Interpolation with Cumulative Chord Cubics

Asymptotics for Length and Trajectory from Cumulative Chord Piecewise-Quartics

We discuss the problem of estimating the trajectory of a regular curve γ : [0, T ] → R and its length d(γ) from an ordered sample of interpolation points Qm = {γ(t0), γ(t1), . . . , γ(tm)}, with tabular points t′is 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 dif...

Smooth interpolation with Cumulative Chord cubics

Cumulative Chords, Piecewise-quadratics and Piecewise-cubics

Cumulative chord piecewise-quadratics and piecewise-cubics are examined in detail, and compared with other low degree interpolants for unparameterized data from regular curves in , especially piecewise-4-point quadratics. Orders of approximation are calculated and compared with numerical experiments. Good performance of the interpolant is also confirmed experimentally on sparse data. This work ...

G1 Hermite interpolation by Minkowski Pythagorean hodograph cubics

As observed by Choi et al. (1999), curves in Minkowski space R2,1 are very well suited to describe the medial axis transform (MAT) of a planar domain, and Minkowski Pythagorean hodograph (MPH) curves correspond to domains, where both the boundaries and their offsets are rational curves (Moon, 1999). Based on these earlier results, we give a thorough discussion of G1 Hermite interpolation by MPH...

Choosing nodes in parametric curve interpolation

Perhaps a few words might be inserted here to avoid In parametric curve interpolation, the choice of the any possible confusion. In the usual function interpolation interpolating nodes makes a great deal of difference in the resulting curve. Uniform parametrization is generally setting, the problem is of the form P~ = (x, y~) where the x~ are increasing, and one seeks a real-valued unsatisfacto...