Geometric continuous patch complexes
Computer Aided Geometric Design
A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Computer Aided Geometric Design
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Bezier and B-Spline Techniques
Bezier and B-Spline Techniques
C2 free-form surfaces of degree (3,5)
Computer Aided Geometric Design
Recursive subdivision algorithms for curve and surface design (subdivision algorithms)
Recursive subdivision algorithms for curve and surface design (subdivision algorithms)
Shape characterization of subdivision surfaces: basic principles
Computer Aided Geometric Design
Shape characterization of subdivision surfaces: case studies
Computer Aided Geometric Design
A unified framework for primal/dual quadrilateral subdivision schemes
Computer Aided Geometric Design
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In this article, we present regularly parametrized Gk free-form spline surfaces that extend box and half-box splines over regular triangular grids. The polynomial degree of these splines is max{4k + 1, ⌈3k/2 + 1⌉r}, where r ∈ &U2115; can be chosen arbitrarily and determines the flexibility at extraordinary points. The Gk splines presented in this article depend crucially on low-degree (re-)parametrizations of piecewise polynomial hole fillings. The explicit construction of such parametrizations forms the core of this work and we present two classes of singular and regular parametrizations. Also, we show how to build box and half-box spline surfaces of arbitrarily high smoothness with holes bounded by only n patches, in principle.