In this paper, we present an optical model that simulates the light trapping and scattering effects of a paraboloid texture surface first time. This model was experimentally verified by measuring the reflectance values of the periodically textured silicon (Si) surface with the shape of a paraboloid under different conditions. A paraboloid texture surface was obtained by electrochemical etching ...

Parabolas and paraboloids are used to introduce curvature, both qualitatively and quantitatively. 1. Introduction. Most of the standard diierential geometry textbooks recognize the oscu-lating paraboloid as a useful interpretation of the second fundamental form of a surface. This interpretation leads to some qualitative conclusions about the shape of the surface in consideration 9, pp.87,91]. T...

Large umbrella space antennas are essential for communication, monitoring and observation of Earth and space objects. Despite investigations devoted to space antenna dynamics, the disturbance impulse shape effect on the root mean square error of spacecraft antenna reflecting surface has not been studied. This paper overcomes this gap describing disturbance impulse impact on root mean square err...

studying gaussian beam is a method to investigate laser beam propagation and abcd matrix is a fast and simple method to simulate gaussian beam propagation in different mediums. of the abcd matrices studied so far, reflection and refraction matrices at various surfaces have attracted a lot of researches. however in previous work the incident beam and the principle axis of surface are in parallel...

Ruled surface design and its applications are widely used in CAGD(Computer Aid Geometric Design) and industrial areas. In this paper, the hyperbolic paraboloid is a particular ruled surface, which is drawn by using the dual De Casteljau algorithm [15]. The characteristics of the hyperbolic paraboloid are analysed in order to match the requirement of the dual De Casteljau algorithm. A new method...

The paper proposes an approach where structural systems can be developed according to the mathematical theory of fractals. Architecture can take advantage of the complexity sciences, by the use of present day computer technology, where algorithms of mathematical and geometric functions can produce new motifs of design. In order to demonstrate this, examples of the use of the elliptic and hyperb...

Reference 1] Pavel Krsek, Tomm a s Pajdla, and VV aclav Hlavv a c. Estimation of differential parameters on triangulated surface. Abstract This paper presents an algorithm for estimation of principal curvatures and principal directions from 3D scanned data. The diierential parameters will be base for nding of diierential structures on the surface. This structures should be used for fusion of ra...

From the differential equation of the doubly curved shell in terms of the displacement components u, v and w it is apparent that, in so far as the flexural phenomena are concerned, the shell can be considered as a flat plate on an elastic foundation, at a~y rate in a region of sufficiently small size to be regarded as quasi-Euclidean around the vertex of the osculating paraboloid. The modulus o...

We revisit the Schr\"{o}dinger equation of a quantum particle that is confined on curved surface. Inspired by novel work R. C. T. da Costa [1] we find field in more convenient notation. The contribution principal curvatures effective binding potential surface emphasized. Furthermore, using so-called Monge-Gauge construct approximate for flat with small fluctuations. Finally, resulting solved so...

Pascal Desnoguès Olivier Devillers y Abstract: Given a set S of data points in IR2 and corresponding data values for a speci c non-convex surface, the unit hyperbolic paraboloid, we consider the problem of nding a locally optimal triangulation of S for the linear approximation of this surface. The chosen optimality criterion will be the L2 norm: it means that we will try to nd directly a triang...