Architectural Structures from Quad Meshes with Planar Parameter Lines. (March 2023) - Wang, Cheng; Jiang, Caigui; Wang, Hui; Tellier, Xavier; Pottmann, Helmut
Abstract: 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. Highlights: Computational design of quad meshes combined with planar parameter lines. Surface approximation by quad meshes with planar parameter lines and planar faces. Surface approximation by funicular quad meshes with planar parameter lines. Two methods for finding quad meshes with orthogonal planar parameter lines. Computational design framework for further studies and architectural applications.