Structured triangular mesh generation method for free-form gridshells based on conformal mapping and virtual interaction forces

With the rapid development of computer-aided design, manufacturing, and construction techniques, free-form single-layer reticulated shells (SLRSs) are increasingly applied in modern architectures. However, generating a uniform and smooth mesh directly on a three-dimensional free-form surface is challenging. This paper proposes a fast and automatic method to generate structured triangular mesh for free-form SLRSs. The difficulty is reduced by generating the mesh on the two-dimensional (2D) parametric plane obtained by conformal mapping. The virtual interaction forces (VIFs) combined with the area map are used to automatically adjust the distribution of the 2D structured base mesh to reduce distortions. Subsequently, mesh clipping and barycentric interpolation are used to map the planar mesh back to the original surface. Finally, the VIF-based mesh smoothing is conducted to improve the mesh uniformity and smoothness. Case studies show that the proposed method successfully generates high-quality structured triangular meshes on various types of free-form SLRSs. Moreover, this method can precisely control the overall size and direction of the mesh, providing architects and engineers with more choices of mesh patterns.