The paper deals with the theoretical investigation of p 3?subdivision schemes in the shift-invariant setting. In Section 2 we collect the available theory on reen-able functions (subdivision surfaces), with emphasis on their Sobolev and HH older smoothness. There we also discuss the computational tools and Matlab routines used for numerically estimating smoothness exponents. Families of interpo...

In this paper, we propose and analyze a subdivision scheme which unifies 3-point approximating subdivision schemes of any arity in its compact form and has less support, computational cost and error bounds. The usefulness of the scheme is illustrated by considering different examples along with its comparison with the established subdivision schemes. Moreover, B-splines of degree 4and well know...

This paper presents a fast radiosity algorithm for illuminating scenes containing large piecewise polygonal surfaces. Dynamic Subdivision is based on the well known Adaptive Subdivision, introduced by M.Cohen et al. [3]. During the illumination process, patches in areas with high intensity gradients are re ned. Contrary to Adaptive Subdivision, the presented algorithm subdivides patches not in ...

We give two different possibilities for subdivision of Powell–Sabin spline surfaces on uniform triangulations. In the first case, dyadic subdivision, a new vertex is introduced on each edge between two old vertices. In the second case, p 3–subdivision, a new vertex is introduced in the center of each triangle of the triangulation. We give subdivision rules to find the new control points of the ...

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...

We present new families of primal and dual subdivision schemes for triangle meshes and √ 3-refinement. The proposed schemes use two simple local rules which cycle between primal and dual meshes a number of times. The resulting surfaces become very smooth at regular vertices if the number of cycles is≥ 2. The C-property is violated only at low-valence irregular vertices, and can be restored by s...

We introduce a new family of subdivision schemes called jet subdivision schemes. Jet subdivision schemes are a natural generalization of the commonly used subdivision schemes for free-form surface modeling. In an order r jet subdivision scheme, rth order Taylor expansions, or r-jets, of functions are the essential objects being generated in a coarse-to-fine fashion. Standard subdivision surface...

We investigate whether dual triangular √ 3 subdivision can be made practical. We conclude that it has serious drawbacks. Our analysis provides insights into the sorts of problem which occur with subdivision schemes which break symmetry.