In this paper, we present a new and automaticnode projection algorithm to generate hexahedral meshes in extrusion geometries. It is designed to preserve the shapeof the cap surfaces in the inner layers of a sweeping mesh. The algorithm is based on least-squares approximation of affine mappings. We report that the functionals that have been traditionally used to compute the affine mapping generate four undesired effects on the inner layers of nodes.Namely, the flattening, skewing, offset scaling, and flipping of the inner layer meshes. To overcome these drawbackswe first analyze several properties of a new functional that depends on two vector parameters. Second, we introduce the concept of the pseudo-area and pseudo-normal vectorsdefined by a loop of nodes. In addition, we prove several geometrical properties of these vectors. Third, based on theproperties of the new functional and on the definition of the pseudo-normal vector, we detail a new projection algorithmthat automatically selects the functional vector parameters. The aim of this paper is to provide the implementation details to developers, although we also present the background of the algorithm. Finally, severalmesh examples are discussed to assess the properties of the proposed algorithm.