def showSolution3D(S, start, goal):
from vedo import Text3D, Cube, Line, Grid, merge, show
pts, cubes, txts = [], [], []
pts = [(x, -y) for y, x in S[0]]
for y, line in enumerate(Z):
for x, c in enumerate(line):
if c: cubes.append(Cube([x, -y, 0]))
path = Line(pts).lw(6).c('tomato')
walls = merge(cubes).clean().flat().texture('wood1')
sy, sx = S[1].shape
gradient = np.flip(S[1], axis=0).ravel()
grd = Grid(pos=((sx - 1) / 2, -(sy - 1) / 2, -0.49),
sx=sx,
sy=sy,
resx=sx,
resy=sy)
grd.lw(0).wireframe(False).cmap('gist_earth_r', gradient, on='cells')
grd.addScalarBar(title='Gradient', horizontal=True, c='k', nlabels=2)
txts.append(__doc__)
txts.append(Text3D('Start', pos=[start[1] - 1, -start[0] + 1.5, 1], c='k'))
txts.append(Text3D('Goal!', pos=[goal[1] - 2, -goal[0] - 2.7, 1], c='k'))
show(path, walls, grd, txts, axes=0, zoom=1.2)
import numpy as np
from vedo import settings, Line, show, interactive
settings.defaultFont = "Theemim"
# Generate random data
np.random.seed(1)
data = np.random.uniform(0, 1, (25, 100))
X = np.linspace(-1, 1, data.shape[-1])
G = 0.15 * np.exp(-4 * X**2) # use a gaussian as a weight
# Generate line plots
lines = []
for i in range(len(data)):
pts = np.c_[X, np.zeros_like(X)+i/10, G*data[i]]
lines.append(Line(pts, lw=3))
# Set up the first frame
axes = dict(xtitle='\Deltat /\mus', ytitle="source", ztitle="")
plt = show(lines, __doc__, axes=axes, elevation=-30, interactive=False, bg='k8')
# vd = Video("anim_lines.mp4")
for i in range(50):
data[:, 1:] = data[:, :-1] # Shift data to the right
data[:, 0] = np.random.uniform(0, 1, len(data)) # Fill-in new values
for i in range(len(data)): # Update data
newpts = lines[i].points()
newpts[:,2] = G * data[i]
lines[i].points(newpts).cmap('gist_heat_r', newpts[:,2])
plt.show()
# vd.addFrame()
"""Use iminuit to find the minimum of a 3D scalar field"""
from vedo import show, Point, Line, printc
from iminuit import Minuit
# pip install iminuit # https://github.com/scikit-hep/iminuit
import numpy as np
def fcn(x, y, z):
f = (x - 4)**4 + (y - 3)**4 + (z - 2)**2
if not vals or f < vals[-1]:
path.append([x, y, z])
vals.append(f)
return f
paths = []
for x, y, z in np.random.rand(200, 3) * 3:
path, vals = [], []
m = Minuit(fcn, x=x, y=y, z=z)
m.errordef = m.LEAST_SQUARES
# m.simplex() # run simplex optimiser
m.migrad() # run migrad optimiser
line = Line(path).cmap('jet_r', vals).lw(2).alpha(0.25)
paths.append(line)
printc('Last optimization output:', c='green7', invert=1)
printc(m, c='green7', italic=1)
show(paths, Point([4, 3, 2]), __doc__, axes=1)
def f(psi):
# a smart numpy way to calculate the second derivative in x:
nabla2psi[1 : N+1] = (psi[0:N] + psi[2 : N+2] - 2 * psi[1 : N+1]) / dx2
return 1j * (nabla2psi - V*psi) # this is the RH of Schroedinger equation!
