This paper presents an approach for mapping layouts of parametric surface patches to a target 3D geometry. Its main contribution is to facilitate the feature based placement of an arbitrary network of patches, assuring that both boundaries and parametric flow conform to features of the target shape. The technique, referred to as dynamic templates, describes the algorithms and interface of a reverse engineering system, Paraform, that integrates techniques relying on a judicious choice of automation and user guided tools. Our approach is based on a novel use of constrained optimization for the fairing of structured surface grids, where grid points can be unconstrained in 3D or constrained to lie within the parameter space of curves, surfaces, or other geometry. We present our results as case studies in large industrial workflow problems, involving the reuse of geometric data.