def epicycles(time, rotation, fourier, order):
global objs
plt.remove(objs)
x, y = [0, 0]
objs, path = [], []
for i in range(len(fourier[:order])):
re, im, freq, amp, phase = fourier[i]
if amp > 0.2:
c = vedo.Circle([x, y], amp).wireframe().lw(0.1)
objs.append(c)
x += amp * np.cos(freq * time + phase + rotation)
y += amp * np.sin(freq * time + phase + rotation)
path.append([x, y])
if len(points):
hline = vedo.Line([x, y], points[-1], c='red5', lw=0.1)
pline = vedo.Line(path, c='green5', lw=2)
oline = vedo.Line(points, c='red4', lw=5)
objs += [hline, pline, oline]
plt.add(objs, resetcam=False)
return [x, y]
def build_manifold(w, q, c_range, n, t3, tlim, out_file):
ADAPT_MAXLEVEL = 2
ADAPT_TOL = 0.2
# Hidden-Nonseizing-Seizing boundary
# c = np.linspace(c_range[0], c_range[1], n)
c = np.linspace(c_range[0], c_range[1], n * 2**ADAPT_MAXLEVEL)
boundary_hns = get_c_hss(w, q, c, tlim, t3)
# Hidden-Hidden-Seizing manifold
verts_hhs, triangs_hhs = get_c_hhs_adaptive(w,
q,
c_range,
n,
c_range,
n,
t3,
tol=ADAPT_TOL,
maxlevel=ADAPT_MAXLEVEL)
# Cutting mesh
cut_line = np.copy(boundary_hns)
cut_line[:, 2] = c_range[0]
cut_line = vp.Line(cut_line)
cut_mesh = cut_line.extrude(zshift=c_range[1] - c_range[0])
# Hidden-Nonseizing-Seizing manifold
vmesh_hhs = vp.Mesh([verts_hhs, triangs_hhs])
vmesh_hns = vmesh_hhs.cutWithMesh(cut_mesh, invert=False)
verts_hns = vmesh_hns.points()
triangs_hns = vmesh_hns.faces()
# Hidden-Nonseizing-Seizing inverted manifold
vmesh_hhs = vp.Mesh([verts_hhs, triangs_hhs])
vmesh_hnsi = vmesh_hhs.cutWithMesh(cut_mesh, invert=True)
verts_hnsi = vmesh_hnsi.points()
triangs_hnsi = vmesh_hnsi.faces()
assert all([len(f) == 3 for f in triangs_hns])
assert all([len(f) == 3 for f in triangs_hnsi])
np.savez(out_file,
boundary_hns=boundary_hns,
verts_hns=verts_hns,
triangs_hns=triangs_hns,
verts_hnsi=verts_hnsi,
triangs_hnsi=triangs_hnsi,
verts_hhs=verts_hhs,
triangs_hhs=triangs_hhs)
def viz_structure(regpos, w, surfaces, w_perc=3):
# Connections
wmax = np.max(w)
vlines = []
for reg1, reg2 in zip(*np.where(
w > np.percentile(w.flat, (100 - w_perc)))):
vlines.append(
vp.Line(regpos[reg1],
regpos[reg2],
c='k',
lw=5 * w[reg1, reg2] / wmax))
# Brain surfaces
vmeshes = [
vp.Mesh([verts, triangs], 'grey', alpha=0.05)
for verts, triangs in surfaces
]
return vlines, vmeshes
def asLine(self,
min_hits=1,
max_hits=1000,
c=None,
cmap_amplitudes="",
vmin=0):
"""Return a vedo.Line object if it has at least min_hits and less than max_hits"""
if min_hits < len(self.path) < max_hits:
ln = vedo.Line(self.path).lw(1)
if cmap_amplitudes:
ln.cmap(cmap_amplitudes, self._amplitudes, vmin=vmin)
elif c is None:
c = vedo.colors.colorMap(self.wave_length, "jet", 450e-09,
750e-09) / 1.5
ln.color(c)
else:
ln.color(c)
return ln
return None
def viz_structure(regpos, w, surfaces, contacts):
# Connections
wmax = np.max(w)
vlines = []
for reg1, reg2 in zip(*np.where(w > np.percentile(w.flat, 97))):
vlines.append(
vp.Line(regpos[reg1],
regpos[reg2],
c='k',
lw=15 * w[reg1, reg2] / wmax))
# Brain surfaces
vmeshes = [
vp.Mesh([verts, triangs], 'grey', alpha=0.05)
for verts, triangs in surfaces
]
# Electrodes
ncontacts = contacts.shape[0]
vcontacts = []
for i in range(ncontacts):
vcontacts.append(vp.Sphere(contacts[i], r=0.8, c='green'))
return vlines, vmeshes, vcontacts
"""Elliptic Fourier Descriptors
parametrizing a closed countour (in red)"""
import vedo, pyefd
shapes = vedo.load(vedo.dataurl+'timecourse1d.npy')
sh = shapes[55]
sr = vedo.Line(sh).mirror('x').reverse()
sm = vedo.merge(sh, sr).c('red5').lw(3)
pts = sm.points()[:,(0,1)]
rlines = []
for order in range(5,30, 5):
coeffs = pyefd.elliptic_fourier_descriptors(pts, order=order, normalize=False)
a0, c0 = pyefd.calculate_dc_coefficients(pts)
