Dedicated to the memory of Gerold Wagner Abstract We study the L w -norm (2 < W < oo) of the discrepancy of a sequence of points in the unit cube relative to similar copies of a given convex polygon. In particular, we prove the rather surprising result that the estimates obtained have the same order of magnitude as the analogous question when the sequence of points is replaced by a set of point...

PURPOSE OF REVIEW Topography-guided laser refractive surgery regularizes the front corneal surface irregularities to achieve the desired refractive outcome. This is particularly applicable in highly aberrated corneas, where wavefront aberrometry is often not possible. This article aims to review the recently published results of topography-guided ablations in normal regular corneas, highly aber...

BACKGROUND Texture, color, and durability are important characteristics to consider for skin replacement in conspicuous and/or mobile regions of the body such as the face, neck, and hands. Although autograft thickness is a known determinant of skin quality, few studies have correlated the subjective and objective characters of skin graft healing with their associated morphologic and cellular pr...

In this paper, a new approach to fitting aspheric surfaces in three-dimensional space is proposed, based on the nonlinear least-squares algorithm. The method is superior to conventional solutions as all the surface parameters can be estimated simultaneously based on the design equation, thus allowing the result to be directly compared to design parameters. Conventionally, aspheric surfaces can ...

The study of the damage of aeronautical materials is important because it may change the microscopic surface structure profiles. The modification of geometrical surface properties can cause small instabilities and then a displacement of the boundary layer. One of the irregularities we can often find is surface roughness. Due to an increase of roughness and other effects, there may be extra mome...

In this paper, we propose a 3D reconstruction approach using shape-based interpolation and extrapolation. This approach aims to generate a 3D geometric model of a human shoulder from a sequence of MR parallel 2D cross-sections. While interpolation generates intermediate slices between every pair of adjacent input slices, extrapolation performs a smooth closing of the external surface of the mod...