G1 – Smooth biquintic approximation of Catmull-Clark subdivision surfaces

Marsala, Michelangelo; Mantzaflaris, Angelos; Mourrain, Bernard

doi:10.1016/j.cagd.2022.102158

Cited by 8 publications

(1 citation statement)

References 33 publications

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“…The shapes of G 2 constructions of degree bi-7 [25] or degree bi-6 [26], and lower-degree tangent-continuous splines [27][28][29][30][31][32][33] are empirically measured via highlighted line distribution [34]. FC surfaces fill irregularities in a C 1 bi-quadratic (bi-2) tensor-product surface, which is attractive since bi-2 splines have minimal bi-degree for smoothing quadrilateral meshes.…”

Section: Related Workmentioning

confidence: 99%

Bicubic Splines for Fast-Contracting Control Nets

Karčiauskas,

Lo,

Gunpinar

et al. 2024

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Merging parallel quad strips facilitates narrowing surface passages, and allows a design to transition to a simpler shape. While a number of spline surface constructions exist for the isotropic case where n pieces join, few existing spline constructions deliver a good shape for control nets that merge parameter lines. Additionally, untilrecently, none provided a good shape for fast-contracting polyhedral control nets. This work improves the state-of-the-art of piecewise polynomial spline surfaces accommodating fast-contracting control nets. The new fast-contracting (FC) surface algorithm yields the industry-preferred uniform degree bi-3 (bi-cubic). The surfaces are by default differentiable, have an improved shape, measured empirically as to highlight the line distribution, and require fewer pieces compared to existing methods.

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