Automatic hexahedral mesh generation using a new grid-based method with geometry and mesh transformation

A geometry and mesh transformation approach is proposed to overcome the traditional problem of poorly shaped elements at the boundary using the grid-based method of mesh generation. This is achieved by transforming the original geometric model to a topologically similar recognition model which conforms fully to the Cartesian directions. Such a recognition model is constructed by tessellating the original model and then employing a fuzzy logic method to determine the normal directions of the faces. A three-dimensional field morphing algorithm is used to position the features of the recognition model. Such a recognition model is then meshed with hexahedral elements without any degeneracy using the new grid-based algorithm. The mesh of the recognition model is mapped back to the original geometric model by employing a transformation based on the Laplacian-isoparametric equation.