Much of this is adapted from http://sagenb.org/home/pub/1337/
var('x,y,z')
@interact
def _(equation=input_box(default=(x-1)^2+(y-2)^2+(z+3)^2==16), size=(5)):
show(implicit_plot3d(equation, (x,-size,size),(y,-size,size),(z,-size,size)))
print html('Enter implicitly defined surface in 3-d (in variables x, y and z) and size of display box.')
Click to the left again to hide and once more to show the dynamic interactive window |
|||||||||||||||||
# the # makes this a comment, so nothing happens
# the equation below is the 3-d surface we graphed in class
# x == y^2 + 4*z^2
|
|
# cylinder as copies of a circle stacked on top of each other:
c=circle((0,0), 1,thickness=3,rgbcolor='red')
#
c.plot3d(z=0)+c.plot3d(z=1)+c.plot3d(z=2)+c.plot3d(z=.5)+c.plot3d(z=1.5)
|
|
Graph of the 3-d surface (cylinder) along with traces in several planes parallel to the xy-plane:
var('x,y,z')
implicit_plot3d(x^2+y^2==1,(x,-2,2), (y,-2,2), (z,-2,2))+sum(c.plot3d(z=i) for i in [-2,-1.5..2])
|
|
p=plot(x^2 + 1, (x, -4, 4),thickness=3,color='red')
p
|
|
sum(p.plot3d(z=i) for i in [-2,-1.5..2])
|
|
Graph of a parabolic cylinder (cylinders don't have to be circular!) along with traces in several planes parallel to the xy-plane:
var('x,y,z')
implicit_plot3d(y==x^2+1,(x,-4,4), (y,-1,20), (z,-2,2))+sum(p.plot3d(z=i) for i in [-2,-1.5..2])
|
|
Graph of a parabolic cylinder in a different direction:
var('x,y,z')
implicit_plot3d(z==y^2+1,(x,-2,2), (y,-4,4), (z,-2,20))
|
|
|
|