def plot_fig(rot_mat_m, pts_m, ang, na):
fig = plt.figure(figsize=(12, 12), facecolor='w')
plt.margins(0.05)
rot_mat = rot_mat_m
pts = pts_m
tout = area_preserv_proj(pts, rot_mat, tol=1e-08)
pt_stereo1 = tout[0]
plt.plot(pt_stereo1[:, 0], pt_stereo1[:, 1], 'o', \
markerfacecolor='red', markersize=2)
### General boundary conditions for rest of the bicrystal symmetries
rot_mat = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
num1 = 100
phi = np.linspace(0, ang, num1)
theta = np.linspace(np.pi/2, np.pi/2, num1)
tpts = np.zeros((num1, 3))
tpts[:, 0] = np.sin(theta)*np.cos(phi)
tpts[:, 1] = np.sin(theta)*np.sin(phi)
tpts[:, 2] = np.cos(theta)
tout = area_preserv_proj(tpts, rot_mat, tol=1e-08)
tpts_stereo = tout[0]
plt.plot(tpts_stereo[:, 0], tpts_stereo[:, 1], color=(0, 0, 0))
num1 = 100
phi = np.linspace(0, 0, num1)
theta = np.linspace(0, np.pi/2, num1)
tpts = np.zeros((num1, 3))
tpts[:, 0] = np.sin(theta)*np.cos(phi)
tpts[:, 1] = np.sin(theta)*np.sin(phi)
tpts[:, 2] = np.cos(theta)
tout = area_preserv_proj(tpts, rot_mat, tol=1e-08)
tpts_stereo = tout[0]
plt.plot(tpts_stereo[:, 0], tpts_stereo[:, 1], color=(0, 0, 0))
num1 = 100
phi = np.linspace(ang, ang, num1)
theta = np.linspace(0, np.pi/2, num1)
tpts = np.zeros((num1, 3))
tpts[:, 0] = np.sin(theta)*np.cos(phi)
tpts[:, 1] = np.sin(theta)*np.sin(phi)
tpts[:, 2] = np.cos(theta)
tout = area_preserv_proj(tpts, rot_mat, tol=1e-08)
tpts_stereo = tout[0]
plt.plot(tpts_stereo[:, 0], tpts_stereo[:, 1], color=(0, 0, 0))
plt.axis('equal')
plt.axis('off')
# plt.tight_layout()
plt.savefig('min_Sig3_' +'bpn' + na + '.png', dpi=100, bbox_inches='tight')
return
def plot_2d_fz(rot_mat_m, pts_m, ang, ct1, sig, r, n):
"""
Creates the boundaries for 2-D FZ of the particular bicrystal symmetry and plots the normals in FZ.
Parameters
----------
rot_mat_m:
pts_m:
ang:
ct1:
sig:
r:
n:
"""
####################################################################################################################
### Creating the plot figure using matplotlib
fig = plt.figure(figsize=(12, 12), facecolor='w')
plt.margins(0.05)
### Plotting the bpn using area preserving projection
rot_mat = rot_mat_m
pts = pts_m
tout = area_preserv_proj(pts, rot_mat, tol=1e-08)
pt_stereo1 = tout[0]
plt.plot(pt_stereo1[:, 0], pt_stereo1[:, 1], 'o', markerfacecolor='red', markersize=4)
####################################################################################################################
### Plotting the boundaries of 2d FZ of the bicrystal point group
if ang == 'O_h':
### Special case for O_h bicrystal symmetry boundaries
rot_mat = np.array([[0,0,1], [1,0,0], [0,1,0]])
num1 = 100
tphi = np.linspace(0, np.pi/4, num1)
tpts1 = np.zeros((num1, 3))
tpts1[:, 0] = np.cos(tphi)
tpts1[:, 1] = np.sin(tphi)
tout = area_preserv_proj(tpts1, rot_mat, tol=1e-08)
tpts1_stereo = tout[0]
plt.plot(tpts1_stereo[:, 0], tpts1_stereo[:, 1], color=(0, 0, 0))
num1 = 100
th1 = np.arctan(np.sqrt(2))
tphi = np.linspace(np.pi/4, np.pi/4, num1)
ttheta = np.linspace(th1, np.pi/2, num1)
tpts1 = np.zeros((num1, 3))
tpts1[:, 0] = np.cos(tphi)*np.sin(ttheta)
tpts1[:, 1] = np.sin(tphi)*np.sin(ttheta)
tpts1[:, 2] = np.cos(ttheta)
tout = area_preserv_proj(tpts1, rot_mat, tol=1e-08)
tpts1_stereo = tout[0]
plt.plot(tpts1_stereo[:, 0], tpts1_stereo[:, 1], color=(0, 0, 0))
num1 = 100
th1 = np.arctan(np.sqrt(2))
tphi = np.linspace(0, np.pi/4, num1)
ttheta = np.arctan(1/np.sin(tphi))
