def __init__(self, physicalEnvironment):
self.logger = logging.getLogger(name='Quadsim.Visualizer')
self.physEnv = physicalEnvironment
self.obj = set()
self.simFrames = 0
self.objUpdates = 0
self.canvas = v.display(title='Simulation', width=1024, height=768, background=(0.2,0.2,0.2))
self.canvas.select()
self.controls = vc.controls(x=640, y=0, range=20)
self.infoLabel = v.label(display=self.controls.display,pos=(-10,-10), text='Click simulation to start', line=False)
self.lastFPSCheckTime = None
self.lastFPS = 0.0
self.simTime = 0.0
self.fpsValues = []
self.geomLookup = {}
import numpy as np
import vpython as vp
"""
Plot the sine and cosine of the waves in 3-D
"""
xmax = 201
scene = vp.display(x=0,
y=0,
width=500,
height=500,
title="sin(6pi*x/201-t)",
background=(1., 1., 1.),
forward=(-0.6, -0.5, 1))
sinWave = vp.curve(x=range(0, xmax), color=color.yellow, radius=4.5)
cosWave = vp.curve(x=range(0, xmax), color=color.red, radius=4.5)
Xaxis = vp.curve(pos=[(-300, 0, 0), (300, 0, 0)], color=color.blue)
incr = np.pi / xmax # x increment
for t in range(0, 10, .02): # time loop
for i in range(0, xmax): # loop through x values
x = i * incr
f = np.sin(6.0 * x - t)
zz = np.cos(6.0 * x - t)
yp = 100 * f
xp = 200 * x - 300
zp = 100 * zz
sinWave.x[i] = xp
sinWave.y[i] = yp
cosWave.x[i] = xp
import vpython as vp
"""
Determine the spherical Bessel functions by downward recursion, yo.
"""
Xmax = 40.
Xmin = 0.25
step = 0.1
order = 10
start = 50
graph1 = vp.display(width=500,
height=500,
title="Spherical Bessel \
L=1 (red) 10",
xtitle="x",
xmin=Xmin,
xmax=Xmax,
ymin=0.2,
ymax=0.5)
funct1 = vp.gcurve(color=color.red)
funct2 = vp.gcurve(color=color.green)
def down(x, n, m): # Recursion woo!
"""
Moving downward in the pyramidal method
we apply the Bessel equation to find the
range of the Bessel function
"""
j = np.zeros((start + 2), float) # initialize zeros
import numpy as np
import vpython as vp
"""
Solve the wave equation for a string of length L = 1m with its ends fixed and with the gently
plucked initial conditions.
"""
# curve
g = vp.display(width=600, height=300, title="Vibrating String")
vibst = vp.curve(x=list(range(0, 100)), color=color.yellow)
ball2 = vp.sphere(pos=(100, 0), color=color.red, radius=2)
ball2 = vp.sphere(pos=(-100, 0), color=color.red, radius=2)
ball2.pos
ball2.pos
vibst.radius = 1
# parameters
rho = .01 # string density
ten = 40 # string tension
c = np.sqrt(ten / rho) # propogation speed
c1 = c # Courant–Friedrichs–Lewy condition
ratio = c * c / (c1 * c1)
# initialize with initialize conditions
xi = np.zeros((101, 3), float)
for i in range(0, 81):
xi[i, 0] = .00125 * i
for i in range(81, 101):
xi[i, 0] = .1 - .005 * (i - 80)
for i in range(0, 100):
vibst.x[i] = 2 * i - 100
# j+=1
# if r==4: # South
# if j==0:
# currentcolor = vpython.color.green
# #continue
# else:
# currentcolor = vpython.color.blue
# j-=1
if edgeflag==True:
return [vpython.vector(i,j,0),edgecolor]
else:
return [vpython.vector(i,j,0),currentcolor]
L = 11 # length of side of lattice
i = j = 5 # starting position of particle -- center of lattice
d = vpython.display(background=vpython.color.white) # for the animations, later
#d.autoscale = False
#d.background=vpython.color.white
currentcolor = vpython.color.white
position = vpython.vector(i,j,0) # 3-D coordinates of starting position
s = vpython.sphere(pos=position,radius=1.5,color=currentcolor)
steps = 100
for t in numpy.arange(steps):
vpython.rate(10) # rate for visualization
l = vpython.sphere(pos=position,radius=1,color=currentcolor)
r = random.randint(1,4)
#update position vector
walk_list = walk(position,L,currentcolor)
position = walk_list[0]
currentcolor = walk_list[1]
final = vpython.sphere(pos=position,radius=1.5,color=vpython.color.black)
================================================================================"""
from __future__ import division, print_function
#import visual as vs
import vpython as vs # for 3D panel
import wxPython as wx # for widgets
# Draw window & 3D pane =================================================
win = vs.window(width=1024,
height=720,
menus=False,
title='SIMULATE VPYTHON GUI')
# make a main window. Also sets w.panel to addr of wx window object.
scene = vs.display(window=win,
width=830,
height=690,
forward=-vs.vector(1, 1, 2))
# make a 3D panel
clr = vs.color
vss = scene
# Draw 3D model ======================
def axes(frame, colour, sz, posn): # Make axes visible (of world or frame).
