Hyperbolic Spline Interpolation

The problem of restoring complex curves and surfaces from discrete data so that their shape is preserved is called isogeometric interpolation. A very popular tool for solving this problem are hyperbolic splines in tension, which were introduced in 1966 by Schweikert. These splines have smoothness sufficient for many applications; combined with algorithms for the automatic selection of the tension parameters, they adapt well to the given data. Unfortunately, the evaluation of hyperbolic splines is a very difficult problem because of roundoff errors (for small values of the tension parameters) and overflows (for large values of these parameters).

Parameters

$n$ : number of points

Filters

Computational Model

Randomization

Approximation

Algorithms Table

Displaying 3 of 3 algorithms


B.I. Kvasov	2008	$O(n^3 \log^2 K)$	$O(n)$
B. I. Kvasov	2000	$O(n^4)$	$O(n)$
P. Costantini, B. I. Kvasov, and C. Manni	1999	$O(n^5 \log K)$	$O(n)$

Reductions Table

Insuffient Data to display table

Other relevant algorithms

Displaying 3 of 3 other relevant algorithms


V. I. Paasonen	2006
V. A. Lyul’ka and I. E. Mikhailov	2003
V. A. Lyul’ka and A. V. Romanenko	1994