y_eu, v_eu = euler(y_eu, v_eu, t, dt)
y_rk, v_rk = rk4(y_rk, v_rk, t, dt)
t += dt
positions_eu.append(y_eu) # store result of integration
positions_rk.append(y_rk)
pb.print("Integrate: RK-4 and Euler")
####################################################
# Visualize the result
####################################################
vp = Plotter(interactive=0, axes=2) # choose axes type nr.2
vp.ytitle = "u(x,t)"
vp.ztitle = "" # will not draw z axis
for i in x:
vp += Point([i, 0, 0], c="green", r=6)
pts_actors_eu = vp.actors # save a copy of the actors list
pts_actors_eu[0].legend = "Euler method"
vp.actors = [] # clean up the list
for i in x:
vp += Point([i, 0, 0], c="red", r=6)
pts_actors_rk = vp.actors # save a copy of the actors list
pts_actors_rk[0].legend = "Runge-Kutta4"
# merge the two lists and set it as the current actors
vp.actors = pts_actors_eu + pts_actors_rk
# let's also add a fancy background image from wikipedia
vp.load(datadir + "images/wave_wiki.png",
""" Text jutification and positioning. (center, top-left, top-right, bottom-left, bottom-right) """ print(__doc__) from vtkplotter import show, Text, Point txt = "I like\nto play\nguitar" tx = Text(txt, pos=[1, 2, 0], s=0.2, c=3, bc=1, depth=0.2, justify="top-left") to = Point([1, 2, 0], c="r") # mark text origin ax = Point([0, 0, 0]) # mark axes origin show(tx, to, ax, axes=8, verbose=0)
y_eu, v_eu = euler(y_eu, v_eu, t, dt)
y_rk, v_rk = rk4(y_rk, v_rk, t, dt)
t += dt
positions_eu.append(y_eu) # store result of integration
positions_rk.append(y_rk)
pb.print("Integrate: RK-4 and Euler")
####################################################
# Visualize the result
####################################################
vp = Plotter(interactive=0, axes=2, bg="w") # choose axes type nr.2
vp.ytitle = "u(x,t)"
vp.ztitle = "" # will not draw z axis
for i in x:
vp.add(Point([i, 0, 0], c="green", r=6))
pts_actors_eu = vp.actors # save a copy of the actors list
pts_actors_eu[0].legend = "Euler method"
vp.actors = [] # clean up the list
for i in x:
vp.add(Point([i, 0, 0], c="red", r=6))
pts_actors_rk = vp.actors # save a copy of the actors list
pts_actors_rk[0].legend = "Runge-Kutta4"
# merge the two lists and set it as the current vtkPlotter actors
vp.actors = pts_actors_eu + pts_actors_rk
# let's also add a fancy background image from wikipedia
vp.load(datadir + "images/wave_wiki.png",
from vtkplotter import Latex, Point, show
# https://matplotlib.org/tutorials/text/mathtext.html
latex1 = r'x= \frac{ - b \pm \sqrt {b^2 - 4ac} }{2a}'
latex2 = r'\mathcal{A}\mathrm{sin}(2 \omega t)'
latex3 = r'I(Y | X)=\sum_{x \in \mathcal{X}, y \in \mathcal{Y}} p(x, y) \log \left(\frac{p(x)}{p(x, y)}\right)'
latex4 = r'\Gamma_{\epsilon}(x)=\left[1-e^{-2 \pi \epsilon}\right]^{1-x} \prod_{n=0}^{\infty} \frac{1-\exp (-2 \pi \epsilon(n+1))}{1-\exp (-2 \pi \epsilon(x+n))}'
latex5 = r'\left( \begin{array}{l}{c t^{\prime}} \\ {x^{\prime}} \\ {y^{\prime}} \\ {z^{\prime}}\end{array}\right)=\left( \begin{array}{cccc}{\gamma} & {-\gamma \beta} & {0} & {0} \\ {-\gamma \beta} & {\gamma} & {0} & {0} \\ {0} & {0} & {1} & {0} \\ {0} & {0} & {0} & {1}\end{array}\right) \left( \begin{array}{l}{c t} \\ {x} \\ {y} \\ {z}\end{array}\right)'
