Revisit Frei Otto: Equal-Length Mesh Algorithm For 3d Surfaces

Meshing algorithms for 3D surfaces are critical to architectural applications. More specifically, in architecture construction, fabricating a large 3D surface typically represents the surface as a mesh since it can be fabricated by assembling members (edges) and joints (nodes). However, most algorithms generate the meshes with the edges that are mostly in different lengths. Thus, it requires to produce a large number of different members, and the process causes much time, labor, and waste of materials. In 1974, Frei Otto proposed an algorithm, compass method, that translates 3D surfaces into equal-length meshes, where all edges are in the same length. Nonetheless, the meshes generated by compass method are suffering severe issue of inaccuracy therefore it is highly limited in architectural applications. This study revisits and advances compass method to increase its accuracy for more architectural applications. A comparison is given to show the improvements and the contributions of this study.