Symmetric Hermite Subdivision Schemes with a General Dilation Matrix
by
Bin Han
University of Alberta
Coauthors: Thomas Yu

Recently, there is a growing interest in generating subdivision surfaces in CAGD using a subdivision scheme with a general dilation matrix. The square-root-3 subdivision and the 4-8 subdivision schemes are two examples. In this talk, we shall discuss a more general class of interpolating schemes - refinable Hermite interpolants for a general dilation matrix. In particular, we shall discuss the symmetry properties and how to construct 2D Hermite interpolants. Interestingly, some of the examples we have of 2D refinable Hermite interpolants have a close connection to some well known spline methods such as Powell-Sabin scheme. Refinable Hermite interpolants and Hermite subdivision schemes have a lot of desirable features in generating subdivision surfaces which we shall discuss in this talk. Examples will be given to demonstrate the possible advantages of refinable Hermite interpolants with a general dilation matrix.

Date received: December 11, 2001