k = 25 # spring constant
m = 20 # block mass
b = 0.5 # viscosity friction (proportional to velocity)
dt = 0.1 # time step
#initial conditions
v = vector(0, 0, 0.2)
x = vector(x0, 0, 0)
xr = vector(l_rest, 0, 0)
sx0 = vector(-0.8, 0, 0)
offx = vector(0, 0.3, 0)
vp.box(pos=(0, -0.1, 0), length=2.0, width=0.02, height=0.5) #surface
vp.box(pos=(-.82, .15, 0), length=.04, width=0.50, height=0.3) #wall
block = vp.cube(pos=x, length=0.2, c='t')
spring = vp.helix(sx0, x, r=.06, thickness=.01, texture='metal1')
pb = ProgressBar(0, 500, c='r')
for i in pb.range():
F = -k * (x - xr) - b * v # Force and friction
a = F / m # acceleration
v = v + a * dt # velocity
x = x + v * dt + 1 / 2 * a * dt**2 # position
block.pos(x) # update block position
spring.stretch(sx0, x) # stretch helix accordingly
trace = vp.point(x + offx, c='r/0.5', r=3) # leave a red trace
vp.camera.Azimuth(.1)
vp.camera.Elevation(.1)
vp.render(trace) # add trace to the list of actors and render
pts2 = vp.points(coords2, r=1, legend='#points = ' + str(len(coords2)))
vp.show([a2, pts2], at=1, interactive=True)
########################################################################################
# Draw a bunch of simple objects on separate parts of the rendering window:
# split window to best accomodate 9 renderers
vp = Plotter(N=9, title='basic shapes')
vp.sharecam = False # each object can be moved independently
vp.show(at=0, actors=vp.arrow([0, 0, 0], [1, 1, 1]), legend='arrow')
vp.show(at=1, actors=vp.line([0, 0, 0], [1, 1, 1]), legend='line')
vp.show(at=2, actors=vp.points([[0, 0, 0], [1, 1, 1]]), legend='points')
vp.show(at=3, actors=vp.text('Hello!'))
vp.show(at=4, actors=vp.sphere())
vp.show(at=5, actors=vp.cube(), legend='cube')
vp.show(at=6, actors=vp.ring(), legend='ring')
vp.show(at=7, actors=vp.helix(), legend='helix')
vp.show(at=8, actors=vp.cylinder(), legend='cylinder', interactive=1)
########################################################################################
# Draw a bunch of objects from various mesh formats. Loading is automatic.
vp = Plotter(shape=(3, 3),
title='mesh formats') # split window in 3 rows and 3 columns
vp.sharecam = False # each object can be moved independently
vp.show('data/beethoven.ply', at=0, c=0, axes=0,
ruler=1) # dont show axes, add a ruler
vp.show('data/cow.g', at=1, c=1, zoom=1.15) # make it 15% bigger
vp.show('data/limb.pcd', at=2, c=2)
vp.show('data/ring.gmsh', at=3, c=3, wire=1)
vp.show('data/images/dog.jpg', at=4) # 2d images can be loaded the same way
vp.show('data/shuttle.obj', at=5, c=5)
vp.show('data/shapes/man.vtk', at=6, c=6,
Fgrav = vector(0, -M*9.81, 0)
gaxis = vector(0, 0, 1) # initial orientation of gyroscope
gaxis = norm(gaxis)
I = 1/2*M*R**2 # moment of inertia of gyroscope
Lrot = I*omega*gaxis # angular momentum
cm = gpos + 0.5*Ls*gaxis # center of mass of shaft
# ############################################################ the scene
vp = Plotter(verbose=0, axes=0, interactive=0)
shaft = vp.cylinder([[0,0,0], Ls*gaxis], r=0.03, c='dg')
rotor = vp.cylinder([(Ls-0.55)*gaxis, (Ls-0.45)*gaxis], r=R, c='t')
bar = vp.cylinder([Ls*gaxis/2-R*vector(0,1,0), Ls*gaxis/2+R*vector(0,1,0)], r=R/6, c='r')
gyro = vp.Assembly([shaft, rotor, bar]) # group actors into a single one
spring= vp.helix(top, gpos, r=0.06, thickness=0.01, c='gray')
vp.box(top, length=0.2, width=0.02, height=0.2, c='gray')
vp.box(pos=(0,.5,0), length=2.2, width=3, height=2.2, c='gray', wire=1, alpha=.2)
# ############################################################ the physics
pb = ProgressBar(0, 5, dt, c='b')
for t in pb.range():
Fspring = -ks*norm(gpos-top)*(mag(gpos-top)-Lrest)
torque = cross(-1/2*Ls*norm(Lrot), Fspring) # torque about center of mass
Lrot += torque*dt
precess += (Fgrav+Fspring)*dt # momentum of center of mass
cm += (precess/M)*dt
gpos = cm - 1/2*Ls*norm(Lrot)
# set orientation along gaxis and rotate it around its axis by omega*t degrees
gyro.orientation(Lrot, rotation=omega*t*57.3).pos(gpos)
vp.box(pos=(bob_x[0], bob_y[0], 0),
length=12,
width=12,
height=.7,
c='k',
wire=1)
bob = [vp.sphere(pos=(bob_x[0], bob_y[0], 0), r=R / 2, c='gray')]
for k in range(1, N + 1):
bob.append(vp.cylinder(pos=(bob_x[k], bob_y[k], 0), r=R, height=.3, c=k))
# Create the springs out of N links
link = [0] * N
for k in range(N):
p0 = bob[k].pos()
p1 = bob[k + 1].pos()
link[k] = vp.helix(p0, p1, thickness=.015, r=R / 3, c='gray')
# Create some auxiliary variables
x_dot_m = [0] * (N + 1)
y_dot_m = [0] * (N + 1)
dij = [0] * (N + 1) # array with distances to previous bob
dij_m = [0] * (N + 1)
for k in range(1, N + 1):
dij[k] = mag([bob_x[k] - bob_x[k - 1], bob_y[k] - bob_y[k - 1]])
fctr = (lambda x: (x - 1) / x)
Dt *= np.sqrt(1 / g)
Dt2 = Dt / 2 # Midpoint time step
DiaSq = (2 * R)**2 # Diameter of bob squared
