After revisiting the Google talk about splines and fractals I had the idea to do this in three-dimensional space by using quaternions instead of complex numbers. It turned out that it wasn’t utterly difficult to render a simple three-dimensional Sierpinski gasket (or Menger-Sponge) using PovRay. At least installing PovRay on my Mac took more time than writting the script.
While fuzzing around with PovRay a crazy idea came to my mind: why not write my own ray tracer. Of course that would only be the simplest possible as I only wanted to get a rough understanding on how this stuff works. After doing a bit of research it turned out that it shouldn’t be a too difficult task. Hey, this is one of the excercises in every “Computer graphics basics” lecture.
Three hours later I had a rough shot, but somehow my maths for calculating the rays was wrong. The day after, a friend of mine and myself went to a maths professor at my University and asked him if he could have a quick look at the formulas. His explanations were (as always) very insightful and simply brilliant. With the ideas he gave us we went on to get the missing bits done. And 4 more hours later we had a working ray tracer. (The sierpinski gasket was not rendered by my ray tracer, but I can’t figure out how to exclude images from the WordPress gallery).
Of course after 7 hours of work the ray tracer is far from being perfect. There are a few neat features missing (which might follow) such as shadows, reflection and radiosity (which would really be a big task). Also the maths concerning the projection plane are not totaly right. We should rather introduce a coordinate system transformation to get this done than hacking things together as it is right now. All in all it was a lot of fun to write that thing. If you want to have a look at the source code, check it out here (username: guest, password: guest).