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

Abstract

Gridshells have been widely used in various public buildings, and many of them are defined over complex free-form surfaces with complex boundaries. This emphasizes the importance of general grid generation and optimization methods in the initial design stage to achieve visually sound and easy-to-manufacture structure. In this paper, a framework is presented to generate uniform, well-shaped and fluency triangular grids for structural design over free-form surfaces, especially those with complex boundaries. The framework employs force-based algorithms and a connectivity-regularization algorithm to optimize grid quality. First, an appropriate distribution of internal points is randomly generated on the surface. Secondly, a bubble-packing method is employed to increase the uniformity of the initial point distribution, and the points are connected using Delaunay-based triangularization to produce an initial grid with rods of balanced length. Thirdly, the grid connectivity is optimized using a range of edge-operations including edge-flip, collapse and split. The optimization process features a grid relaxation objective which includes the degree of the vertices, leading to improved regularity. As a final step, the grid is relaxed to improve fluency using a net-like method. As part of its contribution, this paper, therefore, proposes a metric for fluency, which can be used to quantitatively evaluate the suitability of a given grid for architectural and structural expression. Two case-study examples are presented to demonstrate the effective execution of the grid generation and optimization framework. It is shown that by using the proposed framework, the fluency index of the grid can be improved by up to 157%.