This paper may be regarded as a new numerical method for the analysis of triangular thin plates using the natural area coordinates. Previous studies on the solution of triangular plates with different boundary conditions are mostly based on the Rayleigh-Ritz principle which is performed in the Cartesian coordinates. Consequently, manipulation of the geometry and numerical calculation of the int...

Previous theoretical investigations of the three-dimensional (3-D) angular vestibuloocular reflex (VOR) have separately modeled realistic coordinate transformations in the direct velocity path or the nontrivial problems of converting angular velocity into a 3-D orientation command. We investigated the physiological and behavioral implications of combining both approaches. An ideal VOR was simul...

A simple method of converting scanner (RGB) responses to estimates of object tristimulus (XYZ) coordinates is to apply a linear transformation to the RGB values. The transformation parameters are selected subject to minimization of some relevant error measure. While the linear method is easy, it can be quite imprecise. Linear methods are only guaranteed to work when the scanner sensor responsiv...

This paper describes a geometric correction algorithm for high-resolution pushbroom type sensor images. In the systematic correction module, a sensor-orbit-Earth model was designed by using a vector projection technique which resulted in a forward transformation from raw image coordinates to geocentric coordinates . In order to avoid a large amount of computational load of the forward transform...

Optimal space trajectory problems and the necessaly and sufficient conditions that define their solutions are stated most compactly in terms of position and velocity vectors. To obtain analytical or numerical solutions, however, the problems are expressed using a particular set of coordinates. Each set of coordinates has advantages and disadvantages depending on the application. Thus, it may be...

where vg is the volume form on (M,g) and e( f )(x) := (1/2)‖df (x)‖T∗M⊗ f −1TN is the energy density of f at the point x ∈M. In local coordinates (x)i=1 on M and (y)a=1 on N , the energy density is given by e( f )(x)= (1/2)gi (x)hab( f (x))(∂ f a/∂xi)(∂ f b/∂x j). Critical points of the energy functional are called harmonic maps. The first variational formula of the energy gives the following c...

The transformation of the RGB colour space to a hue, saturation and brightness colour space is essentially a conversion from a rectangular coordinate system to a cylindrical coordinate system. Nevertheless, a bewildering array of such conversions exist. We show that one of the main reasons for this is the dependence of the saturation values on the choice of the brightness function, and suggest ...