We estimate error bounds between binary subdivision curves/surfaces and their control polygons after k-fold subdivision in terms of the maximal differences of the initial control point sequences and constants that depend on the subdivision mask. The bound is independent of the process of subdivision and can be evaluated without recursive subdivision. Our technique is independent of parameteriza...

Nonlinear subdivision schemes that operate on manifolds are of use whenever manifold valued data have to be processed in a multiscale fashion. This paper considers the case where the manifold is a Lie group and the nonlinear subdivision schemes are derived from linear interpolatory ones by the so-called log-exp analogy. The main result of the paper is that a multivariate interpolatory Lie group...

Most filamentous bacteria in biological nutrient removal (BNR) processes have not been identified beyond their morphotype and simple staining reactions. Furthermore, the majority of sludge filaments observed under the microscope do not hybridize to commonly used phylogenetic probes for well characterized bacterial phyla such as the Proteobacteria, Actinobacteria, Firmicutes and BACTEROIDETES: S...

The objective of this paper is to study and construct matrix-valued templates for interpolatory curve subdivision. Since our investigation of this problem was motivated by the need of such subdivision stencils as boundary templates for interpolatory surface subdivision, we provide both spline and non-spline templates that are necessarily symmetric, due to the lack of direction-orientation in ca...

Hermite subdivision schemes have been studied by Merrien, Dyn and Levin and they appear to be very different from subdivision schemes analyzed before since the rules depend on the subdivision level. As suggested by Dyn and Levin, it is possible to transform the initial scheme into a uniform stationary vector subdivision scheme which can be handled more easily. With this transformation, the stud...

We introduce incremental subdivision as a new adaptive subdivision method for triangle meshes. While regular (global) subdivisions produce a smooth surface from a given polygon mesh by refining all of its faces, adaptive subdivision produces a surface by refining only some selected areas of the mesh. Consequently, the selected area becomes fine and high resolution while the rest of mesh is coar...

In this paper we demonstrate that subdivision schemes can be used for modelling and grid generation in aeronautical projects such as that in the collaborative research center SFB401 at the RWTH Aachen: F low Modulation and Fluid-Structure Interaction at Airplane Wings. To make the schemes usable for this purposes their rules have to be modified in such a way that the limit surfaces have the des...

This paper proposes to generalize linear subdivision schemes nonlinear for curve and surface modeling by refining vertex positions together with refinement of unit control normals at the vertices. For each round subdivision, new are obtained projections linearly subdivided onto circle or sphere while updating vertices along directions newly normals. Particularly, position is computed weighted a...

In this survey paper, we discuss subdivision geometry, subdivision schemes, its analysis and applications, especially from the view of solid modeling. Subdivision technique has been widely accepted in computer graphics and geometric design applications. However, it has been largely ignored in solid modeling. The first few sections are devoted to the history of subdivision modeling and the revie...

ÐIn this paper, we develop integrated techniques that unify physics-based modeling with geometric subdivision methodology and present a scheme for dynamic manipulation of the smooth limit surface generated by the (modified) butterfly scheme using physics-based aforceo tools. This procedure-based surface model obtained through butterfly subdivision does not have a closed-form analytic formulatio...