This analysis reveals key advancements in non-linear subdivision schemes for geometric modelling and applications, highlighting their impact on handling irregularities.
Subdivision schemes are a very useful tool in computer graphics and geometric modelling, allowing for the generation of curves and smooth surfaces starting from discrete data. Even though linear subdivision schemes are used profusely, non-linear schemes offer more flexibility, allowing for the handling of data with irregularities and making the shape preservation easier. In addition, these schemes are useful to deal with subdivision on manifolds, to correct Gibbs oscillations around singularities, and, in general, to try to tackle problems where linear approaches do not provide satisfactory results. This article reviews 25 years of contributions related to the construction, analysis, and use, in different applications, of non-linear subdivision schemes.
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Amat et al. (2025) studied this question.
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