This paper tackles a particular shape matching problem: given a data base of shapes (described as triangular meshes), we search for all shapes which describe a human. We do so by applying a 3D face detection approach on the mesh which consists of three steps: first, a local symmetry value is computed for each vertex. Then, the symmetry values in a certain neighborhood of each vertex are analyze...

In this paper, we attempt to reveal the precise relation between the error of linear interpolation on a general triangle and the geometric characters of the triangle. Taking the model problem of interpolating quadratic functions, we derive two exact formulas for the H1-seminorm and L2-norm of the interpolation error in terms of the area, aspect ratio, orientation, and internal angles of the tri...

Abstract: This paper aims to present a new and innovative way to consider 3D urban database through the generation of automatic textured triangular irregular network over cities from oblique imageries. The novelty of this approach lies in the fast and automated algorithms capable of extracting dense 3D volume from airborne imageries compared to traditional methods where such 3D models are usual...

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...

A connected graph is called neighbourly irregular (NI) if it contains no edge between the vertices of the same degree. In this paper we determine the upper bound for chromatic number of a neighbourly irregular graph. We also prove some results on neighbourly irregular graphs and its chromatic number.

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...