# Use None for world.
directions = [
vs.vector(sz, 0, 0),
vs.vector(0, sz, 0),
vs.vector(0, 0, sz)
]
import numpy as np
import vpython as vp
from random import random
"""
Produce a 3-D graph of 3-D Random walk. It's a mathematical
formalization of a path of random steps in succession.
"""
random.seed(123)
jmax = 1000
xx = yy = zz = 0.0
graph1 = vp.display(x=0, y=0, width=600, height=600, title="3D Random Walk", forward=(-.6, -.5, -1))
# Create the curve
pts = np.curve(x=list(range(0, 100)), radius=10.0, color=color.yellow)
xax = np.curve(x=list(range(0, 1500)), color=color.red, pos=[(0, 0, 0), (1500, 0, 0)], radius=10.)
yax = np.curve(x=list(range(0, 1500)), color=color.red, pos=[(0, 0, 0), (0, 1500, 0)], radius=10.)
zax = np.curve(x=list(range(0, 1500)), color=color.red, pos=[(0, 0, 0), (0, 0, 1500)], radius=10.)
xname = np.label(text="X", pos=(1000, 150, 0), box=0)
yname = np.label(text="Y", pos=(-100, 1000, 0), box=0)
zname = np.label(text="Z", pos=(100, 0, 1000), box=0)
# Starting point
pts.x[0] = pts.y[0] = pts.z[0]
for i in range(1, 100):
xx += (random() - 0.5)*2
yy += (random() - 0.5)*2
zz += (random() - 0.5)*2
print(r)
return i, j
def radius(i, j):
dx = i - L // 2
dy = j - L // 2
distance = sqrt(dx**2 + dy**2)
#print(dx,dy)
return distance
# Configuring view
d = display(center=(L // 2, L // 2))
s = sphere()
s.pos = L, L
d.autoscale = False
s.visible = False
grid = zeros((L, L), bool)
center = L // 2, L // 2 #50,50
add(*center)
t = 0
r = 1
while r * 2 < L // 2:
t += 1
i, j = circle(r)
ri = 0
import vpython as vp
from random import random
"""
Simulate the growth of ferns (fractial) in 3-dimensions. Simply beautiful.
"""
imax = 200000 # points
x = .5
y = 0
z = -2
xn = 0
yn = 0
graph1 = vp.display(width=500, height=500, forward=(-1,1),\
title="3D Fractal Fern (rotate via right mosue button)", range=10)
graph1.show_rendertime = True
# Using points: cycle = 27 ms. render = 6 ms.
# Using spheres: cycle = 270 ms. render = 30 ms.
pts = points(color=color.green, size=0.01)
for i in range(1, imax):
r = random()
if r <= .1: # 10% probability
xn = 0
yn = .18 * y
zn = 0
elif r > .1 and r <= .7: # 60% probability
xn = .85 * xn
yn = .85 * y + .1 * z + 1.6
color.cyan,
color.magenta,
color.green,
]
SLEEP_SECONDS = 0.25 # seconds to delay among each simulation dt
SAMPLING_RATE = 0.5 # dts to skip among each sampling
sigma = 10
# maximum displacement applied when computing the particles movement
# Window
window = display(
title=WINDOW_TITLE,
autocenter=1,
autoscale=1,
width=WINDOW_WIDTH,
height=WINDOW_HEIGHT,
)
# Axis X
axisX = curve(pos=[(-sigma, 0, 0), (sigma, 0, 0)],
color=color.white,
radius=CUBE_THICKNESS)
# Axis Y
axisY = curve(
pos=[(0, -4 * sigma, 0), (0, 4 * sigma, 0)],
color=color.white,
radius=CUBE_THICKNESS,
)
import numpy as np
import vpython as vp
"""
Runge-Kutta method (rk4 algorithm) for determining solutions to the 1-Dimensional Schrödinger equation
for bound-state energies.
Now I ain't sayin she a Schrodinger,
but she ain't messin with no old thinker,
"""
psigr = vp.display(x=0, y=0, width=600, height=300, title="R and L Wavefunction")
Lwf = vp.curve(x=list(range(502)), color=color.red)
Rwf = vp.curve(x=list(range(997)), color=color.yellow)
eps = 1e-3
n_steps = 501
E = -17 # Idk I'm just guessing this energy.
h = .04
count_max = 100
Emax = 1.1*E
Emin = E/1.1
def f(x, y, F, E):
"""
Bound state energy function.
"""
F[0] = y[1]
F[1] = -(.4829)*(E-V(x))*y[0]
def V(x):
"""
import numpy as np
import vpython as vp
"""
Solve Maxwell's equations with FDTD time-stepping for circularly polarized wave propogations
in the z-direction in free space.
