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Triangular mesh generation on free-form surfaces based on bubble dynamics simulation

Qisheng Wang (College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, China)
Boqing Gao (College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, China)
Hui Wu (College of Public Administration, Zhejiang University of Finance and Economics, Hangzhou, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 21 January 2019

Issue publication date: 7 March 2019



Modern CAD systems facilitate the creation of any surface geometry imaginable, and complex surfaces for free-form grid shells are often represented by a set of Non-Uniform Rational B-Splines surface patches. But it remains an intractable issue how to generate high-quality grids on complex surfaces efficiently. To solve this issue, an automatic triangular mesh generation method is presented, based on bubble dynamics simulation and a modified Delaunay method.


A moderate amount of points are first distributed on a given surface. Next, by regarding the points as elastic bubbles with the same size and introducing the forces acting on bubbles, the motion control equations of bubbles are established. The equilibrium state of the bubble system is found by Verlet algorithm. Then, the Voronoi diagram on the surface is obtained by calculating the intersection between the surface and the three-dimensional (3D) Voronoi diagram of the centers of bubbles. Finally, a triangular mesh, Delaunay triangulation on the surface, is determined based on the dual change of the Voronoi diagram.


This method generates meshes on the surface directly, unlike mapping-based methods, avoiding the mapping distortion. Examples are given to demonstrate the successful execution of this method. The result also illustrates that this method is applicable to various surfaces in high automation level and resultant meshes are highly uniform and well-shaped.


Thus, this method provides the convenience for the geometry design of complex free-form grid structure.



This research was sponsored by the National Natural Science Foundation of China under Grant 51378457, 51678521, 51778558 and by the Natural Science Foundation of Zhejiang Province LY15E080017. The authors would like to thank them for their financial support.


Wang, Q., Gao, B. and Wu, H. (2019), "Triangular mesh generation on free-form surfaces based on bubble dynamics simulation", Engineering Computations, Vol. 36 No. 2, pp. 646-663.



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