On the convergence of some cubic spline interpolation schemes
SIAM Journal on Numerical Analysis
Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
Choosing nodes in parametric curve interpolation
Computer-Aided Design
Knot selection for parametric spline interpolation
Mathematical methods in computer aided geometric design
Which cubic spline should one use?
SIAM Journal on Scientific and Statistical Computing
Corners, cusps, and parametrizations: variations on a theorem of Epstein
SIAM Journal on Numerical Analysis
Sharp, quantitative bounds on the distance between a polynomial piece and its Bézier control polygon
Computer Aided Geometric Design - Special issue dedicated to Paul de Faget de Casteljau
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
Planar cubic G1 interpolatory splines with small strain energy
Journal of Computational and Applied Mathematics
Parameterization and applications of Catmull-Rom curves
Computer-Aided Design
The approximation order of four-point interpolatory curve subdivision
Journal of Computational and Applied Mathematics
Non-uniform non-tensor product local interpolatory subdivision surfaces
Computer Aided Geometric Design
Computer Aided Geometric Design
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When fitting a parametric curve through a sequence of points, it is important in applications that the curve should not exhibit unwanted oscillations. In this paper we take the view that a good curve is one that does not deviate too far from the data polygon: the polygon formed by the data points. From this point of view, we study periodic cubic spline interpolation and derive bounds on the deviation with respect to three common choices of parameterization: uniform, chordal, and centripetal. If one wants small deviation, the centripetal spline is arguably the best choice among the three.