Bubble Model Based Grid Generation and Grid Size Control over Free-Form Surface

To generate triangular grids with regular shapes and adaptive sizes over free-form surfaces, an automatic grid generation method is presented on the basis of a bubble dynamic model. Grid nodes were first decorated on the discretized surface according to certain rule, and were regarded as elastic bubbles. The inter-bubble forces and the forces from surface adsorption were introduced. The motion control equations of bubbles were established. Then, the equilibrium state of the bubble system was acquired by the numerical simulation algorithm. Finally, the centers of balanced bubbles were connected into a triangular grid by an extended Delaunay method. In the bubble model, the size of a bubble is determined by the relative radius function. And the control of the grid size is realized by adjusting the bubble size. Through the relative radius function factoring in the distance from each bubble center to selected points or curves, the curvature of reference curves or the surface and so on, the method can generate triangular grids with edges adapted to the surface features. Six cases have demonstrated that the grids generated by the proposed method have regular shapes and adaptive sizes, with their shape quality indexes all higher than 0.97. The method provides the convenience for the design of grid structures.