We propose a novel approach to automatically fill holes in triangulated models. Each hole is filled using a minimum energy surface that is obtained in three steps. First, we unfold the hole boundary onto a plane using energy minimization. Second, we triangulate the unfolded hole using a constrained Delaunay triangulation. Third, we embed the triangular mesh as a minimum energy surface in R3. Wh...

We show that any regular quadratic matrix polynomial can be reduced to an upper triangular quadratic matrix polynomial over the complex numbers preserving the finite and infinite elementary divisors. We characterize the real quadratic matrix polynomials that are triangularizable over the real numbers and show that those that are not triangularizable are quasi-triangularizable with diagonal bloc...

What is the smallest circular or square wall hole that a regular tetrahedron can pass? This problem was solved by Itoh–Tanoue– Zamfirescu [8]. Then, we settled the case of equilateral triangular hole in [1]. Motivated by these results, we consider the corresponding problems in higher dimensions. Among other results, we determine the minimum (n−1)-dimensional ball hole that a unit regular n-simp...

A graph is quasi-triangulated if each of its induced subgraphs has a vertex which is either simplicial (its neighbors form a clique) or cosimplicial (its nonneighbors form an independent set). We prove that a graph G is quasi-triangulated if and only if each induced subgraph H of G contains a vertex that does not lie in a hole, or an antihole, where a hole is a chordless cycle with at least fou...

Filling holes of 3D models is an important and complicated process. In this paper, we introduce a new and robust method for filling complex holes in triangular mesh models. In order to fill separate holes, the boundary edges of a hole are smoothly arranged and then locally uniform new points are added to the hole. The new points are selected by minimizing a hole filling area. The Delaunay trian...

We review the way the BTZ black hole relaxes back to thermal equilibrium after a small perturbation and how it is seen in the boundary (finite volume) CFT. The unitarity requires the relaxation to be quasi-periodic. It is preserved in the CFT but is not obvious in the case of the semiclassical black hole the relaxation of which is driven by complex quasi-normal modes. We discuss two ways of mod...

Bridges are one the most important and useful river structure and as a key of Communication ways are very significant. Local Scouring is one the most reason of Instability of bridges and finally its failure annually immense human and financial cost to the government imposes. So far, several studies on ways to control and reduce scouring around piers of the bridges has been done among them, the ...

in design and optimization process of laminated composite structures, the number of layers, layer angles, stacking sequence, material types and etc should be specified. each of aforesaid parameters can be applied as a design variable. in this paper the target is to minimize the weight of laminated composite pin loaded structures. the laminated composite structures are designed based on the load...