"""
scene = vp.display(x=0,
y=0,
width=600,
height=400,
range=200,
title="Circular polarization: E field \
in white. H field in yellow")
global phy, pyx
max = 201
c = .01 # Courant stability condition
# set arrays
Ex = np.zeros((max + 2, 2), float)
Hy = np.zeros((max + 2, 2), float)
Ey = np.zeros((max + 2, 2), float)
Hx = np.zeros((max + 2, 2), float)
arrowcol = color.white
Earrows = []
Harrows = []
for i in range(0, max, 10):
Earrows.append(arrow(pos=(0, i - 100), axis=(0, 0, 0), color=arrowcol))
import vpython as vp import numpy as np """ Use the Numerov method to solve the 1-D time-independent Schrödinger equation for bound-state energies. People generally use the Runge-Kutta model method for solving ODEs (using a search routine for solving the eigenvalue problem). Numerov, on the other hand, is specialized for ODes not contaiing any first derivatives (so we can apply it to the Schrödinger equation). IT's not as general as rk4, but it's of O(h^6) so it's fast with more precision. """ psigr = vp.display(x=0, y=0, width=600, height=300, title="R and L Wave Functions") psi = vp.curve(x=list(range(0, 1000)), display=psigr, color=color.yellow) psi2gr = vp.display(x=0, y=300, width=600, height=300, title="Wave func^2") psio = vp.curve(x=list(range(0, 1000)), color=color.magenta, display=psi2gr) energr = vp.display(x=0, y=500, width=600, height=200, title="Potential and E") poten = vp.curve(x=list(range(0, 1000)), color=color.cyan, display=energr) autoen = vp.curve(x=list(range0, 1000)), display=energr) dl = 1e-6 # interval to stop bisection ul = np.zeros([1501], float) # u value for left side ur = np.zeros([1501], float) # and the right side k2l = np.zeros([1501], float) # k**2 Schrodinger equation left wavefunction k2r = np.zeros([1501], float) # k**2 S. E. right wavefunction n = 1501 m = 5 # plot every 5 points imax = 100 # number of iterations xl0 = -1000 xr0 = 1000 h = (1*(xr0-xl0)/(n-1)) # h constant
import vpython as vp
import numpy as np
"""
Animated visualizations of the Schrodinger's equation solutions
"""
# wave function, probability, potential
dx = 0.04
dx2 = dx**2
k0 = 5.5 * np.pi
dt = dx2 / 20.0
xmax = 6.0
g = vp.display(width=500,
height=250,
title="Wave packet in harmonic oscillator potential")
PlotObj = vp.curve(x=xs, color=color.yellow, radius=0.1)
g.center = (0, 2, 0)
psr = np.exp(-.5 * (xs / .5)**2) * np.cos(k0 * xs)
psi = np.exp(-.5 * (xs / .5)**2) * np.sin(k0 * xs)
v = 15.0 * xs**2
while True:
vp.rate(500)
psr[1:-1] = psr[1:-1] - (dt / dx2) * (
psi[2:] + psi[:-2] - 2 * psi[1:-1]) + dt * v[1:-1] * psi[1:-1]
psi[1:-1] = psi[1:-1] - (dt / dx2) * (
psr[2:] + psr[:-2] - 2 * psr[1:-1]) + dt * v[1:-1] * psr[1:-1]
PlotObj.y = 4 * (psr**2 + psi**2)
import numpy as np
import vpython as vp
"""
Finite-Difference Time Domain Method of findings solutions to Maxwell's equations for linearly
polarized wave propogation in the z-direction in free space.
"""
xmax = 201
ymax = 100
zmax = 100
scene = vp.display(x=0, y=0, width=800, height=500, title="E: cyan, H: red. Periodic Boundary conditions",
forward=(-.6,-.5,-1))
Efield = vp.curve(x=list(range(0, xmax), color=color.cyan, radius=1.5, display=scene))
Hfield = vp.curve(x=list(range(0, xmax), color=color.cyan, radius=1.5, display=scene))
vplane = vp.curve(pos=[(-xmax, ymax), (xmax, ymax), (xmax, -ymax), (-xmax, -ymax),
(-xmax, ymax)], color=color.cyan)
zaxis = vp.curve(pos=[(-xmax, 0), (xmax, 0)], color=color.magenta)
hplace = vp.curve(pos=[(-xmax, 0, zmax), (xmax, 0, zmax), (xmax, 0, -zmax), (-xmax, 0, -zmax),
(-xmax,0, zmax)], color=color.magenta)
ball1 = vp.sphere(pos =(xmax+30, 0, 0), color=color.black, radius=2)
ts = 2
beta = .01
# initialize arrays
Ex = np.zeros((xmax, ts), float)
Hy = np.zeros((xmax, ts), float)
# label
Exlabel1 = label(text="Ex", pos=(-xmax-10, 50), box=0)
