Thread: [Visualpython-users] 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
Sent from my iPad

Maybe this is a use case for the PyGeo package that uses Vpython, I believe?

Michael

On 08.06.2011, at 22:23, Joe Heafner <hea...@gm...> wrote:

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
Sent from my iPad

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Not sure what you're concerned about. It looks smooth to me until the
very end, where there is an abrupt change in the shape of the
rectangle. Also, something like rate(200) gives a better sense of the
morphing than rate(1000), in my opinion.

Bruce

On Wed, Jun 8, 2011 at 2:22 PM, Joe Heafner <hea...@gm...> wrote:
> 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.

You can use the new EXTRUSION object to start with any arbitrary shaped polygon 
in 2D.
I do not know about the solid angles, but if it is able to reduce the number of 
"sides" of the
polygon down to 4 with some algorithm, then you will end up with a 4-sided 
polygon, or a
square if all with right angles.

Kadir





________________________________
From: Joe Heafner <hea...@gm...>
To: Visualpython-users <vis...@li...>
Sent: Wed, June 8, 2011 11:22:23 PM
Subject: [Visualpython-users] 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 HeafnerSent from my iPad