Four-point curve subdivision based on iterated chordal and centripetal parameterizations
Computer Aided Geometric Design
Convergence and C1 analysis of subdivision schemes on manifolds by proximity
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Incenter subdivision scheme for curve interpolation
Computer Aided Geometric Design
Curve subdivision with arc-length control
Computing - Geometric Modelling, Dagstuhl 2008
A 4-point interpolatory subdivision scheme for curve design
Computer Aided Geometric Design
Matching admissible G2 Hermite data by a biarc-based subdivision scheme
Computer Aided Geometric Design
Non-uniform interpolatory subdivision via splines
Journal of Computational and Applied Mathematics
| Hi-index | 0.00 |
Curve subdivision is a technique for generating smooth curves from initial control polygons by repeated refinement. The most common subdivision schemes are based on linear refinement rules, which are applied separately to each coordinate of the control points, and the analysis of these schemes is well understood. Since the resulting limit curves are not sufficiently sensitive to the geometry of the control polygons, there is a need for geometric subdivision schemes. Such schemes take the geometry of the control polygons into account by using non-linear refinement rules and are known to generate limit curves with less artefacts. Yet, only few tools exist for their analysis, because the non-linear setting is more complicated. In this paper, we derive sufficient conditions for a convergent interpolatory planar subdivision scheme to produce tangent continuous limit curves. These conditions as well as the proofs are purely geometric and do not rely on any parameterization.