Bi-cubic Scaffold Surfaces. (September 2022) - Karčiauskas, Kȩstutis; Peters, Jörg
Abstract: Scaffold-like surfaces, ranging from large-scale trusses to engineered micro-structures, are often sketched via repeating patterns of nodes and edges. Offsetting these graphs turns them into meshes for which a smoothly-rounded scaffold surface 'skin' needs to be locally generated on the fly for production or analysis. We focus on minimal single-valence (MSV) quad meshes whose irregular vertices all have the same valence n and closest pairs are separated by exactly one regular, 4-valent vertex. Though at a first glance rather special, MSV meshes can model various micro-structures or trusses that occur in CAD or biology. Remarkably, bi-cubic patches provide a smooth skin of high quality, in many practical configurations with just one patch per quad. Graphical abstract: Highlights: Scaffold-like surfaces range from large-scale trusses to engineered micro-structures. Many can be represented by quad meshes, all whose irregular vertices have the same valence n separated by one regular, 4-valent vertex. These minimal single-valence (MSV) meshes can be smoothly rounded to form scaffold surfaces. Scaffold surfaces of good shape can be generated from bi-cubic patches with just one patch per quad.