This paper describes a new approach to identify freeform shape patterns in measured point data, to extract them and to fit their parameters. The method is based on direct matching of parameterized shape templates to digitized points. For a given class of feature, the optimal pose and the optimal intrinsic feature parameters are determined relative to the point data at hand. Although this principle has been used in digital image processing and also for fitting of prismatic features, it has rarely been applied in 3D to freeform features. Yet, several engineering applications may profit from improved feature fitting. The motivation of our investigation is the supporting of shape modeling using precedent designs available in the form of physical parts. We aim at an extension to what is generally known as reverse engineering. However, the proposed technique can also be used to extract feature parameters from imported CAD models. This paper addresses computational aspects of the method and presents the algorithms, implementation tests and numerical results.