Convexity preserving interpolatory subdivision with conic precision

TL;DR

This paper introduces a non-linear subdivision algorithm for planar data that produces smooth, convexity-preserving curves with conic section reproduction, enhancing shape control in geometric modeling.

Contribution

It presents a novel shape-preserving interpolatory subdivision method that guarantees G^1 continuity, conic reproduction, and convexity preservation for arbitrarily spaced data.

Findings

Produces G^1 continuous limit curves

Reproduces conic sections accurately

Maintains convexity of initial data

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 is presented that results in $G^1$ limit curves, reproduces conic sections and respects the convexity properties of the initial data. Significant numerical examples illustrate the effectiveness of the proposed method.