Constructions of G1 continuous joins of rational Bézier patches Original Research Article

We derive necessary and sufficient conditions for G1 continuity of a join between rational Bézier patches (rectangular, triangular, or of a different shape). Using these conditions, we analyze the problem of fitting a patch to another one so as to create a G1 continuous join. The obtained results characterize the set of solutions of the problem. As an application, we present methods of constructing a join, that can be used in an interactive geometric editor.