  We extend some parts of the representation theory for integral quadratic
forms over the ring of integers of a number field to the case over the
coordinate ring $k[C]$ of an affine curve $C$ over a general base field $k$. By
using the genus theory, we link the strong approximation property of certain
spin groups to the Hasse principle for representations of integral quadratic
forms over $k[C]$ and derive several applications. In particular, we give an
example where a spin group does not satisfy strong approximation.
