The recent non-uniform subdivision approach extends traditional uniform subdivision schemes with variable rules, offering additional shape parameters (such as knot spacings) for feature control. Despite its flexibility, shape modification based on non-uniform subdivision usually requires designers to interactively adjust a large number of degrees of freedom (DOFs) to achieve the desired shapes,...

The need for robust solutions for sets of non-linear multivariate constraints or equations needs no motivation. Subdivision-based multivariate constraint solvers [1–3] typically employ the convex hull and subdivision/domain clipping properties of the Bézier/B-spline representation to detect all regions that may contain a feasible solution. Once such a region has been identified, a numerical imp...

We propose a general study of the convergence of a Hermite subdivision scheme H of degree d > 0 in dimension 1. This is done by linking Hermite subdivision schemes and Taylor polynomials and by associating a so-called Taylor subdivision (vector) scheme S. The main point of investigation is a spectral condition. If the subdivision scheme of the finite differences of S is contractive, then S is C...

Hierarchical subdivision techniques remove the need for a-priori meshing of surfaces when approximating global illumination. In addition they allow progressive reenement of the solution. However, when subdivision is based upon Monte Carlo methods, due to the stochastic nature of such techniques, subdivision decisions cannot be made unless a suuciently large number of samples have been considere...