def d_dt(psi): # find Psi(t+dt)-Psi(t) /dt with 4th order Runge-Kutta method
k1 = f(psi)
k2 = f(psi + dt / 2 * k1)
k3 = f(psi + dt / 2 * k2)
k4 = f(psi + dt * k3)
return (k1 + 2 * k2 + 2 * k3 + k4) / 6
plt = Plotter(interactive=False)
bck = plt.load(dataurl+"images/schrod.png").alpha(.3).scale(.0256).pos([0,-5,-.1])
barrier = Line(np.stack((x, V*15, np.zeros_like(x)), axis=1), c="black", lw=2)
box = bck.box().c('black')
lines = []
for i in range(0, Nsteps):
for j in range(500):
Psi += d_dt(Psi) * dt # integrate for a while before showing things
A = np.real(Psi * np.conj(Psi)) * 1.5 # psi squared, probability(x)
coords = np.stack((x, A), axis=1)
Aline = Line(coords, c="db", lw=3)
plt.show(barrier, bck, Aline, box).remove(Aline)
lines.append([Aline, A]) # store objects
# now show the same lines along z representing time
plt.actors= [] # clean up internal list of objects to show
plt.camera.Elevation(20)
printc("In the example shown:\n", repr(txt), c='y')
print()
printc('Font Summary', c='g', box='-')
for i, f in enumerate(fonts):
printc('Font: ', f, c='g')
################################################################################## 3D
cam = dict(pos=(67.7, -3.94, 145),
focalPoint=(29.3, -37.3, 1.55),
viewup=(-0.0642, 0.976, -0.210),
distance=152,
clippingRange=(122, 194))
ln0 = Line([-1, 1.5], [52, 1.5], lw=0.1, c='grey')
ln1 = Line([-1, -2], [52, -2], lw=0.1, c='grey')
fn3d = [ln0, ln1]
gap = 0
txt = "Font Name\n"
for i, font in enumerate(fonts + ['VTK']):
txt += font + ": abcdefghijklmnopqrtuvwxyz 1234567890"
if font in [
"Theemim", "Kanopus", "Normografo", "VictorMono", "Galax",
"LogoType", "Comae"
]:
txt += "\n αβγδεζηθκλμνξπρστφχψω ΔΘΛΞΠΣΦΨΩ"
gap -= 2
if "Biysk" in font: txt += " v3do"
if "VictorMono" == font or "Kanopus" == font or "LogoType" == font or "Comae" == font:
txt += " БГДЖЗИЙКЛ"
"""Koch snowflake fractal"""
from vedo import sqrt, Line, show
levels = 7
def koch(level):
# Compute Koch fractal contour points
k = sqrt(3)/2
if level:
points = koch(level-1) + [(0, 0)] # recursion!
kpts = []
for i in range(len(points)-1):
p1, p2 = points[i], points[i+1]
dx, dy = (p2[0]-p1[0])/3, (p2[1]-p1[1])/3
pa = (p1[0] + dx , p1[1] + dy )
pb = (p1[0] + dx*2, p1[1] + dy*2)
z = complex(pb[0]-pa[0], pb[1]-pa[1]) * (0.5-k*1j)
p3 = (pa[0]+z.real, pa[1]+z.imag)
kpts += [p1, pa, p3, pb]
return kpts
else:
return [(0, 0), (1, 0), (0.5, k)]
kochs = []
for i in range(levels):
# Create a Line from the points and mesh the inside with minimum resolution
kmsh = Line(koch(i)).tomesh(resMesh=1).lw(0).color(-i).z(-i/1000)
kochs.append(kmsh)
show(kochs, __doc__+ f"\nlevels: {levels}\npoints: {kmsh.N()}", axes=10)
v = TestFunction(V)
a = dot(grad(w), grad(v)) * dx
L = p * v * dx
# Compute solution
w = Function(V)
solve(a == L, w, bc)
p = interpolate(p, V)
# Curve plot along x = 0 comparing p and w
import numpy as np
tol = 0.001 # avoid hitting points outside the domain
y = np.linspace(-1 + tol, 1 - tol, 101)
points = [(0, y_) for y_ in y] # 2D points
w_line = np.array([w(point) for point in points])
p_line = np.array([p(point) for point in points])
#######################################################################
from vedo.dolfin import plot
from vedo import Line, Latex
pde = r'-T \nabla^{2} D=p, ~\Omega=\left\{(x, y) | x^{2}+y^{2} \leq R\right\}'
tex = Latex(pde, pos=(0, 1.1, .1), s=0.2, c='w')
wline = Line(y, w_line * 10, c='white', lw=4)
pline = Line(y, p_line / 4, c='lightgreen', lw=4)
plot(w, wline, tex, at=0, N=2, bg='bb', text='Deflection')
plot(p, pline, at=1, bg='bb', text='Load')
# time goes from 0 to 90 hours
pb = ProgressBar(0, 50, step=0.1, c=1)
for t in pb.range():
msg = "[Nb,Ng,Nr,t] = "
plt.actors = [] # clean up the list of actors
for colony in colonies:
newcells = []
for cell in colony.cells:
if cell.dieAt(t):
continue
if cell.divideAt(t):
newc = cell.split() # make daughter cell
plt += Line(cell.pos, newc.pos, c="k", lw=3, alpha=0.5)
newcells.append(newc)
newcells.append(cell)
colony.cells = newcells
pts = [c.pos for c in newcells] # draw all points at once
plt += Points(pts, c=colony.color, r=5, alpha=0.80) # nucleus
plt += Points(pts, c=colony.color, r=15, alpha=0.05) # halo
msg += str(len(colony.cells)) + ","
pb.print(msg + str(int(t)))
plt.show(resetcam=0)
if plt.escaped: exit(0) # if ESC is hit during the loop
# draw the oriented ellipsoid that contains 50% of the cells
for colony in colonies:
) # this is the RH of Schroedinger equation!
