Bi-cubic Scaffold Surfaces

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 be locally generated on the fly production or analysis. We focus minimal single-valence (MSV) quad whose irregular vertices all have same valence n closest pairs separated by exactly one regular, 4-valent vertex. Though at first glance rather special, MSV can model various micro-structures that occur in CAD biology. Remarkably, bi-cubic patches provide smooth skin high quality, many practical configurations with just patch per quad.