The quick advance in remote sensing technologies provides the ability to acquire high quality metric information. This is achievable by forming the relationship between image coordinates and ground coordinates as 2D and 2D-to3D transformation models. Most of these models are based on point features. Although point-based transformation models are well developed, it is time-consuming and costly t...

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.

A general uid moment in the particle coordinates is represented in terms of uid moments in modied guiding-centre coordinates with strong E × B ow derived by the phase space Lagrangian Lie-transform method [N. Miyato et al., J. Phys. Soc. Jpn. 78, 104501 (2009)]. It is called the push-forward representation of the particle uid moment associated with the guiding-centre transformation. The re...

The non-orthogonal boundary-fitted coordinate transformation method is applied to the solution of steady three-dimensional momentum and energy equations in laminar flow to obtain temperature field and Nusselt numbers in the thermal entry region of straight ducts of different cross sectional geometries. The conservation equations originally written in Cartesian coordinates are parabolized in the...

Increasingly, geoscientists and biologists are monitoring the natural environment with total station and terrestrial laser scanning surveys. Due to the remote nature of many of the sites monitored (e.g., streams, rivers, glaciers, etc.) the surveys are often done in unprojected, Cartesian, local, assumed coordinate systems. However, without the survey data projected in real world coordinates th...

The article considers findings and concepts on vestibular-proprioceptive interaction for self-motion perception and postural control under the form of simple describing models. It points out that vestibular-neck interaction is only a small fraction of an extended mechanism of co-ordinate transformations. This links together the different parts of our bodies, so that sensory information arising ...

This paper presents a method for determining the six-degreeof-freedom (DOF) transformation between a camera and a base frame of interest, while concurrently estimating the 3D base-frame coordinates of unknown point features in the scene. The camera observes the reflections of fiducial points, whose base-frame coordinates are known, and reconstruction points, whose base-frame coordinates are unk...

computer graphics, transformations, texture mapping In a 3D graphics application, a common operation is the binding of a 2D texture onto a triangle in a 3D positional space. For light-dependent or view-dependent texture mapping, a need may arise in the graphics pipeline to transform the light or view direction vector into texture space. The affine transformation is unique within the plane of th...

Abstract In this work, the Mellin transform method was used to obtain solutions for the stress field components in two dimensional (2D) elasticity problems in terms of plane polar coordinates. the Mellin transformation was applied to the biharmonic stress compatibility equation expressed in terms of the Airy stress potential function, and the boundary value problem transformed to an algebraic  ...

This note describes a method for computing estimates of the rigid transformation G and estimates of the coordinates of a set of n points P1, . . . ,Pn in the two camera reference frames from the n pairs (x1,y ′ 1), . . . (xn,y ′ n) of noisy measurements of their corresponding images. The transformation G is called camera motion, and the point coordinates Xi, Xi of the world points in the two re...