def d_dt(psi): # find Psi(t+dt)-Psi(t) /dt with 4th order Runge-Kutta method
k1 = f(psi)
k2 = f(psi + dt / 2 * k1)
k3 = f(psi + dt / 2 * k2)
k4 = f(psi + dt * k3)
return (k1 + 2 * k2 + 2 * k3 + k4) / 6
vp = Plotter(interactive=0, axes=2, size=(1000, 500))
vp.xtitle = ""
vp.ytitle = "|\Psi(x,t)|\^2"
bck = vp.load(datadir + "images/schrod.png").scale(0.015).pos([0, 0, -0.5])
barrier = Line(np.stack((x, V * 15), axis=1), c="dr", lw=3)
lines = []
for j in range(150):
for i in range(500):
Psi += d_dt(Psi) * dt # integrate for a while
A = np.real(Psi * np.conj(Psi)) * 1.5 # psi squared, probability(x)
coords = np.stack((x, A, np.zeros_like(x)), axis=1)
Aline = Tube(coords, c="db", r=0.08)
vp.show(Aline, barrier, bck, zoom=2)
lines.append(Aline)
interactive()
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()
import numpy as np
# create 5 whisker bars with some random data
ws = []
for i in range(5):
xval = i * 2 # position along x axis
data = xval / 4 + np.random.randn(25)
w = whisker(data, bc=i, s=0.5).x(xval)
ws.append(w)
# print(i, 'whisker:\n', w.info)
# build some theoretical expectation to be shown as a grey band
x = np.linspace(-1, 9, 100)
y = x / 5 + 0.2 * np.sin(x)
ye = y**2 / 5 + 0.1 # error on y
line = Line(np.c_[x, y])
band = Ribbon(np.c_[x, y - ye], np.c_[x, y + ye]).c('black', 0.1)
# build braces to inndicate stats significance and dosage
bra1 = Brace([0, 3], [2, 3], comment='*~*', s=0.7, style='[')
bra2 = Brace([4, -1], [8, -1], comment='dose > 3~\mug/kg', s=0.7)
# build custom axes
axes = Axes(
xrange=[-1, 9],
yrange=[-3, 5],
htitle='\beta_c -expression: change in time',
xtitle=' ',
ytitle='Level of \beta_c protein in \muM/l',
xValuesAndLabels=[
(0, 'Experiment^A\nat t=1h'),
"""Forward kinematics: hover the mouse to drag the chain"""
from vedo import Plotter, versor, Plane, Line
n = 15 # number of points
l = 3 # length of one segment
def move(evt):
if not evt.actor:
return
coords = line.points()
coords[0] = evt.picked3d
for i in range(1, n):
v = versor(coords[i] - coords[i - 1])
coords[i] = coords[i - 1] + v * l
line.points(coords) # update positions
nodes.points(coords)
plt.render()
plt = Plotter()
plt.addCallback("mouse move", move)
surf = Plane(sx=60, sy=60)
line = Line([l * n / 2, 0], [-l * n / 2, 0], res=n, lw=12)
nodes = line.clone().c('red3').pointSize(15)
plt.show(surf, line, nodes, __doc__, zoom=1.3).close()
"""Share the same color and trasparency mapping across different volumes"""
from vedo import Volume, Line, show
import numpy as np
arr = np.zeros(shape=(50, 50, 50))
for i in range(50):
for j in range(50):
for k in range(50):
arr[i, j, k] = j
vol1 = Volume(arr).mode(1).cmap('jet', alpha=[0, 1], vmin=0,
vmax=80).addScalarBar("vol1")
vol2 = Volume(arr + 30).mode(1).cmap('jet', alpha=[0, 1], vmin=0,
vmax=80).addScalarBar("vol2")
# or equivalently, to set transparency:
# vol1.alpha([0,1], vmin=0, vmax=70)
# can also manually build a scalarbar object to span the whole range:
sb = Line([50, 0, 0],
[50, 50, 0]).cmap('jet', [0, 70]).addScalarBar3D("vol2",
c='black').scalarbar
show([(vol1, __doc__), (vol2, sb)], N=2, axes=1)
