Abstract Spherical surfaces are essential components of optical systems and imaging devices. Moreover, precision spheres calibration standards for many accurate instruments in dimensional mass metrology. A spherical surface's main property is its radius curvature, which can be measured using contact or non-contact methods. Interferometry an technique, but some error sources impact it. This stud...

A natural way to measure protein surface curvature is to generate the least squares fitted (LSF) sphere to a surface patch and use the radius as the curvature measure. While the concept is simple, the sphere-fitting problem is not trivial and known means of protein surface curvature measurement use alternative schemes that are arguably less straightforward to interpret. We have developed an app...

Let X be a compact Riemann surface of genus ≥ 2 of constant negative curvature −1. An extremal disk is an embedded (resp. covering) disk of maximal (resp. minimal) radius. A surface containing an extremal disk is an extremal surface. This paper gives formulas enumerating extremal surfaces of genus ≥ 4 up to isometry. We show also that the isometry group of an extremal surface is always cyclic o...

A prosthetic foot is a key element of a prosthetic leg, literally forming the basis for a stable and efficient amputee gait. We determined the roll-over characteristics of a broad range of prosthetic feet and examined the effect of a variety of shoes on these characteristics. The body weight of a person acting on a prosthetic foot during roll-over was emulated by means of an inverted pendulum-l...

The current effort to make integrated optical chips requires guiding light around sharp corners with a radius of curvature on the order of a wavelength. Light propagates in conventional waveguides as a result of total internal reflection at the interface between the high-refractive index guiding layer and its low-index surroundings. However, bends in the conventional index-contrast waveguides a...

Here H = div (n) is the mean curvature, n is the outward unit normal, x is the position vector and 〈, 〉 denotes the Euclidean inner product. One reason that selfshrinking solutions to the mean curvature flow are particularly interesting is that they provide singularity models of the flow; see [20, 21], [24] and [46]. Throughout, O is the origin of R; BR denotes the open ball in R n+1 centered a...

We propose a method of calculating the corneal asphericity (Q) and analyze the characteristics of the anterior corneal shape using the tangential radius. Fifty-eight right eyes of 58 subjects were evaluated using the Orbscan II corneal topographer. The Q-values of the flat principal semi-meridians calculated by the sagittal radius were compared to those by the tangential radius. Variation in th...

A method to generate a quintic B-spline curve which passes through the given points is described. In this case, there are four more equations than there are control point positions. Therefore, four gradients which are the first derivative of a quintic B-spline equation are assigned to the given points. In addition to this method, another method to generate a quintic B-spline curve which passes ...

Recall that the radius of a compact metric space (X, dist) is given by rad X = minx∈X maxy∈X dist(x, y). In this paper we generalize Berger’s 1 4 -pinched rigidity theorem and show that a closed, simply connected, Riemannian manifold with sectional curvature ≥ 1 and radius ≥ π2 is either homeomorphic to the sphere or isometric to a compact rank one symmetric space. The classical sphere theorem ...

We analyze the stability of naturally curved, inextensible elastic ribbons. In experiments, we first show that a loop formed using a metallic strip can become unstable if its radius is smaller than its natural radius of curvature (undercurved case): the loop then folds onto itself into a smaller, multiply-covered loop. Conversely, a multi-covered, overcurved metallic strip can unfold dynamicall...