#!/usr/bin/env python2
from pylab import *
from matplotlib import patches, path
class FlowField:
def __init__(self, v, R):
self.v = v
self.R = R
def __call__(self, x,y):
r2 = x**2 + y**2
theta = arctan(y/x)
vr = self.v*(1 - self.R**2/r2)*cos(theta)
vtheta = -self.v*(1 + self.R**2/r2)*sin(theta)
return (vr*cos(theta) - vtheta*sin(theta),
        vr*sin(theta) + vtheta*cos(theta))
R=3
v = -10
vel = FlowField(v, R)
width = 12
span = arange(0,width,1.3) 
span = r_[-span[::-1],span]
X,Y = meshgrid(span,span)
R2 = X**2 + Y**2
U,V = vel(X,Y)
U = U - v
U[R2 < R**2] = nan
V[R2 < R**2] = nan
#make up a trajectory. This is a totally made up trajectory.
dy = -0.001
x,y = 2.5,width
ux, uy = 0, -30000.0
traj = []
for i in range(int(abs(width/dy))):
uxp,uyp = vel(x,y)
ux += uxp-v;    uy += uyp
t = dy/uy
y += uy*t;      x += ux*t
traj.append((x,y))
traj = array(traj)
traj = traj[sum(traj**2,1) > R*R]
raycolor = 'brown'
earthcolor = (0.4,0.4,0.9)
fig = figure(figsize=(3.5,3.5), facecolor='white')
ax = Axes(fig,[0,0,1,1],yticks=[],xticks=[],frame_on=False)
fig.add_axes(ax)
ax.add_patch(patches.FancyArrowPatch(path=path.Path(traj),arrowstyle='-