TY - JOUR
T1 - Planar Panels and Planar Supporting Beams in Architectural Structures
AU - Jiang, Caigui
AU - Wang, Cheng
AU - Tellier, Xavier
AU - Wallner, Johannes
AU - Pottmann, Helmut
PY - 2022/11/22
Y1 - 2022/11/22
N2 - In this article, we investigate geometric properties and modeling capabilities of quad meshes with planar faces whose mesh polylines enjoy the additional property of being contained in a single plane. This planarity is a major benefit in architectural design and building construction: If a structural element is contained in a plane, it can be manufactured on the ground without scaffolding and put into place as a whole. Further, the plane it is contained in serves as part of a so-called support structure. We discuss design of meshes under the requirement that one half of mesh polylines are planar (“P meshes”), and we also investigate the geometry and design of meshes where all polylines enjoy this property (“PP meshes”). We work in the space of planes and with appropriate transformations of that space. We also incorporate further properties relevant for architectural design, such as near-rectangular panels and repetitive nodes. We provide geometric insights, give explicit constructions, and show an approach to geometric modeling of both P meshes and PP meshes, in particular, the case of nearly rectangular panels.
AB - In this article, we investigate geometric properties and modeling capabilities of quad meshes with planar faces whose mesh polylines enjoy the additional property of being contained in a single plane. This planarity is a major benefit in architectural design and building construction: If a structural element is contained in a plane, it can be manufactured on the ground without scaffolding and put into place as a whole. Further, the plane it is contained in serves as part of a so-called support structure. We discuss design of meshes under the requirement that one half of mesh polylines are planar (“P meshes”), and we also investigate the geometry and design of meshes where all polylines enjoy this property (“PP meshes”). We work in the space of planes and with appropriate transformations of that space. We also incorporate further properties relevant for architectural design, such as near-rectangular panels and repetitive nodes. We provide geometric insights, give explicit constructions, and show an approach to geometric modeling of both P meshes and PP meshes, in particular, the case of nearly rectangular panels.
KW - architectural geometry
KW - discrete differential geometry
KW - Laguerre geometry
KW - planar beams
KW - Quad mesh
KW - support structure
UR - http://www.scopus.com/inward/record.url?scp=85144626291&partnerID=8YFLogxK
U2 - 10.1145/3561050
DO - 10.1145/3561050
M3 - Article
SN - 0730-0301
VL - 42
SP - 1
EP - 17
JO - ACM Transactions on Graphics
JF - ACM Transactions on Graphics
IS - 2
M1 - 19
ER -