  We study what we call quasi-spline sheaves over locally Noetherian schemes.
This is done with the intention of considering splines from the point of view
of moduli theory. In other words, we study the way in which certain objects
that arise in the theory of splines can be made to depend on parameters. In
addition to quasi-spline sheaves, we treat ideal difference-conditions, and
individual quasi- splines. Under certain hypotheses each of these types of
objects admits a fine moduli scheme. The moduli of quasi-spline sheaves is
proper, and there is a natural compactification of the moduli of ideal
difference-conditions. We include some speculation on the uses of these moduli
in the theory of splines and topology, and an appendix with a treatment of the
Billera-Rose homogenization in scheme theoretic language.
