This thesis tackles the geometric modeling of quad meshes for fabrication-aware design, with a focus on introducing planarity to the structural elements for efficient manufacturing in architectural practice. Many architectural structures can be computationally represented by quad meshes which obey various constraints. These constraints concern planarity of faces, planarity of vertex stars, configuration of supporting structures, static equilibrium and others. This thesis draws attention to novel methods of computing such constrained quad meshes.
A new methodology is proposed based on the diagonal meshes of a quad mesh. It simplifies the transfer from the differential geometric theory of smooth surfaces to the discrete setting of quad meshes. This is illustrated with planar quad meshes and asymptotic nets, in particular with those exhibiting a constant node angle.
Furthermore, the thesis investigates geometric properties and modeling capabilities of quad meshes with planar faces whose mesh parameter lines are contained in a plane. The plane functionally serves as part of a supporting structure. The thesis discusses design of meshes under the requirement that one half of mesh polylines are planar, as well as the geometry and design of meshes where all polylines own this property. The proposed design methods work in the space of planes and with appropriate transformations of that space.
Last but not least, the thesis is extended to fully explore the shape space of quad meshes with planar parameter lines. The study imposes further constraints including planarity of faces, static equilibrium, and right node angles, and discusses in which way these may be combined.
|Date of Award
- Computer, Electrical and Mathematical Sciences and Engineering
|Helmut Pottmann (Supervisor)
- Digital Fabrication
- Geometry Processing
- Computer-Aided Geometric Design
- Computer Graphics and 3D Modeling