A Study of Improved Meshless Method Visualization Based on Delaunay Triangulation

In recent years, meshless methods have been widely used in computational fluid dynamics and computational mechanics of materials in aeronautics. It constructs the interpolation function discrete control equations according to some arbitrarily distributed coordinate points, so as to simulate the flow field of various complex shapes or the mechanical behavior of solids. However, there is no connection information between each discrete point, so the visualization and post-processing of meshless numerical results is an important task. Generating triangular mesh through Delaunay triangulation can be an effective way to solve this problem. Firstly, the basic principles of Delaunay triangulation and Voronoi diagram are introduced. Then, the visualization research of improved meshless method based on Delaunay triangulation is described. Firstly, Bowyer-Watson algorithm is used to perform Delaunay triangulation on the point set, and then the Incremental Remeshing method proposed by Botsch and Kobbelt is used to optimize the initial node position to generate better quality triangular mesh and generate its Voronoi diagram. Finally, the effectiveness of the algorithm is verified by an example of mesh generation. The algorithm is based on C++ language and SFML library. It can optimize the scatter position according to the random distribution point set, and generate high-quality triangular mesh and Voronoi diagram, so as to solve the visualization problem of scattered data.