We present a novel approach to morph between two isometric poses of the same non-rigid object given as triangular meshes. We model the morphs as linear interpolations in a suitable shape space S. For triangulated 3D polygons, we prove that interpolating linearly in this shape space corresponds to the most isometric morph in R. We extend this shape space to arbitrary triangulations in 3D using a...

We refine a result concerning singular matrix pencils and the Wong sequences. In our recent paper [T. Berger and S. Trenn, SIAM J. Matrix Anal. Appl., 33 (2012), pp. 336–368] we have shown that the Wong sequences are sufficient to obtain a quasi-Kronecker form. However, we applied the Wong sequences again on the regular part to decouple the regular matrix pencil corresponding to the finite and ...

Refinement operators for triangular meshes as used in subdivision schemes or remeshing are discussed. A numbering scheme is presented, covering all refinement operators that (topologically) map vertices onto vertices. Using this characterization, some special properties of n-adic and √ 3-subdivision are easy to see.

and Applied Analysis 3 f continuous on R. We know that C(R) is a Banach space with norm 󵄩󵄩󵄩f 󵄩󵄩󵄩∞ := sup x∈R 󵄨󵄨󵄨f (x) 󵄨󵄨󵄨 , f ∈ C (R) . (12) We denote by C 2π (R) the space of all 2π-periodic functions f ∈ C(R) which is a Banach space with 󵄩󵄩󵄩f 󵄩󵄩󵄩2π = sup t∈R 󵄨󵄨󵄨f (t) 󵄨󵄨󵄨 . (13) The classical Korovkin first and second theorems statewhatfollows [15, 16]: Theorem I. Let (T n ) be a sequence of p...

This paper describes an approach for 3D triangular meshes segmentation. The method that we adopt for the 3D mesh segmentation is based on the unbiased hierarchical queue which has been used for 2D images. Our method uses the hierarchical transformation on a connected faces structure. The approach that we propose is based on the principal curvature to calculate the faces curvature. The results s...

The problem of efficiently accessing and maintaining adjacency information for triangulations over general surface domains is addressed. Rapid access to adjacent vertices, edges, and triangles is an important aspect of multiresolution techniques, from subdivision surfaces to mesh simplification. Novel data structures and algorithms for the construction, manipulation, and traversal of triangulat...

In this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. Also, density and balanced irregular vague graphs are discussed and some of their properties are established. Finally we give an application of vague digraphs.

in this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. also, density and balanced irregular vague graphs are discussed and some of their properties are established. finally we give an application of vague digraphs.

The neighbourhood may provide resources for health. It is to date unknown whether people who live in neighbourhoods with more social capital have more access to practical and emotional support by neighbours, or whether this is a resource only available to those who are personally connected to people in their neighbourhood. We investigated whether support by neighbours of people with chronic ill...