The Optimum Circular Interpolation with a Specified Error Value for Involute Contours.

Circular Arc Reconstruction of Digital Contours with Chosen Hausdorff Error

We address the problem of constructing an approximate continuous representation of a digital contour with guarantees on the Hausdorff error between the digital shape and its reconstruction. Instead of polygonalizing the contour, we propose to reconstruct the shape with circular arcs. To do so, we exploit the recent curvature estimators. From their curvature field, we introduce a new simple and ...

Interpolation error estimates for mean value coordinates over convex polygons

In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, to appear], we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard finite element analysis. Our analysis is based on providing a uniform bound on the gradient of the mean value functions for all convex polygons of diameter on...

Interpolation with Bounded Error

Given n general points p1, p2, . . . , pn ∈ Pr it is natural to ask whether there is a curve of given degree d and genus g passing through them; by counting dimensions a natural conjecture is that such a curve exists if and only if n ≤ ⌊ (r + 1)d− (r − 3)(g − 1) r − 1 ⌋ . The case of curves with nonspecial hyperplane section was recently studied in [1], where the above conjecture was shown to h...

Symmetric contours and convergent interpolation

The essence of Stahl-Gonchar-Rakhmanov theory of symmetric contours as applied to the multipoint Padé approximants is the fact that given a germ of an algebraic function and a sequence of rational interpolants with free poles of the germ, if there exists a contour that is “symmetric” with respect to the interpolation scheme, does not separate the plane, and in the complement of which the germ h...

The Interpolation of Hydraulic Head Contours