GradH-Correction: guaranteed sizing gradation in multi-patch parametric surface meshing

In this paper a new method, called GradH-Correction, for the generation of multi-patch parametric surface meshes with controlled sizing gradation is presented. Such gradation is obtained performing a correction on the size values located on the vertices of the background mesh used to define the control space that governs the meshing process. In the presence of a multi-patch surface, like shells of BREP solids, the proposed algorithm manages the whole composite surface simultaneously and as a unique entity. Sizing information can spread from a patch to its adjacent ones and the resulting size gradation is independent from the surface partitioning. Theoretical considerations lead to the assertion that, given a parameter , after performing a GradHCorrection of level over the control space, the unit mesh constructed using the corrected control space is a mesh of gradation in the real space (target space). This means that the length ratio of any two adjacent edges of the mesh is bounded between 1/ and . Numerical results show that meshes generated from corrected control spaces are of high quality and good gradation also when the background mesh has poor quality. However, due to mesh generator imprecision and theoretical limitations, guaranteed gradation is achieved only for the sizing specifications and not for the generated mesh