Flash Ray Tracer Reflections

Finally managed to get reflections properly working in my actionscript raytracer. The mathematics behind reflections is very simple. Given an incoming light ray V, and a surface normal N, we can calculate the reflected light ray R using:

a = V.N
R = V + 2*a*N

I applied this theory to the ray tracer and the results are beautiful. Its amazing how much realism a few shadows and reflections can create! The number of reflections obviously changes the image realism. The images below show 1, 2 and 3 reflections per ray. Surprisingly there really isn't much of a reduction in performance - and for the purposes of a flash raytracer 3 reflections should be plenty!

Just need to add some functionality for box reflection and then I'll set the engine rendering some nice scenes!

One further extension I might set myself is diffuse reflections. Instead of light being reflected directly along the normal, there could be random fluctuations in the reflection vector. I think this could produce quite a nice wave effect. I'll keep you posted!

On a performance note the image with 3 reflections took just over 2 minutes to render in 1600x1600 with no real optimisation. For a resolution of 400x400 pixels it takes about 2.5 seconds. Not too bad at all in my opinion!

Update: Here are a few fuzzy shots. The first one is less fuzzy and the second one is more fuzzy. Quite an interesting effect I think:

Decided to go a bit mad and rendered a rather large image with a load of boxes and reflective spheres. Inspired by SuperJers PixelMachine, but rendered completely using flash and AS3, not OpenGL and C++. Here it is (Something has gone wrong with the reflections of the boxes - there is no shadowing - but I didn't have the heart to stop it once it was half way through!):

Here is another nice one, 2880 by 2880 pixels, back to the original room but with the reflection stuff added. Looks quite nice in the super high resolution!

Update: I've rendered few more large reflective images - there is still something slightly wrong with the reflections I think, check them out: