Composite Primal/Dual sqrt(3)-Subdivision Schemes

We present new families of primal and dual subdivision schemes for triangle meshes and sqrt(3)-refinement. The proposed schemes use two simple local rules which cycle between primal and dual meshes a number of times. The resulting surfaces become very smooth at regular vertices if the number of cycles is > 2. The C (sup) 1-property is violated only at low-valence irregular vertices, and can be restored by slight modifications of the local rules used....