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

Abstract Computer-aided design software enables the rapid conceptual creation of a curved surface geometry, whereas it is not a convenient task for engineers to create a discrete grid structure on a complex surface that meets architectural and aesthetic requirements. This emphasizes the importance of grid generating tools and methods. A new triangular mesh generator for the free-form curved surfaces of architectural structures is developed based on the mapping truss-like method. The mapping truss-like method builds a bidirectional mapping mechanism between 3D domain and 2D domain, generates meshes in 2D domain using constrained Delaunay triangulation, and relaxes the mesh iteratively with the planar mesh regarded as a plane truss structure. This generator can generate uniform meshes and adaptive meshes in harmony with the surface features by a relative edge size function for various free-form surfaces. The directional trend of the mesh is adjustable by rotating the initial node placement, and selected points can be fixed to mesh multi-surfaces. In addition, methods are proposed to counteract mapping distortion by adjusting the mesh-generating algorithm locally. Examples illustrate that the generator has wide adaptability, high automation and comprehensive control of resulting meshes. Thus, this paper presents a useful design tool for free-form surfaces of grid structures.

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