 


63K 

The initial frame of this movie shows stereographic projection of the cube
looking directly at one of its faces, so we see a square within a square.
As the movie progresses, the distance to the light source is increased
toward infinity, and at the end, the light source is infinitely far away,
so its rays are parallel. Thus the images of both the closest and farthest
squares are the same size. We only see one square in the projection as
both squares now overlap.




155K 

This movie shows our (orthographic) view of a cube as we move from
looking directly at a face to looking directly at an edge. At several
points in the movie, we rotate the cube slightly so that you can see all of
its faces. This is to help you understand the "sliding squares" image
that you are viewing. The front face is colored blue and the back face
red. In the orthographic projections, the two squares seem to slide past
each other.




183K 

This movie shows the same sequence of motions as the previous one, but
this time the two side faces of the cube are colored. In the initial view,
the sides are projected as lines (since they are parallel to the light
source) so we don't see the color.




188K 

This movie shows the cube rotating from a view that is directly at an
edge to a view that is directly at a corner. Again, we tilt the cube
slightly at several points in the movie so that you can follow the action a
bit better. The final position is looking directly down the long diagonal
of the cube.




124K 

This movie shows the cube rotating from a viewpoint were we look
directly at a face to where we look direclty at a corner, down the long
diagonal of the cube. This corresponds to our earlier view of the cube as
two squares moving apart. That original movie was a correct shadow (as
the light source moves from directly above to a slanted direction), but it
does not represent a view of the cube we could ever actually see, since our
image is always perpendicular to the direction of sight. This movie
shows a more correct view of the cube.




114K 

This movie shows the same sequence of motions as the previous one, but
with a different set of faces colored. We now color the left and right
faces rather than the front and back. Notice that in the final view, these
faces have the same shape as in the previous movie. In fact, in this
view, all the faces of the cube have the same shape in the projection, so
this is one of the most symetric views of the cube.




113K 

This movie show the rotation from looking directly at a face, to
looking direclty at an edge and then to looking direclty at a corner. Now
that you have seen the other ones, this one should make more sense.
