Convexity preserving interpolatory subdivision with conic precision
It addresses shape-preserving interpolation for geometric modeling, but the method is incremental as it extends existing subdivision techniques.
The paper presents a non-linear interpolatory subdivision algorithm for planar data that produces $G^1$ limit curves, reproduces conic sections, and preserves convexity. Numerical examples demonstrate its effectiveness.
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.