#generate a bunch of random points on the surface of a sphere
n=10000
x = random_sample(n)-0.5
y = random_sample(n)-0.5
z = random_sample(n)-0.5
for i, (xval,yval,zval) in enumerate(zip(x,y,z)):
norm = np.sqrt(xval*xval+yval*yval+zval*zval)
x[i] = x[i]/norm
y[i] = y[i]/norm
z[i] = z[i]/norm
#Calculate latitude and longitude of the random points
colats = np.arccos( z/np.sqrt(x*x+y*y+z*z))
lats = np.pi/2. - colats
lons = np.arctan2( y, x )+np.pi
#evaluate a spherical harmonic on that sphere
vals = sph_harm(4,9, lons, colats).real
vals = vals/np.amax(vals)
#interpolate onto a regular grid with C0 interpolation
meshlon, meshlat, values = ssrfpy.interpolate_regular_grid( lons, lats, vals, method = 'cubic', degrees=False)
#Plot the result
plt.contourf( meshlon, meshlat, values)
plt.scatter(lons, lats, s=1)
plt.show()
y[i] = y[i]/norm
z[i] = z[i]/norm
#Calculate latitude and longitude of the random points
colats = np.arccos( z/np.sqrt(x*x+y*y+z*z))
lats = np.pi/2. - colats
lons = np.arctan2( y, x )+np.pi
#evaluate a Fisher distribution on the surface of a sphere
xm = 1./np.sqrt(3.)
ym = 1./np.sqrt(3.)
zm = 1./np.sqrt(3.)
vals = np.empty(n)
kappa = 1.0 #concentration parameter
c = kappa / (4.*np.pi * np.sinh(kappa) )# normalization constant
for i in range(n):
vals[i] = c * np.exp( kappa * (x[i]*xm + y[i]*ym + z[i]*zm) )
#interpolate onto a regular grid with C0 interpolation
meshlon, meshlat, values, weights = ssrfpy.interpolate_regular_grid( lons, lats, vals, method = 'linear', degrees=False, use_legendre=True)
#Compute the integral
tot = np.sum( values * weights )
err = np.abs((1.0-tot)/tot * 100.)
print("Integral of the Fisher distribution: ", tot, ", or %5.2e"%(err), "percent error")
#Plot the result
plt.contourf( meshlon, meshlat, values)
plt.scatter(lons, lats, s=1)
plt.show()
#Calculate latitude and longitude of the random points
colats = np.arccos(z / np.sqrt(x * x + y * y + z * z))
lats = np.pi / 2. - colats
lons = np.arctan2(y, x) + np.pi
#evaluate a Fisher distribution on the surface of a sphere
xm = 1. / np.sqrt(3.)
ym = 1. / np.sqrt(3.)
zm = 1. / np.sqrt(3.)
vals = np.empty(n)
kappa = 1.0 #concentration parameter
c = kappa / (4. * np.pi * np.sinh(kappa)) # normalization constant
for i in range(n):
vals[i] = c * np.exp(kappa * (x[i] * xm + y[i] * ym + z[i] * zm))
#interpolate onto a regular grid with C0 interpolation
meshlon, meshlat, values, weights = ssrfpy.interpolate_regular_grid(
lons, lats, vals, method='linear', degrees=False, use_legendre=True)
#Compute the integral
tot = np.sum(values * weights)
err = np.abs((1.0 - tot) / tot * 100.)
print("Integral of the Fisher distribution: ", tot, ", or %5.2e" % (err),
"percent error")
#Plot the result
plt.contourf(meshlon, meshlat, values)
plt.scatter(lons, lats, s=1)
plt.show()
