ABSTRACT
This chapter introduces the notion of subdivision operators to describe the subdivision schemes defined by the subdivision matrices. The refinement sequence of any compactly supported scaling function can be used to formulate a subdivision matrix that has a chance for the subdivision scheme to converge, as long as it satisfies the sum-rule condition. The chapter studies the implications of subdivision convergence and provides an algorithm with only finite sequences and sums for the rendering of the graph of the scaling functions.
