Architectural Structures from Quad Meshes with Planar Parameter Lines

We address the computational design of architectural structures which are based on a grid of intersecting beams that are aligned with the parameter lines of a quad mesh. While previous work mainly put a planarity constraint onto the faces of the mesh, we focus on the planarity of long-range supporting beams which follow selected polylines in the underlying mesh. In addition to that, we impose further constraints including planarity of faces, right node angles and static equilibrium, and discuss in which way these may be combined. Some of the studied meshes are discrete counterparts of certain well-known surfaces in classical geometry, whose knowledge is helpful for initializing the proposed optimization algorithms.(c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper focuses on the computational design of architectural structures based on a grid of intersecting beams aligned with parameter lines of a quad mesh. It addresses the planarity of long-range supporting beams along selected polylines in the underlying mesh, as well as other constraints such as planarity of faces, right node angles, and static equilibrium. The discrete counterparts of well-known surfaces in classical geometry are studied, and their knowledge is used to initialize the proposed optimization algorithms.