def schwarz_christoffel_coeff(points):
a = exp(2j*pi*linspace(0, 1, len(points), endpoint=False))
a.shape = (1, -1)
p = [points[-1]] + points + points[0:1]
b = array([ (angle( (p[k-1]-p[k])/(p[k+1]-p[k]) )/pi)%2.0 - 1.0
for k in xrange(1, len(p)-1) ])
b.shape = (1,-1)
return (a,b)
if loop:
pa.append(path.closepath())
return pa
# Get transformation coefficients, and print them out
figure = figures[opts.figure]
a, b = schwarz_christoffel_coeff(figure)
print a
print b+1.0
# Set up discretization points for the grid
M = opts.M
N = opts.N * len(figure)
R = 1.0 - 2**linspace(0, -M, M+1, endpoint=True)
Theta = linspace(0, 2*pi, N, endpoint=False)
if not opts.show_domain:
# Compute f(z) over grid
W = zeros(shape=(M, N), dtype=complex)
for v in xrange(0, N):
Z = R * exp(1j*Theta[v])
for u in xrange(0, M):
W[u,v] = gauss_quad32(schwarz_christoffel_integrand,
(a, b, Z[u], Z[u+1]-Z[u]))
W = cumsum(W, axis=0)
else:
# Domain contours are just concentric circles
W = 36.0 * R[1:].reshape(-1,1) * exp(1j*Theta).reshape(1,-1)
