Let $X=\mathbb{P}^1 \times \mathbb{P}^1$ and let $\mathcal{O}(a,b):=\pi^*_1\mathcal{O}(a)\otimes \pi^*_2\mathcal{O}(b)$. Is there a general expression for $$RHom_X(\mathcal{O}(a,b),\mathcal{O}(x,y))$$
Are you looking for something different than $H^0(X, \mathcal{O}(x-a, y-b))$? –  Mike Skirvin Jun 30 '10 at 17:52