In this paper we discuss the challenges of processing and converting 3D scanned data to representations suitable for interactive manipulation in the context of virtual restoration applications. We present a constrained parametrization approach that allows us to represent 3D scanned models as parametric surfaces defined over polyhedral domains. A combination of normal- and spatial-based clustering techniques is used to generate a partition of the model into regions suitable for parametrization. Constraints can be optionally imposed to enforce a strict correspondence between input and output features. We consider two types of virtual restoration methods: (a) a paint restoration method that takes advantage of the normal-based coarse partition to identify large regions of reduced metric distortion suitable for texture mapping and (b) a shape restoration approach that relies on a refined partition used to convert the input model to a multiresolution subdivision representation suitable for intuitive interactive manipulation during digital studies of historical artifacts.