IS2780 students,

Some hints on the perspective part of asn02.  There shouldn't be any special
cases in the perspective_project() function for different z values.  That is,
exactly the same mathematical operations apply in all cases so long as the
eye stays in front of the cube...  (DON'T WORRY about what happens if you move
the eye further in than the front of the cube!!!)  The visual motion of the
cube should be entirely smooth as you move the eye in XY or drag the cube.
Similarly, there should not be any discontinuous jumps as you move the eye
position in or out using the "i' and 'o' keys.  If these things happen then
you're probably doing something as an integer calculation rather than float.

A good way to see if your results are correct is to use a ruler to measure
the lengths of the front, middle and rear cube edges as they appear
on your screen with the cube kept in its unrotated and untranslated
position.  For the start (or reset) position on my screen the green
mid level (ie. z==0) edges of the cube happen to be 3 inches long.
Since the cube edges are 4 world units we now know that one world
unit actually corresponds to 0.75 inches on my screen.
(The actual length on your screen may be different depending on your
particular display size and resolution.)  Note that initially these
green lines are 16 Z units from the eye and their lengths do not
change as we drag the eye position in XY.  We can think of the Z=0
plane as the basic reference scale and things that are closer or
further from the eye must be drawn accordingly larger or smaller.
The eyez at 16 also tells us that the correct viewing distance from
my screen is 0.75 inches * 16 = 12 inches.

As discussed in class the projected size on the sreen is proportional
to the z distance from the eye. Therefore we can calculate the length of
the rear cube edges, that are 18 Z units from the eye, should be 16/18ths
as long as the green reference plane lines so that is 2.67 inches.
Similarly the front blue edges, that are initially 14 units from the
eye, project to 3*16/14 inches or ~3.43 inches.  Again, your inch values
may be different but the ratios will be the same.  In your program
you will of course compute these relative magnifications based on the
current eye position, view_plane_z and of course the XYZ of the point
you are projecting.  (Recall I said you can assume view_plane_z stays
at 0 but you can change that later after the rest is working if you want.)

Now test a special case that is easy to check...  Use the 'i' key
to move the eye in to Z=6 units.  At that position the front face of
the cube, at z = 4, is only half as far from the eye as the rear face
which is still at z = 8.  Therefore the front face lines should now be
exactly twice as long as the rear face lines.  The rear cube edges
are now 3*6/8 = 2.25 inches and the front edges 3*6/4 = 4.5 inches.
(The size of the P was also chosen so that for this position its top
should now just touch the height of the top rear edge.)  If you drag
the eye XY position you will see that none of the front, mid or rear
cube edges change length although the diagonal projections of the
front to rear edges definately change.

The size of the world units has not changed just because the eye
is now nearer to the screen.  So, for eyez=6 the correct viewing
position is only 4.5 inches from my screen.  This explains the
exagerated perspective which is the same as you would get by holding
a real 3inch cube this far from your eyes or equivalently looking
into a cubical room that would be 8*8*8 feet at 1 foot per world unit
while standing 12 feet from the middle of the room.  (ie. you would
be 8 feet away from the near wall and 16 feet from the far wall.)

For the purpose of this assignment don't worry about what happens
to points that reach z=0 relative to the eye or that go behind the
eye.  In most situations we would remove those points from the
viewing frustum according to a near clipping plane. (I guess I said
that earlier)

I hope this helps!!!!

Art