Irregularities in the perimeter of a water droplet adhering to a vertical pane of glass cause perturbations in the curvature of the droplet surface. When laser light passes through such a droplet, the perturbations produce a far field refraction caustic, which is a section of the caustic known as the parabolic umbilic in the catastrophe theory classification. As the water evaporates and the dro...

Recent advances in 3D scanning technology have enabled the development of interesting applications of 3D human body modelling and shape analysis, especially in the areas of virtual shopping, custom clothing and sizing surveys for the clothing industry. Most of the current applications have so far been concerned with automatic tape measurement extraction, i.e. simulation of the manual procedure ...

A technique for generating a triangular net from an implicit surface description is presented. This technique can be applied to 2-order differentiable functions describing the surface and is based on finding the principal curvatures at each generated point. It is therefore well adapted to the shape of the surface, taking more samples in the areas with high curvature. The triangular net is compe...

The non-asymmetric rolling process of copper and brass wire has been simulated with the Abaqus software. Presented finite element model in this simulation of rolling predicted output curvature and contact surface width in the non-asymmetric mode (in equality of diameter of rollers, the rotational speed of the rollers and the rollers’ surface finish). The material used in this research has strai...

A new technique for computing the differential invariants of a surface from 3D sample points and normals. It is based on a new conformal geometric approach to computing shape invariants directly from the Gauss map. In the current implementation we compute the mean curvature, the Gauss curvature, and the principal curvature axes at 3D points reconstructed by area-based stereo. The differential i...

PURPOSE To quantify the error introduced by videokeratographic corneal topography devices in using a paraxial formula to calculate power over the entire corneal surface, including areas removed from the central paraxial region where the formula is known to be invalid. METHODS Corneal refractive power and two paraxial power approximations were computed as a function of distance from the apex f...

We consider the problem " 2 u ? u + f (u) = 0 in u > 0 in ; @u @ = 0 on @; (0.1) where is a bounded smooth domain in R N , " > 0 is a small parameter and f is a superlinear, subcritical nonlinearity. It is known that this equation possesses multiple boundary spike solutions that concentrate, as " approaches zero, at multiple critical points of the mean curvature function H(P); P 2 @. It is also...

The contact between a liquid and an elastic solid generates a stress vector depending on the curvature tensor in each point of the separating surface. For nanometer values of the mean curvature and for suitable materials, the stress vector takes significant amplitude on the surface. Although the surface average action of the liquid on the solid is the hydrostatic pressure, the local strain gene...

Rescaled spike and slab models are a new Bayesian variable selection method for linear regression models. In high dimensional orthogonal settings such models have been shown to possess optimal model selection properties. We review background theory and discuss applications of rescaled spike and slab models to prediction problems involving orthogonal polynomials. We first consider global smoothi...