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

Abstract

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value Thus, this method provides the convenience for the geometry design of complex free-form grid structure.

A triangular grid generation and optimization framework for the design of free-form gridshells

“…The resulting average edge length of both roof 1 (from Section 6) and roof 2 (from Section 8.2) are close to the expected member length of 24.4m and 3.1m, respectively. Compared to the grids generated by only the bubble-packing method [30], the results from the connectivity optimization have smaller fluency index in terms of point degree (improved connectivity) in both roof 1 and roof 2. However, for roof 1, the edge length index and angle fluency index deteriorate due to the presence of more ill-shaped triangles resulting from the edge operations.…”

“…17 Angles of a node As a result, an angle fluency index of an interior regular vertex is defined by Eqns. ( 28)- (30).…”

Building information model visualisation in augmented reality

“…A small area of the physical environment is represented by a spatial surface as a triangle mesh attached to the spatial coordinate system locked in position. Spatial surfaces are illustrated as numerous triangle meshes (Wang et al , 2019). A large amount of computational and storage resources is needed to store, render and process such meshes.…”

A novel progressive grid generation method for free-form grid structure design and case studies

“…In its actual implementation, the bubble method generated node configurations that yielded virtually no ill-shaped triangles or tetrahedrals. Wang et al [30][31] extended the bubble grid generation method to the free form curved surface, and proposed a grid generation and optimization framework for the design of free form grid shells. In order to obtain a grid with balanced rod length and fluent lines, Gao et al [32] presented an efficient design tool for the grid generation of free form surface based on the concept of guide lines.…”