Angular orientation refers to the position of a rigid body intrinsic coordinate system relative to a reference coordinate system with the same origin. It is determined with a sequence of rotations needed to move the rigid-body coordinate-system axes initially aligned with the reference coordinate-system axes to their new position. In this paper we present a novel way for representing angular or...

In this paper, we propose a physical layer security scheme that exploits novel index modulation (IM) technique for coordinate interleaved orthogonal designs (CIOD). Utilizing the diversity gain of CIOD transmission, proposed scheme, named CIOD-IM, provides an improved spectral efficiency by means IM. order to provide satisfactory secrecy rate, design particular artificial noise matrix, which do...

This paper deals with a special case of the Euclidean Travelling Salesman Problem known as the x-and-y-axes TSP. In this special case, all cities are situated on the x-axis and on the y-axis of an orthogonal coordinate system for the Euclidean plane. We show that the problem can be solved in O(n) time.

We present an efficient solution to the eikonal equation on parametric manifolds, based on the fast marching approach. This method overcomes the problem of a non-orthogonal coordinate system on the manifold by creating an appropriate numerical stencil. The method is tested numerically and demonstrated by calculating distances on various parametric manifolds. It is further used for two applicati...

Constructing a CAD model from a physical model plays a key role in some productdevelopment processes. To be presented is an “indirect” method of fitting NURBS-surfaces for rotational-freeform shapes: 1) Cloud-of-points data representing a rotational-freeform shape are transformed into an orthogonal-coordinate (sphericalor cylindrical-) system, 2) a single-valued Bspline surface is fitted to the...

The unit vectors transformation between the Cartesian and novel similar oblate spheroidal coordinates, vice versa, is derived. It facilitates of vector fields these two types orthogonal coordinates can advantageously simplify solutions problems exhibiting geometry. Several examples demonstrate use derived relations. Generalized sine cosine applicable in coordinate system are introduced as well.

The fundamental tool in the classification of orthogonal coordinate systems in which the Hamilton–Jacobi and other prominent equations can be solved by a separation of variables are second order Killing tensors which satisfy the Nijenhuis integrability conditions. The latter are a system of three non-linear partial differential equations. We give a simple and completely algebraic proof that for...