latex6 = r'\mathrm{CO}_{2}+6 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+6 \mathrm{O}_{2}'
latex7 = r'x \mathrm{(arb. units)}'
l = Latex(latex4,
s=1,
c='white',
bg='',
alpha=0.9,
usetex=False,
fromweb=False)
l.crop(0.3, 0.3) # crop top and bottom 30%
l.pos(2, 0, 0)
p = Point()
box = l.box() # return the bounding box of an actor
show(p, l, box, axes=8)
R12 = Pos[s2]-Pos[s1]
nR12 = np.linalg.norm(R12)
d12 = Radius[s1]+Radius[s2] - nR12
tau = R12/nR12
DR0 = d12*tau
x1 = Mass[s1]/(Mass[s1]+Mass[s2])
x2 = 1-x1 # x2 = Mass[s2]/(Mass[s1]+Mass[s2])
Pos[s1] -= x2*DR0
Pos[s2] += x1*DR0
DV0 = 2*dot(Vel[s2]-Vel[s1], tau)*tau
Vel[s1] += x2*DV0
Vel[s2] -= x1*DV0
# Update the location of the spheres
for s in range(Nsp): Spheres[s].pos([Pos[s][0],Pos[s][1],0])
if not int(i)%10: # every ten steps:
rsp = [Pos[0][0],Pos[0][1],0]
rsv = [Vel[0][0],Vel[0][1],0]
vp.add(Point(rsp, c='r', r=5, alpha=0.1)) # leave a point trace
vp.show() # render scene
pb.print('#actors='+str(len(vp.actors)))
vp.show(interactive=1)
from vtkplotter import Plotter, mag, Points, Point
import numpy as np
dt = 0.002
y = [25.0, -10.0, -7.0] # Starting point (initial condition)
pts, cols = [], []
for t in np.linspace(0, 20, int(20 / dt)):
# Integrate a funny differential equation
dydt = np.array([
-8 / 3.0 * y[0] + y[1] * y[2], -10.0 * (y[1] - y[2]),
-y[1] * y[0] + 28.0 * y[1] - y[2]
])
y = y + dydt * dt
c = np.clip([mag(dydt) * 0.005], 0, 1)[0] # color by speed
pts.append(y)
cols.append([c, 0, 1 - c])
scene = Plotter(title="Lorenz attractor", axes=2, verbose=0, bg="w")
scene.add(Point(y, r=20, c="g", alpha=0.3))
scene.add(Points(pts, r=5, c=cols, alpha=0.3))
scene.show()
import numpy as np
dt = 0.002
y = (25.0, -10.0, -7.0) # Starting point (initial condition)
pts, cols = [], []
for t in np.linspace(0, 20, int(20 / dt)):
# Integrate a funny differential equation
dydt = np.array([
-8 / 3.0 * y[0] + y[1] * y[2], -10.0 * (y[1] - y[2]),
-y[1] * y[0] + 28.0 * y[1] - y[2]
])
y = y + dydt * dt
c = np.clip([np.linalg.norm(dydt) * 0.005], 0, 1)[0] # color by speed
cols.append([c, 0, 1 - c])
pts.append(y)
from vtkplotter import Plotter, Line, Point, Points, settings
settings.renderPointsAsSpheres = False # render points as squares
scene = Plotter(title="Lorenz attractor", axes=1, verbose=0, bg="w")
scene += Point(y, r=10, c="g") # end point
scene += Points(pts, r=3, c=cols)
scene += Line(pts).off().addShadow(x=3) # only show shadow, not line
scene += Line(pts).off().addShadow(z=-30)
scene.show(viewup='z')
from vtkplotter import Plotter, mag, Points, Point
import numpy as np
dt = 0.002
y = [25.0, -10.0, -7.0] # Starting point (initial condition)
pts, cols = [], []
for t in np.linspace(0, 20, int(20 / dt)):
# Integrate a funny differential equation
dydt = np.array([
-8 / 3.0 * y[0] + y[1] * y[2], -10.0 * (y[1] - y[2]),
-y[1] * y[0] + 28.0 * y[1] - y[2]
])
y = y + dydt * dt
c = np.clip([mag(dydt) * 0.005], 0, 1)[0] # color by speed
pts.append(y)
cols.append([c, 0, 1 - c])
scene = Plotter(title="Lorenz attractor", axes=2, verbose=0, bg="w")
scene += Point(y, r=20, c="g")
scene += Points(pts, r=5, c=cols)
scene.show()
"""
Text jutification and positioning:
top-left, top-right, bottom-left, bottom-right,
center-left, center-right, center-left, center-right
