# 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)
"""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)
"""
Example usage of addTrail().
Add a trailing line to a moving object.
"""
print(__doc__)
from vedo import Plotter, sin, Sphere, Point
vp = Plotter(axes=6, interactive=False)
s = Sphere().c("green").bc("tomato")
s.cutWithPlane([-0.9, 0, 0]) # cut left part of sphere
p = Point([1, 1, 1], r=12, c="black")
# add a trail to point p with max length 0.5 and 50 segments
p.addTrail(lw=3, maxlength=0.5, n=50)
# add meshes to Plotter list
vp += [s, p]
for i in range(200):
p.pos(-2 + i / 100.0, sin(i / 5.0) / 15, 0)
vp.camera.Azimuth(-0.2)
vp.show()
vp.show(interactive=True)
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",
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
####################################################
settings.useDepthPeeling = False
plt = Plotter(interactive=0, axes=2) # choose axes type nr.2
plt.ytitle = "u(x,t)"
plt.ztitle = "" # will not draw z axis
for i in x:
plt += Point([i, 0, 0], c="green", r=6)
pts_actors_eu = plt.actors # save a copy of the actors list
pts_actors_eu[0].legend = "Euler method"
plt.actors = [] # clean up the list
for i in x:
plt += Point([i, 0, 0], c="red", r=6)
pts_actors_rk = plt.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
plt.actors = pts_actors_eu + pts_actors_rk
# let's also add a fancy background image from wikipedia
plt.load(dataurl + "images/wave_wiki.png").alpha(0.8).scale(0.4).pos(
allLatIdx, allLatCoord, allLatVal = utils.mapSamps(mapIdx, mapCoord,
OrigLatCoords, OrigLatVals)
M = len(allLatIdx)
# For colorbar ranges
MINLAT = math.floor(min(allLatVal) / 10) * 10
MAXLAT = math.ceil(max(allLatVal) / 10) * 10
allPoints = Points(allLatCoord, r=10).cmap('gist_rainbow',
allLatVal,
vmin=MINLAT,
vmax=MAXLAT).addScalarBar(c='white')
vplt = Plotter(N=1, axes=0, interactive=True)
for i in range(M):
idx = allLatIdx[i]
coord = allLatCoord[i]
val = allLatVal[i]
# plot current point as larger than the others
testPoint = Point(coord, r=20).cmap('gist_rainbow', [val],
vmin=MINLAT,
vmax=MAXLAT).addScalarBar(c='white')
vplt.show(mesh,
allPoints,
testPoint,
title='i={:g}/{:g}'.format(i, M),
bg='black')
vplt.close()
"""Set custom lights to a 3D scene"""
from vedo import Plotter, load, dataurl, Point, Light, show
man = load(dataurl + 'man.vtk').c('white').lighting('glossy')
p1 = Point([1, 0, 1], c='y')
p2 = Point([0, 0, 2], c='r')
p3 = Point([-1, -0.5, -1], c='b')
p4 = Point([0, 1, 0], c='k')
# Add light sources at the given positions
l1 = Light(p1, c='y') # p1 can simply be [1,0,1]
l2 = Light(p2, c='r')
l3 = Light(p3, c='b')
l4 = Light(p4, c='w', intensity=0.5)
show(man, l1, l2, l3, l4, p1, p2, p3, p4, __doc__, axes=1, viewup='z')
#####################################################
##### Equivalent code using a Plotter instance: #####
#####################################################
# plt = Plotter(axes=1)
# plt += [man, p1, p2, p3, p4, l1, l2, l3, l4]
# plt.show(viewup='z')
#####################################################
