CS40: Computer Graphics, Lab 7
3D Solids
By Jeff Kaufman
In this lab I extended the graphics library I started in
lab 2 by adding support for solid objects.
Required Images
Cubism
Transformation Results
Note: in all of these images there are gaps between many polygons.
These are the result of pesky off-by-one errors in my scanline
fill code which I should go back and track down. Because I've not
yet implemented shading, though, they aren't all bad, helping us
see the shapes of the objects. And we can use them to see that
backfaces really are being clipped properly, as we never get bits
of the backs of objects showing through in those gaps.
The images below are all example frames from short movies that
demonstrate the appropriate transformations by varying a
transformation parameter smoothly over time.
Rotate X
Rotate Y
While in this video there appears to be some sort of Z-ordering going
on, such that objects that are close to the viewer don't show up with
other objects in front of them, this is just an ugly hack. The code
that generated the animation knew which frame it was drawing and for
the second half of the frames reversed the order in which the objects
were added to the module, reversing the order in which they were drawn.
Rotate Z
Rotate XYZ
Using the rotateXYZ function and a cosine to make smooth movements.
Scale
Translate
Backface Culling
Most solid objects will only ever be seen from either inside or
outside. We can make the rendering process more efficient, then,
by makeing polygons optionally one sided. To implement this I
added a field, Vector polyNorm to the Polygon object
to hold a normal. If the normal is set to the zero vector the
polygon is visible from both sides. Otherwise the polygon is
drawn only if after the application of the perspective
transformations the Z component is poistive. To keep
compatibility with the spec and previous versions, polygon
functions assume that the user wants two sided polygons unless
otherwise specified.
The movie below shows a four colored sphere rotating with
backfaces not drawn. Backfaces were also culled from the images
above.
Jeff Kaufman : 2006
cbr at sccs
dot swarthmore dot spam edu. Remove spam.
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