The proposed work consists of designing and developing a new algorithm for generating block-structured hexahedral meshes using a “Polycube”-typed strategy. Usually, these methods deform a geometric domain G to be discretized into a polycube P, i.e. a polyhedron whose all the faces are orthogonal to one of the X, Y, or Z axes. This polyhedron can be easily discretized using a hexahedral mesh, which is then transformed via the inverse deformation to pave G.

Unlike traditional approaches, which are based on constructing the deformation function, we focus on the inverse function by treating the pair (geometry G, polycube P) as input. Our goal is to compute the inverse function F that transforms P into G, and, depending on some local properties of F, modify P to provide a “better” mesh of G from a geometric point of view.