SIAM Journal on Mathematical Analysis
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Spectral Analysis of the Transition Operator and Its Applications to Smoothness Analysis of Wavelets
SIAM Journal on Matrix Analysis and Applications
Computer Aided Geometric Design
Computer Aided Geometric Design
From extension of Loop's approximation scheme to interpolatory subdivisions
Computer Aided Geometric Design
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Refinable compactly supported bivariate C2 quartic and quintic spline function vectors on the four-directional mesh are introduced in this paper to generate matrix-valued templates for approximation and Hermite interpolatory surface subdivision schemes, respectively, for both the √2 and 1-to-4 split quadrilateral topological rules. These splines have their full local polynomial preservation orders. In addition, we extend our study to parametric approach and use the symmetric properties of our refinable quintic spline components as a guideline to reduce the number of free parameters in constructing second order C2 Hermite interpolatory quadrilateral subdivision schemes with precisely six components.