def _get_stream_func_bdy(self):
# calculate stream function on boundary
# - continuous on boundary (also should be periodic)
import numpy as np
import geometry_planar as GP
# coordinates of polygon
x,y = np.array(self.coords).transpose()
Nx = len(x)
nvec = np.arange(Nx)
sfun = 0*x
# for each singularity (just outside polygon)
perimeter,resolution,\
spacings,tangent_dirn = GP.curve_info(self.singularities)
for i,sing in enumerate(self.singularities):
an = self.sing_coeffs[i]
branch_dir = np.pi/2.+tangent_dirn[i]
atan2 = GP.arctan2_branch(y,x=x,branch_point=sing,branch_dir=branch_dir)
atan2 = GP.make_arctan2_cts(atan2)
sfun = sfun+an*atan2
self.stream_func_bdy = sfun
return
def plot_stream_func_bdy(self, pobj=None, show=True, i_test=None):
import numpy as np
import shapefile_utils as SFU
import geometry_planar as GP
if pobj is None:
# set a plot object if none exists
from matplotlib import pyplot as pobj
ss = self.get_arc_length() / 1.e3 # km
if i_test is None:
# just plot values of stresm function at boundary
pobj.plot(ss, self.stream_func_bdy, 'b')
out = None
xc = np.round(10. * self.coords[0][0] / 1.e3) / 10. # km (1dp)
yc = np.round(10. * self.coords[0][1] / 1.e3) / 10. # km (1dp)
pobj.xlabel('arc length (km) from ' + str((xc, yc)) + ' (km)')
pobj.ylabel('values of stream function')
else:
# coordinates of polygon
x, y = np.array(self.coords).transpose()
Nx = len(x)
nvec = np.arange(Nx)
# for each singularity (just outside polygon)
sing = self.singularities[i_test]
branch_dir = np.pi / 2. + self.tangent_dirn[i_test]
atan2 = GP.arctan2_branch(y,
x=x,
branch_point=sing,
branch_dir=branch_dir)
pobj.plot(ss, atan2 / np.pi, 'r')
out = [atan2]
atan2 = GP.make_arctan2_cts(atan2)
pobj.plot(ss, atan2 / np.pi, 'b')
out.append(atan2)
if show:
pobj.show()
return out