rpts = pyefd.reconstruct_contour(coeffs, locus=(a0,c0), num_points=400)
color = vedo.colorMap(order, "Blues", 5,30)
rline = vedo.Line(rpts).lw(3).c(color)
rlines.append(rline)
sm.z(0.1) # move it on top so it's visible
vedo.show(sm, *rlines, __doc__, axes=1, bg='k', size=(1190, 630), zoom=1.8)
vedo.dolfin.plot(mesh, arrow, txt, c='grey5', at=i, N=N,
zoom=1.1) #PRESS q
dmesh_i = meshes[0] # initial mesh
dmesh_f = meshes[-1] # final mesh
vmesh_i = vedo.Mesh([dmesh_i.coordinates(), dmesh_i.cells()], c='grey5').z(-1)
vmesh_f = vedo.Mesh(
[dmesh_f.coordinates(), dmesh_f.cells()], c='grey3').wireframe()
plt = vedo.Plotter()
# move a few points along the deformation of the circle
seeds = vedo.Circle(r=50,
res=res).points()[:,
(0, 1)] # make points 2d with [:,(0,1)]
endpoints = []
for i, p in enumerate(seeds):
line = [p]
for u in displacements:
p = p + u(p)
line.append(p)
plt += vedo.Line(line, c=i, lw=4).z(1)
endpoints.append(p)
plt += [vmesh_i, vmesh_f, __doc__]
plt.show(axes=1)
# to invert everything and move the end points back in place, check out discussion:
#https://fenicsproject.discourse.group/t/precision-in-hyperelastic-model/6824/3
def elephant(t, p):
Cx = np.zeros((6, ), dtype='complex')
Cy = np.zeros((6, ), dtype='complex')
Cx[1], Cy[1] = p[0].real * 1j, p[3].imag + p[0].imag * 1j
Cx[2], Cy[2] = p[1].real * 1j, p[1].imag * 1j
Cx[3], Cy[3] = p[2].real, p[2].imag * 1j
Cx[5] = p[3].real
x = np.append(fourier(t, Cy), [p[4].imag])
y = -np.append(fourier(t, Cx), [-p[4].imag])
return np.array([x, y])
# draw the body of the elephant
ele = elephant(np.linspace(0.4 + 1.3 * np.pi, 2 * np.pi + 0.9 * np.pi, 100), p)
body = vedo.Line(ele.T).tomesh().lw(0).c('r4')
plt = vedo.show(body, __doc__ + str(p), zoom=0.8, axes=1, interactive=False)
ltrunk = None
# wiggle trunk
#vd = vedo.Video()
for i in range(50):
trunk = elephant(
np.linspace(2 * np.pi + 0.9 * np.pi, 0.4 + 3.3 * np.pi, 500), p)
x, y = trunk
for ii in range(len(y) - 1):
y[ii] -= np.sin(
((x[ii] - x[0]) * np.pi / len(y))) * np.sin(float(i)) * p[4].real
plt.remove(ltrunk) # remove old trunk before drawing at new position
ltrunk = vedo.Line(trunk.T).lw(6).c('r3')
plt.add(ltrunk)
left = r * A
right = np.sinh(A)
A = A + dA
A = A - dA
a = dx / (2 * A)
b = xb - a * 1 / 2 * np.log((1 + dy / L) / (1 - dy / L))
c = y0 - a * np.cosh((x0 - b) / a)
x = x0
ddx = 0.001
pts = []
while x < x1:
y = a * np.cosh((x - b) / a) + c
x = x + ddx
pts.append([x, y])
pts.append([x1, y1])
coords = vedo.Spline(pts, res=n).points()
line.points(coords) # update coords
nodes.points(coords).z(.01)
plt.render()
surf = vedo.Plane(sx=1, sy=1).shift(0.51, 0, 0)
line = vedo.Line(P1, P2, res=n, lw=10)
nodes = line.clone().c('red3').pointSize(8).z(.01)
plt = vedo.Plotter()
plt.addCallback("hover", move)
plt.show(__doc__, surf, line, nodes, axes=1, mode='image')
x += amp * np.cos(freq * time + phase + rotation)
y += amp * np.sin(freq * time + phase + rotation)
path.append([x, y])
if len(points):
hline = vedo.Line([x, y], points[-1], c='red5', lw=0.1)
pline = vedo.Line(path, c='green5', lw=2)
oline = vedo.Line(points, c='red4', lw=5)
objs += [hline, pline, oline]
plt.add(objs, resetcam=False)
return [x, y]
# Load some 2D shape and make it symmetric
shape = vedo.load(vedo.dataurl + 'timecourse1d.npy')[55]
shaper = vedo.Line(shape).mirror('x').reverse()
shape = vedo.merge(shape, shaper)
x, y, _ = shape.points().T
# Compute Fourier Discrete Transform in x and y separately:
fourierX = DFT(x)
fourierY = DFT(y)
vedo.settings.defaultFont = 'Glasgo'
plt = vedo.Plotter(size=(1500, 750), bg='black', axes=1, interactive=False)
txt = vedo.Text2D(f"{__doc__} (order={order})",
c='red9',
bg='white',
pos='bottom-center')
plt.show(shape, txt, mode='image', zoom=1.9)