Improved Caps for Improved Subdivision Surfaces

• Published in: Computer aided design Vol. 162; p. 103543
• Main Authors: Karčiauskas, Kȩstutis, Peters, Jörg
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2023
• Subjects: Finitely-many patches; Smoothness; Subdivision surface; Surface shape; Surface shape; Finitely-many patches; Smoothness; Subdivision surface
• ISSN: 0010-4485; 1879-2685
• DOI: 10.1016/j.cad.2023.103543

The quest for a finite number of bicubic (bi-3) polynomial pieces to smoothly fill multi-sided holes after a fixed number of surface subdivision steps has motivated a number of constructions of finite surface caps. Recent bi-3 and bi-4 subdivision algorithms have improved surface shape compared to classic Catmull–Clark and curvature-bounded ‘tuned’ subdivision. Since the older subdivision algorithms exhibit artifacts that obscure the shortcomings of corresponding caps, it is worth re-visiting their multi-sided fill surfaces. The improved caps address the challenge so that either bi-3 or bi-4 data can be accommodated, as needed. The derivation illustrates the subtle fundamental trade off between formal algebraic mathematical smoothness constraints and good shape in the large. [Display omitted] •Smoothly fill multi-sided holes after a fixed number of surface subdivision steps.•Recent bi-3 and bi-4 subdivision improved surface shape.•Transitioning from high-end subdivision to accommodate existing caps harms the shape.•The improved caps accommodate bi-3 or bi-4 data, as needed.•The derivation illustrates the trade off between formal smoothness and good shape.