Need coding suggestions

I want to create some VPython simulations related to Gauss's law, flux, and solid angle. I want to get across the point that any arbitrarily shaped surface can, mathematically, be morphed into a sphere using the concept of solid angle. Is there a way to make an arbitrarily shaped patch of area morph SMOOTHLY into a square in VPython? Below is the code I have so far. It works, but it's not as smooth as I'd like it to be.



from visual import *


# a field arrow
E = vector(1,-0.5,0)
Earrow = arrow(pos=vector(0,0,0),axis=E,shaftwidth=0.01,color=color.red)
Ehat = norm(E)

# a patch of area
# include option for circular patches
direction = vector(1,1,1)
patch = box(pos=(0,0,0),axis=direction,length=0.02,width=0.5,height=0.5)
# patch morphing is smoother if height > width

# patch's initial area
patch.height0 = patch.height
patch.area = patch.height*patch.width
print ("initial area        ", patch.area)

# a unit normal to patch
nhat = norm(patch.axis)
nhatarrow = arrow(pos=Earrow.pos,axis=nhat,shaftwidth=0.01,color=color.green)

scene.forward = -nhat

# get angle between the two vectors
newtheta = acos(dot(Ehat,nhat))
# check for newtheta = 0
# check for newtheta = pi
print ("angle               ",newtheta*180.0/pi)
print ("predicted perp area ", patch.area * cos(newtheta))

# get the new rotation axis
newaxis = cross(Ehat,nhat)

# rotation animation
scene.mouse.getclick()
print ("rotating...")

dtheta=0.001
theta=0.0
while theta < newtheta:
    rate(1000)
    nhatarrow.rotate(angle=-dtheta,axis=newaxis)
    patch.rotate(angle=-dtheta,axis=newaxis)
    patch.height = patch.height0*cos(abs(theta))
    theta += dtheta
patch.area = patch.area * cos(newtheta)
patch.width = sqrt(patch.area)
patch.height = patch.width

print ("actual perp area    ", patch.height*patch.width)
print ("patch axis ",norm(patch.axis))
print ("field axis ",norm(Earrow.axis))

Joe Heafner
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