We present a framework for analyzing non-linear Rd-valued
subdivision schemes which are geometric in the sense that they commute with
similarities in Rd. It admits to establish
C1,α-regularity for arbitrary schemes of this type, and
C2,α-regularity for an important subset thereof, which includes all
real-valued schemes. Our results are constructive in the sense that they can be
verified explicitly for any scheme and any given set of initial data by a
universal procedure. This procedure can be executed automatically and
rigorously by a computer when using interval arithmetics.Comment: 31 pages, 1 figur