Interpolatory root 3-subdivision

We represent a new interpolatory subdivision scheme for triangle meshes. In stead of splitting each edge and performing a 1-to-4 split for every triang le we compute a new vertex for every triangle and retriangulate the old and the new vertices. Using this refinement operator the number of triangles o nly triples in each step. New vertices are computed with a Butterfly like s cheme. In order to obtain overall smooth surfaces special rules are necessa ry in the neighborhood of extraordinary vertices. The scheme is suitable fo r adaptive refinement by using an easy forward strategy. No temporary trian gles are produced here which allows simpler data structures and makes the s cheme easy to implement.