def morph(clm1, clm2, t, lmax):
"""Interpolate linearly the two sets of sph harm. coeeficients."""
clm = (1 - t) * clm1 + t * clm2
grid_reco = clm.expand(lmax=lmax) # cut "high frequency" components
agrid_reco = grid_reco.to_array()
pts = []
for i, longs in enumerate(agrid_reco):
ilat = grid_reco.lats()[i]
for j, value in enumerate(longs):
ilong = grid_reco.lons()[j]
th = np.deg2rad(90 - ilat)
ph = np.deg2rad(ilong)
r = value + rbias
p = np.array([sin(th) * cos(ph), sin(th) * sin(ph), cos(th)]) * r
pts.append(p)
return pts
def makeGrid(shape, N):
rmax = 2.0 # line length
agrid, pts = [], []
for th in np.linspace(0, np.pi, N, endpoint=True):
lats = []
for ph in np.linspace(0, 2 * np.pi, N, endpoint=True):
p = np.array([sin(th) * cos(ph), sin(th) * sin(ph), cos(th)]) * rmax
intersections = shape.intersectWithLine([0, 0, 0], p)
if len(intersections):
value = mag(intersections[0])
lats.append(value - rbias)
pts.append(intersections[0])
else:
lats.append(rmax - rbias)
pts.append(p)
agrid.append(lats)
agrid = np.array(agrid)
actor = Points(pts, c="k", alpha=0.4, r=1)
return agrid, actor
def derivs(state, t):
dydx = np.zeros_like(state)
dydx[0] = state[1]
a = state[2] - state[0]
sina, cosa = sin(a), cos(a)
den1 = (M1 + M2) * L1 - M2 * L1 * cosa * cosa
dydx[1] = (M2 * L1 * state[1] * state[1] * sina * cosa + M2 * G *
sin(state[2]) * cosa + M2 * L2 * state[3] * state[3] * sina -
(M1 + M2) * G * sin(state[0])) / den1
dydx[2] = state[3]
den2 = (L2 / L1) * den1
dydx[3] = (-M2 * L2 * state[3] * state[3] * sina * cosa +
(M1 + M2) * G * sin(state[0]) * cosa -
(M1 + M2) * L1 * state[1] * state[1] * sina -
(M1 + M2) * G * sin(state[2])) / den2
return dydx
sin(state[2]) * cosa + M2 * L2 * state[3] * state[3] * sina -
(M1 + M2) * G * sin(state[0])) / den1
dydx[2] = state[3]
den2 = (L2 / L1) * den1
dydx[3] = (-M2 * L2 * state[3] * state[3] * sina * cosa +
(M1 + M2) * G * sin(state[0]) * cosa -
(M1 + M2) * L1 * state[1] * state[1] * sina -
(M1 + M2) * G * sin(state[2])) / den2
return dydx
t = np.arange(0.0, 10.0, dt)
state = np.radians([th1, w1, th2, w2])
y = integrate.odeint(derivs, state, t)
P1 = np.dstack([L1 * sin(y[:, 0]), -L1 * cos(y[:, 0])]).squeeze()
P2 = P1 + np.dstack([L2 * sin(y[:, 2]), -L2 * cos(y[:, 2])]).squeeze()
ax = Axes(xrange=(-2, 2), yrange=(-2, 1), htitle=__doc__)
pb = ProgressBar(0, len(t), c="b")
for i in pb.range():
j = max(i - 5, 0)
k = max(i - 10, 0)
l1 = Line([[0, 0], P1[i], P2[i]]).lw(7).c("blue2")
l2 = Line([[0, 0], P1[j], P2[j]]).lw(6).c("blue2", 0.3)
l3 = Line([[0, 0], P1[k], P2[k]]).lw(5).c("blue2", 0.1)
pt = Points([P1[i], P2[i], P1[j], P2[j], P1[k], P2[k]],
r=8).c("blue2", 0.2)
show(l1, l2, l3, pt, ax, interactive=False, size=(900, 700), zoom=1.4)
pb.print()