A method for decomposing a volume with a prescribed quadrilateral surface mesh, into a hexahedral-dominated mesh is proposed. With this method, known as Hex-kforphing (HMorph), an initial tetrahedral mesh is provided. Tetrahedral are transformed and combined starting from the boundary and working towards the interior of the volume. The quadrilateral faces of the hexahedra are treated as interna...

Integer programs defined by two equations with two free integer variables and nonnegative continuous variables have three types of nontrivial facets: split, triangle or quadrilateral inequalities. In this paper, we compare the strength of these three families of inequalities. In particular we study how well each family approximates the integer hull. We show that, in a well defined sense, triang...

THIS is a report of seven cases of chronic occlusive arterial disease of the extremities of young adults that initially involved the smaller primary arteries of all four limbs. There were consistent pathologic findings, distinctive arteriograms, and constant clinical features in these cases. The disease process presenting in these patients is easily distinguished from common arteriosclerotic di...

Refinable compactly supported bivariate C quartic and quintic spline function vectors on the four-directional mesh are introduced in this paper to generate matrix-valued templates for approximation and Hermite interpolatory surface subdivision schemes, respectively, for both the √ 2 and 1-to-4 split quadrilateral topological rules. These splines have their full local polynomial preservation ord...

Topology optimization can be divided into continuum and discrete types, the latter being the emphasis of the present work. In the field of discrete structural topology optimization of trusses, the generation of an initial ground structure is crucial. Thus, this paper examines the generation of ground structures for generic structural domains in two and three dimensions. It compares two methods ...

We prove that any PSLG has a conforming quadrilateral mesh with O(n) elements, all angles ≤ 120◦ and all new angles ≥ 60◦ (the complexity and the angle bounds are both sharp). Moreover, all but O(n) of the angles may be taken in a smaller interval, say [89◦, 91◦]. Date: January 2011. 1991 Mathematics Subject Classification. Primary: 30C62 Secondary:

An important problem in geometric compression is to find succinct representations (encoding schemes) for the conectivity of polygonal meshes. In this note, we show that the encoding scheme discussed in [1] for quadrilateral mesh connectivity can be improved from 3.5 bits per vertex to less than 3 bits per vertex. We also show that an easy equivalence between the labelling schemes of King et al ...

Motivated by the classical studies on transformations of conjugate nets, we develop the general geometric theory of transformations of their discrete analogues: the multidimensional quadrilateral lattices, i.e. lattices x : Z −→ R , N ≤ M , whose elementary quadrilaterals are planar. Our investigation is based on the discrete analogue of the theory of the rectilinear congruences, which we also ...

We investigate the locomotion of a surface-walking/climbing robot, the Planar Walker, based on a novel planar eight-bar closed-loop mechanism. The robot can produce inchworm-like movements in two orthogonal directions and can rotate about itself. The locomotion mechanism to achieve such motions comprises four two-way linear cylinders forming a deformable quadrilateral and four two-way gripper m...

The need of polygonal elements to represent the domain is gaining interest among structural engineers. The objective is to perform static analysis and topology optimization of a given continuum domain using the rational fraction type shape functions of six node hexagonal elements. In this paper, the main focus is to perform the topology optimization of two-dimensional plate structures using Evo...