Remeshing Schemes for semi-regular tilings

Most frequently used subdivision schemes such as Catmull-Clark create regular regions after several applications. This paper shows that all semi-regular regions can be created by subdivision schemes and each semi-regular region type can be created with one application of a particular subdivision scheme to a particular regular region. Using this property of subdivision schemes it is easy to cover any given surface with semi-regular tiles by applying one semi-regularity creating subdivision after several applications of a regularity creating subdivision.