Non-uniform recursive subdivision surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Extended subdivision surfaces: Building a bridge between NURBS and Catmull-Clark surfaces
ACM Transactions on Graphics (TOG)
A non-stationary uniform tension controlled interpolating 4-point scheme reproducing conics
Computer Aided Geometric Design
An interpolating 4-point C2 ternary non-stationary subdivision scheme with tension control
Computer Aided Geometric Design
On the deviation of a parametric cubic spline interpolant from its data polygon
Computer Aided Geometric Design
Non-uniform subdivision for B-splines of arbitrary degree
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics
Four-point curve subdivision based on iterated chordal and centripetal parameterizations
Computer Aided Geometric Design
On the parameterization of Catmull-Rom curves
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
A circle-preserving C2 Hermite interpolatory subdivision scheme with tension control
Computer Aided Geometric Design
Variations on the four-point subdivision scheme
Computer Aided Geometric Design
A fast interactive reverse-engineering system
Computer-Aided Design
Polynomial-based non-uniform interpolatory subdivision with features control
Journal of Computational and Applied Mathematics
Advances in Computational Mathematics
Algebraic conditions on non-stationary subdivision symbols for exponential polynomial reproduction
Journal of Computational and Applied Mathematics
Construction and characterization of non-uniform local interpolating polynomial splines
Journal of Computational and Applied Mathematics
Uniform interpolation curves and surfaces based on a family of symmetric splines
Computer Aided Geometric Design
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In this paper we exploit a class of univariate, C^1 interpolating four-point subdivision schemes featured by a piecewise uniform parameterization, to define non-tensor product subdivision schemes interpolating regular grids of control points and generating C^1 limit surfaces with a better behavior than the well-established tensor product subdivision and spline surfaces. As a result, it is emphasized that subdivision methods can be more effective than splines, not only, as widely acknowledged, for the representation of surfaces of arbitrary topology, but also for the generation of smooth interpolants of regular grids of points. To our aim, the piecewise uniform parameterization of the univariate case is generalized to an augmented parameterization, where the knot intervals of the kth level grid of points are computed from the initial ones by an updating relation that keeps the subdivision algorithm linear. The particular parameters configuration, together with the structure of the subdivision rules, turn out to be crucial to prove the continuity and smoothness of the limit surface.