Finite Element Method - Elastic Ball

This video is part of the assignemnt of class Physical-based Animation.
I implement the elastic effect with standard Finite Element Method: http://graphics.berkeley.edu/papers/Obrien-GMA-1999-08/

On Going Ray-tracing Class Project

Here is my ray-tracing class on going project page:
http://www.cs.utah.edu/~owuntu/cs6620/index.html

Feel free to leave some comments, ask questions, point out problem, or rush my ray!

Ray-tracing Refraction - Floating Point Error

To implement refraction in ray-tracing rendering, we can simply use the refraction equation:

sin(theta1)/sin(theta2) = n2/n1

http://en.wikipedia.org/wiki/Refraction

To compute sin(theta1), simply:

cos(theta1)= v1.dot(N);

sin(theta1) = sqrt(1-cos(theta1) * cos(theta1)); 

where v1 is the incomming ray direction, and N is the surface normal.

However, there may be trouble when this implementation runs in computer. In C++, since we can't avoid floating point error, when v1 is almost perpendicular to the surface, that is, v1 and N almost the same (or they just be the same), cos(theta1) could slightly greater than 1 (something like 1.00001). Then, this result would cause:

1-cos(theta1) * cos(theta1) < 0

And sqrt(a) would return invalid result if a<0. So that sin(theta1) becomes a invalid value. Eventually, all the computation mess up. The pixel we want to shade becomes an error pixel. 

To avoid this, simply put a check routine like:

cos(theta1) = min(1.0f, v1.dot(N))

Never trust floating point number!!