Non-self-overlapping structured grid generation on an n-sided surface

Most existing meshing algorithms for a 2D or shell figure requires the figure to have exactly four sides. Generating structured grids in the n-sided parametric region of a trimmed surface thus usually requires to first partition the region into four-sided sub-regions. We address the automatic structured grid generation problem in an n-sided region by fitting a planar Gregory patch so that the partition requirement is naturally avoided. However, self-overlapping may occur in some portions of the algebraically generated grid; this severely limits its usage in most of engineering and scientific applications where a grid system with no self-intersecting is strictly required. To solve the problem, we use a functional optimization approach to move grid nodes in the u-v domain of the trimmed surface to eliminate the self-overlapping. The derivatives of a Gregory patch, which are extremely difficult to compute analytically, are not required in our method. Thus, our optimization algorithm compares favourably at least in terms of speed with some other mesh optimization algorithms, such as the elliptic PDE method. In addition, to overcome the difficulty of guessing a good initial position of every grid node for the conjugate gradient method, a progressive optimization algorithm is incorporated in our optimization. Experiment results are given to illustrate the usefulness and effectiveness of the presented method.