Abstract
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.
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