tpts1 = np.zeros((num1, 3))
tpts1[:, 0] = np.cos(tphi)*np.sin(ttheta)
tpts1[:, 1] = np.sin(tphi)*np.sin(ttheta)
tpts1[:, 2] = np.cos(ttheta)
tout = area_preserv_proj(tpts1, rot_mat, tol=1e-08)
tpts1_stereo = tout[0]
plt.plot(tpts1_stereo[:, 0], tpts1_stereo[:, 1], color=(0, 0, 0))
elif ang == 'D_3d':
### Special case for D_3d bicrystal symmetry boundaries
rot_mat = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
num1 = 100
phi = np.linspace(-np.pi/6, np.pi/6, num1)
theta = np.linspace(np.pi/2, np.pi/2, num1)
tpts = np.zeros((num1, 3))
tpts[:, 0] = np.sin(theta)*np.cos(phi)
tpts[:, 1] = np.sin(theta)*np.sin(phi)
tpts[:, 2] = np.cos(theta)
tout = area_preserv_proj(tpts, rot_mat, tol=1e-08)
tpts_stereo = tout[0]
plt.plot(tpts_stereo[:, 0], tpts_stereo[:, 1], color=(0, 0, 0))
num1 = 100
phi = np.linspace(-np.pi/6, -np.pi/6, num1)
theta = np.linspace(0, np.pi/2, num1)
tpts = np.zeros((num1, 3))
tpts[:, 0] = np.sin(theta)*np.cos(phi)
tpts[:, 1] = np.sin(theta)*np.sin(phi)
tpts[:, 2] = np.cos(theta)
tout = area_preserv_proj(tpts, rot_mat, tol=1e-08)
tpts_stereo = tout[0]
plt.plot(tpts_stereo[:, 0], tpts_stereo[:, 1], color=(0, 0, 0))
num1 = 100
phi = np.linspace(np.pi/6, np.pi/6, num1)
theta = np.linspace(0, np.pi/2, num1)
tpts = np.zeros((num1, 3))
tpts[:, 0] = np.sin(theta)*np.cos(phi)
tpts[:, 1] = np.sin(theta)*np.sin(phi)
tpts[:, 2] = np.cos(theta)
tout = area_preserv_proj(tpts, rot_mat, tol=1e-08)
tpts_stereo = tout[0]
plt.plot(tpts_stereo[:, 0], tpts_stereo[:, 1], color=(0, 0, 0))
else:
### General boundary conditions for rest of the bicrystal symmetries
rot_mat = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
num1 = 100
phi = np.linspace(0, ang, num1)
theta = np.linspace(np.pi/2, np.pi/2, num1)
tpts = np.zeros((num1, 3))
tpts[:, 0] = np.sin(theta)*np.cos(phi)
tpts[:, 1] = np.sin(theta)*np.sin(phi)
tpts[:, 2] = np.cos(theta)
tout = area_preserv_proj(tpts, rot_mat, tol=1e-08)
tpts_stereo = tout[0]
plt.plot(tpts_stereo[:, 0], tpts_stereo[:, 1], color=(0, 0, 0))
if abs(ang - 2*np.pi) > 1e-08:
### Special case when the FZ is not a sector but a circle
num1 = 100
phi = np.linspace(0, 0, num1)
theta = np.linspace(0, np.pi/2, num1)
tpts = np.zeros((num1, 3))
tpts[:, 0] = np.sin(theta)*np.cos(phi)
tpts[:, 1] = np.sin(theta)*np.sin(phi)
tpts[:, 2] = np.cos(theta)
tout = area_preserv_proj(tpts, rot_mat, tol=1e-08)
tpts_stereo = tout[0]
plt.plot(tpts_stereo[:, 0], tpts_stereo[:, 1], color=(0, 0, 0))
num1 = 100
phi = np.linspace(ang, ang, num1)
theta = np.linspace(0, np.pi/2, num1)
tpts = np.zeros((num1, 3))
tpts[:, 0] = np.sin(theta)*np.cos(phi)
tpts[:, 1] = np.sin(theta)*np.sin(phi)
tpts[:, 2] = np.cos(theta)
tout = area_preserv_proj(tpts, rot_mat, tol=1e-08)
tpts_stereo = tout[0]
plt.plot(tpts_stereo[:, 0], tpts_stereo[:, 1], color=(0, 0, 0))
####################################################################################################################
### removing axis
plt.axis('equal')
plt.axis('off')
### saving the plots
if n != 0:
plt.savefig('Sig_'+str(sig)+'_Mis_'+str(ct1)+'_R_'+str(r)+'_N_'+str(n)+'.png', dpi=100, bbox_inches='tight')
fig_path = os.getcwd() + '/Sig_'+str(sig)+'_Mis_'+str(ct1)+'_R_'+str(r)+'_N_'+str(n)+'.png'
else:
plt.savefig('Sig_'+str(sig)+'_Mis_'+str(ct1)+'_R_'+str(r)+'.png', dpi=100, bbox_inches='tight')
fig_path = os.getcwd() + '/Sig_'+str(sig)+'_Mis_'+str(ct1)+'_R_'+str(r)+'.png'
return fig_path
