Localized remeshing for polyhedral splines

• Published in: Computers & graphics Vol. 106; pp. 58 - 65
• Main Authors: Karčiauskas, Kȩstutis, Peters, Jörg
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2022
• Subjects: Free-form surface; Localized refinement; Polyhedral control net; Polyhedral spline; Quad-dominant mesh; T-junction; Polyhedral control net; Quad-dominant mesh; T-junction; Free-form surface; Polyhedral spline; Localized refinement
• ISSN: 0097-8493; 1873-7684
• DOI: 10.1016/j.cag.2022.05.019

Smooth spline surfaces can now be built with polyhedral control nets rather than just grid-like tensor-product control nets. However, irregularities such as T-junctions, multi-sided facets, and n-valent vertices need to be sufficiently separated. Automatically generated quad-dominant meshes, and meshes created by designers unaware of the requirements for spline surfaces often pack irregularities too tightly. Global refinement, e.g. via two steps of subdivision, can sufficiently separate irregularities. However, each refinement quadruples the number of polynomial pieces. Moreover, first-step artifacts can lead to oscillating and pinched highlight line distributions. We therefore investigate minimal, single edge insertion, re-connection and localized refinement of quad-dominant meshes to make them suitable for polyhedral splines. [Display omitted] •Smooth polyhedral spline surfaces can be built and controlled by polyhedral control nets.•T-junctions, multi-sided facets, and n-valent vertices must be sufficiently separated.•Two steps of global refinement separate but increase the pieces and may harm shape.•Localized edge insertion, re-connection and refinement are suggested instead.•The impact of these localized operations on shape is analyzed.