The structured grid generation using Beta-spline curve/surface modeling Original Research Article

The Beta-spline curve/surface is used in CAD/CAGD technique for several years. Its several special features make it very suitable to be applied in the grid generation system. It can control the bias and curvature of the curve/surface more flexibly by using two shape parameters. The Beta-spline curve/surface can be applied in the grid generation to maintain the fidelity of a curve/surface and to generate grid with different distribution. Generally, there are two different strategies to apply the Beta-spline curve/surface to generate the grid. The first strategy is based on the control vertices to derive the equations of the Beta-spline curve/surface, and then interpolates the grid points on the curve/surface. The second strategy is based on some known points on a curve/surface to derive the corresponding control vertices and then applies the first strategy to interpolate the grid points on the original curve/surface. The consecutive concave curve/surface can also be generated by setting the tension parameter to be a negative value. Several results are presented in this paper to show the success of this technique.