Polynomial-based non-uniform interpolatory subdivision with features control

Beccari, Carolina ; Casciola, Giulio ; Romani, Lucia (2010) Polynomial-based non-uniform interpolatory subdivision with features control. [Preprint]
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Starting from a well-known construction of polynomial-based interpolatory 4-point schemes, in this paper we present an original affine combination of quadratic polynomial samples that leads to a non-uniform 4-point scheme with edge parameters. This blending-type formulation is then further generalized to provide a powerful subdivision algorithm that combines the fairing curve of a non-uniform refinement with the advantages of a shape-controlled interpolation method and an arbitrary point insertion rule. The result is a non-uniform interpolatory 4-point scheme that is unique in combining a number of distinctive properties. In fact it generates visually-pleasing limit curves where special features ranging from cusps and flat edges to point/edge tension effects may be included without creating undesired undulations. Moreover such a scheme is capable of inserting new points at any positions of existing intervals, so that the most convenient parameter values may be chosen as well as the intervals for insertion. Such a fully flexible curve scheme is a fundamental step towards the construction of high-quality interpolatory subdivision surfaces with features control.

Document type
Beccari, Carolina
Casciola, Giulio
Romani, Lucia
Subdivision; Interpolation; Non-uniform parameterization; Features control; Arbitrary point insertion
Deposit date
15 Mar 2010 08:25
Last modified
17 Feb 2016 15:07

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