Equidistant

Abstract: A plate and more generally a shell is a special three-dimensional body whose boundary surface has special features. Although we defer defining a shell-like body in precise terms until Sect. 4, for the purpose of these preliminary remarks consider a surface—called a reference surface—and imagine material filaments from above and below surrounding the surface along the normal at each point of the reference surface. Suppose further that the bounding surfaces formed by the end points of the material filaments are equidistant from the reference surface. Such a three-dimensional body is called a shell if the dimension of the body along the normals, called the thickness, is small. A shell is said to be thin if its thickness is much smaller than a certain characteristic length of the reference surface, e.g., the minimum radius of the curvature of the reference surface for initially curved shells.2

Abstract: A backlight illumination system for illuminating a large area with light of a uniform color has a set of a pre-determined number of light emitters arranged along a straight line The set is divided in a plurality of subsets, each subset including at least two light emitters Each subset comprises light emitters with substantially the same light-emission color point, the respective subsets having color points different from each other As a first step, the light emitters of the subset with a smallest number of light emitters are assigned to respective substantially equidistant positions The light emitters of the set are assigned to the respective positions by iteratively starting with the subset with the smallest number of light emitters, assigning the light emitters of the subset to substantially equidistant positions which are not yet occupied The backlight illumination system according to the invention has a uniform light and color distribution

Abstract: A conservative transport scheme based on the discontinuous Galerkin (DG) method has been developed for the cubed sphere. Two different central projection methods, equidistant and equiangular, are employed for mapping between the inscribed cube and the sphere. These mappings divide the spherical surface into six identical subdomains, and the resulting grid is free from singularities. Two standard advection tests, solid-body rotation and deformational flow, were performed to evaluate the DG scheme. Time integration relies on a third-order total variation diminishing (TVD) Runge–Kutta scheme without a limiter. The numerical solutions are accurate and neither exhibit shocks nor discontinuities at cube-face edges and vertices. The numerical results are either comparable or better than a standard spectral element method. In particular, it was found that the standard relative error metrics are significantly smaller for the equiangular as opposed to the equidistant projection.