A triangular mesh generator over free-form surfaces for architectural design

Wang, Qisheng; Gao, Boqing; Li, Tierui; Wu, Hui; Kan, Jianzhong; Hu, Bo

doi:10.1016/j.autcon.2018.05.018

Cited by 11 publications

(4 citation statements)

References 19 publications

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“…However, as the number of particles increases, the computation efficiency decreases rapidly, and the mapping distorting limits the application scope of this method. Similarly to the molecular method, Wang et al (2018) proposed a mesh generation method based on the mapping method and the truss-like method, and three measures were taken to counteract mapping distortion by adjusting the mesh-generating algorithm locally. However, the method is only applicable to single parameterized surfaces, while complex surfaces tend to be represented by multiple parameterized surfaces.…”

Section: Related Workmentioning

confidence: 99%

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

Wang

Gao

2019

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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.

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Section: Related Workmentioning

confidence: 99%

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

Wang

Gao

2019

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“…The Delaunay triangulation technique was used to connect these particles into well-shaped triangles. In a similar fashion to the molecular method, Wang et al [21] suggested a grid generation strategy based on a mapping technique and a truss-like method. Delaunay triangulation was used to construct a planar triangular grid, which was then optimized by treating the grid as a truss in the parametric domain.…”

Section: Introductionmentioning

confidence: 99%

“…Combining the bubble method with edge operations, Wang et al [4] developed a framework for triangular grid generation, resulting in highly structured grids. While these force-based methods [4,[18][19][20][21] have been developed and employed for grid generation, the primary goals have been grid uniformity and regularity, with a dearth of effective actions to account for grid fluency.…”

Section: Introductionmentioning

confidence: 99%

Digital and automatic design of free-form single-layer grid structures

Gao

et al. 2022

Automation in Construction

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“…In another similar work [20], the authors first mapped the NURBS boundary surfaces (boundary curves of trimmed surfaces) from the physical surface onto the parameter domain and later generated the initial sample points directly onto the parameter domain. The initial uniform sample points are created based on distance function between the sample points.…”

Section: Introductionmentioning

confidence: 99%

New approaches for Delaunay triangulation and optimisation

Perumal

2019

Heliyon

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New techniques are presented for Delaunay triangular mesh generation and element optimisation. Sample points for triangulation are generated through mapping (a new approach). These sample points are later triangulated by the conventional Delaunay method. Resulting triangular elements are optimised by addition, removal and relocation of mapped sample points (element nodes). The proposed techniques (generation of sample points through mapping for Delaunay triangulation and mesh optimisation) are demonstrated by using Mathematica software. Simulation results show that the proposed techniques are able to form meshes that consist of triangular elements with aspect ratio of less than 2 and minimum skewness of more than 45°.

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A triangular mesh generator over free-form surfaces for architectural design

Cited by 11 publications

References 19 publications

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

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

Digital and automatic design of free-form single-layer grid structures

New approaches for Delaunay triangulation and optimisation

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