
self.Po_bar[:,1] = self.Po[:,1]+self.r_mag*(delta_Pc_o[:,1]+delta_Pt_o[:,1])
self.Pi_bar[:,0] = delta_Pc_i[:,0]
self.Pi_bar[:,1] = self.Pi[:,1]+self.r_mag*(delta_Pc_i[:,1]-delta_Pt_i[:,1])
#transform to cartesian coordinates
self.outer_coords = Coordinates(self.Po_bar,cartesian=False)
self.inner_coords = Coordinates(self.Pi_bar,cartesian=False)
#Perform axial roation of 2-d polar coordiantes
#outer surface
self.Po_bar_cart = self.outer_coords.cartesian
self.Xo = self.Po_bar_cart[:,0]
self.Yo = self.Po_bar_cart[:,1]
self.Zo = self.Po_bar_cart[:,2]
self.outer_stl.update_points(self.Po_bar_cart)
#inner surface
self.Pi_bar_cart = self.inner_coords.cartesian
self.Xi = self.Po_bar_cart[:,0]
self.Yi = self.Po_bar_cart[:,1]
self.Zi = self.Po_bar_cart[:,2]
self.inner_stl.update_points(self.Pi_bar_cart)
return self.Po_bar,self.Pi_bar
if __name__ == "__main__":
p = [[0,0,0],[0,0,1],[0,1,0]]
p_prime = Coordinates(p,cartesian=True)
print p_prime.cartesian
print p_prime.cylindrical
p = [[0,0,0],[0,1,0],[0,1,np.pi/2]]
p_prime = Coordinates(p,cartesian=False)
print p_prime.cartesian
print p_prime.cylindrical