Automatic Hybrid Mesh Generation: a Novel Normal Calculation Technique Using the Eikonal Equation and Its Applications in Geometric Modeling and Mesh Generation

The main contribution of the proposed method is the presented front propagation methodology which is directly inspired from marching technology. All the points located on the original front are propagated along the local normal directions. The main difference between the current method and traditional marching methods lies in the way that local normal direction is computed. Traditionally, the local normal directions are computed using geometric information, such as the average normal of neighboring points or facets surrounding the point to be propagated. In this method, the local normal directions are calculated using the solution of a variation of the Eikonal equation. The benefit of calculating normal directions in such a way is that self-intersections are avoided in a natural way. Since normal directions are represented using the numerical solution of the PDE, propagation is thus performed in the field of the solution of the equation rather than geometric space. In addition, the proposed method transports the original parameterization to the propagated surface in a one-to-one manner between the original front and its offset, which allows rigorous matching of block interfaces