Four point parabolic interpolation
Computer Aided Geometric Design
Corners, cusps, and parametrizations: variations on a theorem of Epstein
SIAM Journal on Numerical Analysis
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
High order approximation method for curves
Computer Aided Geometric Design
A general framework for high-accuracy parametric interpolation
Mathematics of Computation
The NURBS book (2nd ed.)
Optimal geometric Hermite interpolation of curves
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Length Estimation for Curves with Different Samplings
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Length Estimation for Curves with epsilon-Uniform Sampling
CAIP '01 Proceedings of the 9th International Conference on Computer Analysis of Images and Patterns
External versus internal parameterizations for lengths of curves with nonuniform samplings
Proceedings of the 11th international conference on Theoretical foundations of computer vision
High accuracy geometric Hermite interpolation
Computer Aided Geometric Design
Asymptotics for Length and Trajectory from Cumulative Chord Piecewise-Quartics
Fundamenta Informaticae
Length estimation for the adjusted exponential parameterization
ICCVG'12 Proceedings of the 2012 international conference on Computer Vision and Graphics
Sharpness in trajectory estimation by piecewise-quadratics(-cubics) and cumulative chords
ICCVG'12 Proceedings of the 2012 international conference on Computer Vision and Graphics
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Cumulative chord C 1 piecewise-cubics, for unparameterized data from regular curves in R n, are constructed as follows. In the first step derivatives at given ordered interpolation points are estimated from ordinary (non-C 1) cumulative chord piecewise-cubics. Then Hermite interpolation is used to generate a C 1 piecewise-cubic interpolant. Theoretical estimates of orders of approximation are established, and their sharpness verified through numerical experiments. Good performance of the interpolant is also confirmed experimentally on sparse data.