Martin Josefsson [1] has coined the term ‘bisect-diagonal quadrilateral’ for a quadrilateral with at least one diagonal bisected by other diagonal, and extensively explored some of its properties. This also been called ‘bisecting [2], ‘sloping-kite’ or ‘sliding-kite’ [3], ‘slant kite’ [4]. The purpose this paper is to explore more properties quadrilateral.

In this paper we consider deflations (inverse pocket flips) of n-gons for small n. We show that every pentagon can be deflated after finitely many deflations, and that any infinite deflation sequence of a pentagon results from deflating an induced quadrilateral on four of the vertices. We describe a family of hexagons that deflate infinitely for a specific deflation sequence, yet induce no infi...

Several new excitation and load models are proposed for electromagnetic analysis in the context of a Galerkin-type large-domain (higherorder) boundary element method (BEM) or Method of moments for structures composed of thin wires, metallic surfaces, and imperfect inhomogeneous dielectric bodies. The models represent a natural generalization of point-delta generators and loads for wires. They a...

Polynomials suffice as finite element basis functions for triangles, parallelograms, and some other elements of little practical importance. Rational basis functions extend the range of allowed elements to the much wider class of well-set algebraic elements, where well-set is a convexity type constraint. The extension field from R(x, y) to R(x, y, √ x2 + y2) removes this quadrilateral constrain...

Amethod to optimize triangular and quadrilateral meshes on parameterized surfaces is proposed. The optimization procedure relocates the nodes on the surface to improve the quality (smooth) and ensures that the elements are not inverted (untangle). We detail how to express any measure for planar elements in terms of the parametric coordinates of the nodes. The extended measures can be used to ch...

Domain decomposition methods based on the Schwarz framework were originally proposed for the h-version nite element method for elliptic problems. In this paper, we consider instead the p-version, in which increased accuracy is achieved by increasing the degree of the elements while the mesh is xed. We consider linear, scalar, self adjoint, second order elliptic problems and quadrilateral elemen...

Determining the shear stress of a structural element caused by torsion is vital problem. The analytical solution Saint-Venant only suitable for simple cross-sections. numerical method to evaluate complicated cross-sections indispensable. Many methods have been studied scientists. Among these studies, Gruttmann proposed an excellent method, which inherited theory. However, use isoparametric four...

Abstract In this paper, we give upper and lower bounds on the number of Steiner points required to onstru t a stri tly onvex quadrilateral mesh for a planar point set. In parti ular, we show that 3⌊ 2 ⌋ internal Steiner points are always suÆ ient for a onvex quadrilateral mesh of n points in the plane. Furthermore, for any given n ≥ 4, there are point sets for whi h ⌈ 2 ⌉ − 1 Steiner points are...