"""
print(__doc__)
from vtkplotter import show, Text, Point
txt = "Text\njustification\n& position"
pos = [1, 2, 0]
tx = Text(txt, pos, s=1, depth=0.1, justify="bottom-left")
t0 = Point(pos, c="r") # mark text position
ax = Point(c="blue") # mark axes origin
show(tx, tx.box().c("y"), t0, ax, axes=8, bg="lb", size=(500, 500))
from vtkplotter import Plotter, mag, Points, Point
import numpy as np
dt = 0.002
y = [25., -10., -7.] # Starting point (initial condition)
pts, cols = [], []
for t in np.linspace(0,20, int(20/dt)):
# Integrate a funny differential equation
dydt = np.array([-8/3.*y[0]+ y[1]*y[2],
-10.*(y[1]-y[2]),
-y[1]*y[0]+28.*y[1]-y[2]])
y = y + dydt * dt
c = np.clip( [mag(dydt) * 0.005], 0, 1)[0] # color by speed
pts.append(y)
cols.append([c,0, 1-c])
scene = Plotter(title='Lorenz attractor', axes=2, verbose=0, bg='w')
scene.add(Point(y, r=20, c='g', alpha=0.3))
scene.add(Points(pts, r=5, c=cols, alpha=0.3))
scene.show()
'''
Example usage of addTrail(). Add a triling line to a moving object.
'''
print(__doc__)
from vtkplotter import Plotter, sin, Sphere, Point
vp = Plotter(axes=6, interactive=0)
s = Sphere(c='green', res=24)
s.cutWithPlane([-0.9, 0, 0], showcut=True) #cut left part of sphere
p = Point([1, 1, 1], r=12, c='k')
# add a trail to point p with maximum length 0.5 and 50 segments
p.addTrail(c='k', lw=3, maxlength=0.5, n=50)
vp.add([s, p])
for i in range(200):
p.pos([-2 + i / 100., sin(i / 5.) / 15, 0])
vp.show()
vp.camera.Azimuth(-0.2)
vp.show(interactive=1)
y_eu, v_eu = euler(y_eu, v_eu, t, dt)
y_rk, v_rk = rk4(y_rk, v_rk, t, dt)
t += dt
positions_eu.append(y_eu) # store result of integration
positions_rk.append(y_rk)
pb.print('Integrate: RK-4 and Euler')
####################################################
# Visualize the result
####################################################
vp = Plotter(interactive=0, axes=2, bg='w') # choose axes type nr.2
vp.ytitle = 'u(x,t)'
vp.ztitle = '' # will not draw z axis
for i in x:
vp.add(Point([i, 0, 0], c='green', r=6))
pts_actors_eu = vp.actors # save a copy of the actors list
pts_actors_eu[0].legend = 'Euler method'
vp.actors = [] # clean up the list
for i in x:
vp.add(Point([i, 0, 0], c='red', r=6))
pts_actors_rk = vp.actors # save a copy of the actors list
pts_actors_rk[0].legend = 'Runge-Kutta4'
# merge the two lists and set it as the current vtkPlotter actors
vp.actors = pts_actors_eu + pts_actors_rk
# let's also add a fancy background image from wikipedia
vp.load('data/images/wave_wiki.png', alpha=.8).scale(0.4).pos([0, -100, -20])
from vtkplotter import Plotter, mag, Points, Point
import numpy as np
dt = 0.002
y = [25.0, -10.0, -7.0] # Starting point (initial condition)
pts, cols = [], []
for t in np.linspace(0, 20, int(20 / dt)):
# Integrate a funny differential equation
dydt = np.array([
-8 / 3.0 * y[0] + y[1] * y[2], -10.0 * (y[1] - y[2]),
-y[1] * y[0] + 28.0 * y[1] - y[2]
])
y = y + dydt * dt
c = np.clip([mag(dydt) * 0.005], 0, 1)[0] # color by speed
pts.append(y)
cols.append([c, 0, 1 - c])
scene = Plotter(title="Lorenz attractor", axes=2, verbose=0, bg="w")
scene += Point(y, r=20, c="g", alpha=0.3)
scene += Points(pts, r=5, c=cols, alpha=0.3)
scene.show()
"""
Mark a specific point on a mesh with some text.
