15 citations · 60 across the 17 of their papers we have counts for
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A Quadratic Spline Approximation of the Sphere over Uniform Polyhedra
Ema Češek, Aleš Vavpetič
In this paper, we study geometrically continuous quadratic splines over triangulations. While a rich variety of quadratic splines is available over planar domains, and such s…
Curvature-Based Optimal Polynomial Geometric Interpolation of Circular Arcs
Ema Češek, Aleš Vavpetič
The problem of the optimal approximation of circular arcs by parametric polynomial curves is considered. The optimality relates to the curvature error. Parametric polynomial curves…
Optimal one-sided approximants of circular arc
Ada Šadl Praprotnik, Aleš Vavpetič, Emil Žagar
The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an…
Optimal approximation of spherical squares by tensor product quadratic Bézier patches
Aleš Vavpetič, Emil Žagar
In [1], the author considered the problem of the optimal approximation of symmetric surfaces by biquadratic Bézier patches. Unfortunately, the results therein are incorrect, which…
Geometric approximation of the sphere by triangular polynomial spline patches
Aleš Vavpetič, Emil Žagar
A sphere is a fundamental geometric object widely used in (computer aided) geometric design. It possesses rational parameterizations but no parametric polynomial parameterization e…
On optimal polynomial geometric interpolation of circular arcs according to the Hausdorff distance
Aleš Vavpetič, Emil Žagar
The problem of the optimal approximation of circular arcs by parametric polynomial curves is considered. The optimality relates to the Hausdorff distance and have not been studied…
A general framework for the optimal approximation of circular arcs by parametric polynomial curves
Aleš Vavpetič, Emil Žagar
We propose a general framework for geometric approximation of circular arcs by parametric polynomial curves. The approach is based on constrained uniform approximation of an error…