The automation of the function-based (FRep) volumetric modeling task is tackled by introducing template parameterized models and a procedure for recovery of constructive models from segmented point-sets. In order to reuse existing models, we propose to parameterize them and to fit the parameters to different point-sets for optimizing and adapting the shape to different objects of the same class of shapes. The automation of the creation of a constructive FRep model is also considered by creating a recovery procedure for a given segmented point-set and a list of corresponding primitives. A genetic algorithm is used to find the best constructive expression for the object with the given set of primitives in the point cloud segmentation and the set of available operations. The proposed approach is illustrated by fitting of different models to point clouds and by the automatic generation of constructive trees from segmented point-sets for real mechanical parts.