A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
Intrinsic parametrization for approximation
Computer Aided Geometric Design
Approximate parametrization of algebraic curves
Theory and practice of geometric modeling
Four point parabolic interpolation
Computer Aided Geometric Design
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Approximating band- and energy-limited signals in the presence of jitter
Journal of Complexity
Complexity and information
Geometric Continuity of Parametric Curves: Three Equivalent Characterizations
IEEE Computer Graphics and Applications
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]
Digital and image geometry: advanced lectures
Digital and image geometry: advanced lectures
C1 Interpolation with cumulative chord cubics
Fundamenta Informaticae
External versus internal parameterizations for lengths of curves with nonuniform samplings
Proceedings of the 11th international conference on Theoretical foundations of computer vision
C1 Interpolation with cumulative chord cubics
Fundamenta Informaticae
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We discuss the problem of estimating the trajectory of a regular curve γ : [0, T] → Rn and its length d(γ) from an ordered sample of interpolation points Qm = {γ(t0), γ(t1),...,γ(tm)}, with tabular points ti's unknown, coined as interpolation of unparameterized data. The respective convergence orders for estimating γ and d(γ) with cumulative chord piecewise-quartics are established for different types of unparameterized data including ε-uniform and more-or-less uniform samplings. The latter extends previous results on cumulative chord piecewise-quadratics and piecewise-cubics. As shown herein, further acceleration on convergence orders with cumulative chord piecewise-quartics is achievable only for special samplings (e.g. for ε-uniform samplings). On the other hand, convergence rates for more-or-less uniform samplings coincide with those already established for cumulative chord piecewise-cubics. The results are experimentally confirmed to be sharp for m large and n=2,3. A good performance of cumulative chord piecewise-quartics extends also to sporadic data (m small) for which our asymptotical analysis does not apply directly.