Understanding an implementation of Jacobi SVD

I found the following link: Jacobi SVD link

I want to understand how to complete the Jacobi SVD method that is provided, but the algorithm is stated in a confusing way... In the code skeleton, the author does not seem consistent with the algorithm. Really, my confusion is how to implement alpha, beta, and gamma, since it seems straightforward that:

     c = 1/sqrt(1+t^2);
     s = c*t;

     V(:,i) = c*t - s*V(:,j);
     V(:,j) = s*t + c*V(:,j);

toward the bottom. Can anyone provide more clarity? Thank you.