The paper is concerned with the problem of shape preserving interpolatory subdivision. For arbitrarily spaced, planar input data an efficient non-linear subdivision algorithm reproducing conic sections and respecting the convexity properties of the initial data, is here presented. Significant numerical examples are included to illustrate the effectiveness of the proposed method and the smoothness of the limit curves.
Albrecht, G., Romani, L. (2012). Convexity preserving interpolatory subdivision with conic precision. APPLIED MATHEMATICS AND COMPUTATION, 219(8), 4049-4066 [10.1016/j.amc.2012.10.048].
Convexity preserving interpolatory subdivision with conic precision
ROMANI, LUCIA
2012
Abstract
The paper is concerned with the problem of shape preserving interpolatory subdivision. For arbitrarily spaced, planar input data an efficient non-linear subdivision algorithm reproducing conic sections and respecting the convexity properties of the initial data, is here presented. Significant numerical examples are included to illustrate the effectiveness of the proposed method and the smoothness of the limit curves.
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