Modification of a standard Goldmann goniolens by reducing the curvature of the contact surface to 8.5 mm radius of curvature (from the standard curvature of 7.4 mm) enabled gonioscopy to be carried out without the nuisance of air bubbles.

This article explores the impact of surface area, volume, curvature, and Lennard-Jones (LJ) potential on solvation free energy predictions. Rigidity surfaces are utilized to generate robust analytical expressions for maximum, minimum, mean, and Gaussian curvatures of solvent-solute interfaces, and define a generalized Poisson-Boltzmann (GPB) equation with a smooth dielectric profile. Extensive ...

We prove that any strongly regular Weingarten surface in Euclidean space carries locally geometric principal parameters. The basic theorem states that any strongly regular Weingarten surface is determined up to a motion by its structural functions and the normal curvature function satisfying a geometric differential equation. We apply these results to the special Weingarten surfaces: minimal su...

Beam shaping is becoming increasingly important for synchrotron X-ray applications. Although routine for visible light lasers, this is challenging for X-rays due to the limited source coherence and extreme optical tolerances required for the shaping mirrors. In deliberate defocusing, even surface errors <5 nm r.m.s. introduce damagingly large striations into the reflected beam. To counteract su...

Estimation of surface curvature from range data is important for a range of tasks in computer vision and robotics, object segmentation, object recognition and robotic grasping estimation. This work presents a fast method of robustly computing accurate metric principal curvature values from noisy point clouds which was implemented on GPU. In contrast to existing readily available solutions which...

Surface curvature properties are often as important as surface position in understanding shape. Curvature properties are typically computed at mesh vertices by operating on an associated ring neighbourhood of faces. Such approaches are not well suited to noisy, non-uniformly sampled meshes with irregular tessellations. In this paper, we present a principled approach to curvature estimation that...

We find bounds for Weil-Petersson holomorphic sectional curvature, and the Weil-Petersson curvature operator in several regimes, that do not depend on the topology of the underlying surface. Among other results, we show that the minimal (most negative) eigenvalue of the curvature operator at any point in the Teichmüller space Teich(Sg) of a closed surface Sg of genus g is uniformly bounded away...

Any planar shape P can be embedded isometrically as part of a convex surface S ⊂ R such that ∂P supports the positive curvature of S. Of particular interest is the case when P is a filled polynomial Julia set and the curvature is proportional to the measure of maximal entropy. The (flat) surface Q = S \P is the associated cap. In this article, we study the cap construction when the curvature is...

We study, analytically and theoretically, defects in a nematically-ordered surface that couple to the extrinsic geometry of a surface. Though the intrinsic geometry tends to confine topological defects to regions of large Gaussian curvature, extrinsic couplings tend to orient the nematic in the local direction of maximum or minimum bending. This additional frustration is unavoidable and most im...

‎let $m^n$ be an $n(ngeq 3)$-dimensional complete connected and‎ ‎oriented spacelike hypersurface in a de sitter space or an anti-de‎ ‎sitter space‎, ‎$s$ and $k$ be the squared norm of the second‎ ‎fundamental form and gauss-kronecker curvature of $m^n$‎. ‎if $s$ or‎ ‎$k$ is constant‎, ‎nonzero and $m^n$ has two distinct principal‎ ‎curvatures one of which is simple‎, ‎we obtain some‎ ‎charact...