"""
from vtkplotter import Sphere, Point, show, Text
sp = Sphere().wire(True)
pcoords = sp.getPoint(144)
pt = Point(pcoords, r=12, c='white')
tx = Text('my fave\npoint',
pcoords,
s=0.1,
c='lightblue',
bc='green',
followcam=False)
show([sp, pt, tx, Text(__doc__)], verbose=0)
"""
Example usage of addTrail().
Add a trailing line to a moving object.
"""
print(__doc__)
from vtkplotter import Plotter, sin, Sphere, Point
vp = Plotter(axes=6, bg='white', interactive=0)
s = Sphere(c="green", res=24)
s.cutWithPlane([-0.9, 0, 0], showcut=True) # cut left part of sphere
p = Point([1, 1, 1], r=12, c="k")
# add a trail to point p with maximum length 0.5 and 50 segments
p.addTrail(c="k", lw=3, maxlength=0.5, n=50)
vp += [s, p]
for i in range(200):
p.pos([-2 + i / 100.0, sin(i / 5.0) / 15, 0])
vp.show()
vp.camera.Azimuth(-0.2)
vp.show(interactive=1)
# Check to see if the spheres are colliding
for ij in hitlist:
s1, s2 = divmod(ij, Nsp) # decode the spheres pair (s1,s2) colliding
hitlist.remove(s2 * Nsp +
s1) # remove symmetric (s2,s1) pair from list
R12 = Pos[s2] - Pos[s1]
nR12 = np.linalg.norm(R12)
d12 = Radius[s1] + Radius[s2] - nR12
tau = R12 / nR12
DR0 = d12 * tau
x1 = Mass[s1] / (Mass[s1] + Mass[s2])
x2 = 1 - x1 # x2 = Mass[s2]/(Mass[s1]+Mass[s2])
Pos[s1] -= x2 * DR0
Pos[s2] += x1 * DR0
DV0 = 2 * dot(Vel[s2] - Vel[s1], tau) * tau
Vel[s1] += x2 * DV0
Vel[s2] -= x1 * DV0
# Update the location of the spheres
for s in range(Nsp):
Spheres[s].pos([Pos[s][0], Pos[s][1], 0])
if not int(i) % 10: # every ten steps:
rsp = [Pos[0][0], Pos[0][1], 0]
rsv = [Vel[0][0], Vel[0][1], 0]
vp += Point(rsp, c="r", r=5, alpha=0.1) # leave a point trace
vp.show() # render scene
pb.print()
vp.show(interactive=1)
"""
Mark a specific point
on a mesh with some text.
"""
from vtkplotter import Sphere, Point, show, Text
sp = Sphere().wire(True)
pcoords = sp.getPoint(144)
pt = Point(pcoords, r=12, c="white")
tx = Text("my fave\npoint",
pcoords,
s=0.1,
c="lightblue",
bc="green",
followcam=False)
show(sp, pt, tx, Text(__doc__), axes=1)
In this example we modify the mesh of a shape
by moving the points along the normals to the surface
and along the radius of a sphere centered at the center of mass.
At each step we redefine the actor so that the normals are
recalculated for the underlying polydata.
'''
from __future__ import division, print_function
from vtkplotter import Plotter, norm, mag, settings, Point, Text
settings.computeNormals = True # on object creation by default
vp = Plotter(axes=0, verbose=0, bg='w')
s = vp.load('data/290.vtk', c='red', bc='plum')
c = s.centerOfMass()
vp.add(Point(c))
Niter = 4
for t in range(Niter):
print('iteration', t)
coords = s.coordinates()
normals = s.normals()
aves = s.averageSize() * 1.5
for i in range(s.N()):
n = normals[i]
p = coords[i]
q = norm(p - c) * aves + c
dp = mag(q - p)
alongn = n * dp
alongr = q - p # bias normal
