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...

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...

We prove an inequality for the area of a bicentric quadrilateral in terms of the radii of the two associated circles and show how to construct the quadrilateral of maximal area.

In this paper, we propose a novel adaptive mesh fitting algorithm that fits a triangular model with G1 smoothly stitching bi-quintic Bézier patches. Our algorithm first segments the input mesh into a set of quadrilateral patches, whose boundaries form a quadrangle mesh. For each boundary of each quadrilateral patch, we construct a normal curve and a boundary-fitting curve, which fit the normal ...

This study aims to assess the biomechanical properties of a novel fixation system (named AFRIF) and to compare it with other five different fixation techniques for quadrilateral plate fractures. This in vitro biomechanical experiment has shown that the multidirectional titanium fixation (MTF) and pelvic brim long screws fixation (PBSF) provided the strongest fixation for quadrilateral plate fra...

Quadrilateral space syndrome (QSS) is a rare nerve entrapment disorder that occurs when the axillary nerve and posterior circumflex humeral artery (PCHA) become compressed in the quadrilateral space. QSS presents as vague posterolateral shoulder pain that is exacerbated upon the abduction and external rotation of the shoulder. Diagnosis of QSS is difficult because of the vague presentation of Q...

A popular three-dimensional mesh generation scheme is to start with a quadrilateral mesh of the surface of a volume, and then attempt to fill the interior of the volume with hexahedra, so that the hexahedra touch the surface in exactly the given quadrilaterals[24]. Folklore has maintained that there are many quadrilateral meshes for which no such compatible hexahedral mesh exists. In this paper...

The aims ofthis study were (1) to apply the quadrilateral analysis to Saudi adult male and female patients with normal occlusion, (2) to compare the results to Saudi adult male and female with anterior openbite, and (3) to evaluate the correlation of the quadrilateral variables. The normal occlusion sample consisted of 60 lateral skull radiographs (30 male and 30 female) of Saudi adults with no...

We prove ten necessary and sufficient conditions for a convex quadrilateral to have perpendicular diagonals. One of these is a quite new eight point circle theorem and three of them are metric conditions concerning the nonoverlapping triangles formed by the diagonals. 1. A well known characterization An orthodiagonal quadrilateral is a convex quadrilateral with perpendicular diagonals. The most...