Shape artifacts, especially for convex input polyhedra, make Doo and Sabin’s generalization of bi-quadratic (bi-2) subdivision surfaces unattractive for general design. Rather than tuning the eigenstructure of the subdivision matrix, we improve shape by adding a point and enriching the refinement rules. Adding a guiding point can also yield a polar bi-2 subdivision algorithm. Both the augmented...

Partition of Unity Parametrics (PUPs) are a generalization of NURBS that allow us to use arbitrary basis functions for modeling parametric curves and surfaces. One interesting problem is finding subdivision schemes for this recently developed and flexible class of parametrics. In this paper, we introduce a systematic approach for determining uniform subdivision of PUPs curves and tensorproduct ...

This paper develops the basic theory of conformal structures on finite subdivision rules. The work depends heavily on the use of expansion complexes, which are defined and discussed in detail. It is proved that a finite subdivision rule with bounded valence and mesh approaching 0 is conformal (in the combinatorial sense) if there is a partial conformal structure on the model subdivision complex...

Standard binary subdivision operators may generate surfaces with unbounded curvatures at points corresponding to extraordinary vertices. This defect can be removed by manipulating the eigenvalues of the subdivision operator to impose a bounded curvature spectrum. This procedure may enlarge the support of an extraordinary vertex beyond its two-ring. In the ternary subdivision setting, where mesh...

We introduce the concept of subdivision drawings of hypergraphs. In a subdivision drawing each vertex corresponds uniquely to a face of a planar subdivision and, for each hyperedge, the union of the faces corresponding to the vertices incident to that hyperedge is connected. Vertex-based Venn diagrams and concrete Euler diagrams are both subdivision drawings. In this paper we study two new type...

ePlan is a collaborative program between the Australian land authorities and the surveying industry, in conjunction with the Intergovernmental Committee on Surveying and Mapping (ICSM) which aims to replace paper and PDF plans with digital files based on a national standard. ePlan was introduced in Victoria in 2011 and has been operational in this jurisdiction for 2D (non-building) plans since ...

Statistical shape analysis has become of increasing interest to the neuroimaging community due to its potential to locate morphological changes. In this paper, we present the a novel combination of shape analysis and Diffusion Tensor Image (DTI) Tractography to the computation of a probabilistic, model based corpus callosum (CC) subdivision. The probabilistic subdivision is based on the distanc...

Convergence and continuity analyses as well as exact evaluation of non-uniform subdivision surfaces at arbitrary parameter values have been very difficult because the subdivision matrix varies at each iteration step, unlike uniform subdivision surfaces. Using eigenanalysis and convergence properties of non-uniform subdivision surfaces that have been given by authors recently, a parameterization...

Reverse subdivision constructs a coarse mesh of a model from a finer mesh of this same model. In [1] Lanquetin and Neveu propose a reverse mask for the Catmull-Clark scheme which consists in locally reversing Catmull-Clark original formula for even control points, but this mask can not be applied in reversing other variants such as Quad-averaging scheme of Warren and Weimer [2]. In this paper, ...