A structured grid generation framework based on parameterization for the design of free-form gridshells

Abstract

Free-form gridshells have become a regional landmark because of their light and smooth architectural style. Structured grids with regular and straightforward topological connections are often the best choice for the holistic design of free-form gridshells. However, it is difficult to create a structured grid that can embody the architectural connotation and facilitate manufacturing and construction process over free-form surfaces, especially surfaces with complex shapes. To generate structured grids with fair lines, regular cells, and uniform edges over surfaces and to better interactively control the direction and size of grids, this paper proposes a parameterization-based grid generation framework. Firstly, a bubble-packing method is applied to obtain an initial grid over the given surface. Secondly, a grid parameterization algorithm that is as shape-preserving as possible is proposed and used to produce the parameter domain of the initial grid. Thirdly, a fair, regular, and uniform planar structured grid is generated in the parameter domain, and the direction and size of the grid can be adjusted by changing corresponding parameters. Finally, the planar structured grid is mapped to the given surface to obtain the final grid. As part of the new contribution of this paper, the calculation method of the fairness index is improved to quantitatively evaluate the fairness of the structured grid. The regularity and uniformity are also evaluated in terms of grid cell shape quality and grid edge lengths. Three case studies are presented to demonstrate the validity of the proposed framework. The proposed framework can be effective at reducing mapping distortion and can produce grids that meet the requirements of fairness, regularity, and uniformity.