Bivariate interpolatory Hermite subdivision schemes have recently been applied to build free-form subdivision surfaces. It is well known to geometric modelling practitioners that interpolatory schemes typically lead to “unfair” surfaces—surfaces with unwanted wiggles or undulations—and noninterpolatory (a.k.a. approximating in the CAGD community) schemes are much preferred in geometric modellin...

Problem statement: Subdivision surfaces were applied to the entire meshes in order to produce smooth surfaces refinement from coarse mesh. Several schemes had been introduced in this area to provide a set of rules to converge smooth surfaces. However, to compute and render all the vertices are really inconvenient in terms of memory consumption and runtime during the subdivision process. It will...

In this paper, we introduce two generalizations of midpoint subdivision and analyze the smoothness of the resulting subdivision surfaces at regular and extraordinary points. The smoothing operators used in midpoint and mid-edge subdivision connect the midpoints of adjacent faces or of adjacent edges, respectively. An arbitrary combination of these two operators and the refinement operator that ...

Subdivision has gained popularity in computer graphics and shape modeling during the past two decades, yet volumetric subdivision has received much less attention. In this paper, we develop a new subdivision scheme which can interpolate all of the initial control points in 3D and generate a continuous volume in the limit. We devise a set of solid subdivision rules to facilitate a simple subdivi...

‎in this paper we prove that a simplicial complex is determined‎ ‎uniquely up to isomorphism by its barycentric subdivision as well as‎ ‎its comparability graph‎. ‎we also put together several algebraic‎, ‎combinatorial and topological invariants of simplicial complexes‎.

This paper deepens the connections between critically finite rational maps and finite subdivision rules. The main theorem is that if f is a critically finite rational map with no periodic critical points, then for any sufficiently large integer n the iterate f is the subdivision map of a finite subdivision rule. We are interested here in connections between finite subdivision rules and rational...

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...