One way of studying geometry is to think about the sizes and shapes
of geometric figures like circles and triangles. Another way is to
think about how we can manipulate and transformation such geometric
figures. Computer graphics provide an excellent example of why both points
of view are important.
Almost all computer graphics are ultimately constructed by drawing
points, lines and various polygons, especially triangles. By using
many small polygons, the eye perceives the illusion of a smooth
object. Indeed, special effects companies like Industrial
Light and Magic have elevated making illusions to an art form.
However, even the most breathtaking scenes from Jurassic Park
still boil down to drawing and moving polygons.
Sometimes, the hardest part of a computer graphics project is
figuring out how to draw something. Even though you only have to be
able to draw lots of squares, figuring out how to arrange lots of them to
even roughly approximate a sphere can be quite a challenge:
Of course, once you have a polygonal model, the temptation to try to
animate it is nearly irresistable. Fortunately, unlike creating
the model in the first place, where each polygon must be individually
positioned, once you understand how to move one polygon
on the screen, you can move the entire model by mechanically
moving one polygon at a time. It just takes longer.
Next: Computer animation basics in "Traveling Triangles".
