Some coordinate transformations relevant to refractive indices

3D affine coordinate transformations

Landsat MSS Coordinate Transformations

, A number of image a n a l y s i s t a s k s r e q u i r e t h e r e g i s t r a t i o n of a s u r f a c e model w i t h an image. I n t h e case o f s a t e l l i t e images, t h e s u r f a c e model may be a map o r d i g i t a l t e r r a i n model i n t h e form o f surface e l e v a t i o n s on a g r i d o f p o i n t s. We develop here an a f f i n e transformation between coordinates...

Vectors, Matrices and Coordinate Transformations

For our purposes we will think of a vector as a mathematical representation of a physical entity which has both magnitude and direction in a 3D space. Examples of physical vectors are forces, moments, and velocities. Geometrically, a vector can be represented as arrows. The length of the arrow represents its magnitude. Unless indicated otherwise, we shall assume that parallel translation does n...

Coordinate transformations in object recognition.

A basic problem of visual perception is how human beings recognize objects after spatial transformations. Three central classes of findings have to be accounted for: (a) Recognition performance varies systematically with orientation, size, and position; (b) recognition latencies are sequentially additive, suggesting analogue transformation processes; and (c) orientation and size congruency effe...

Nonlinear coordinate transformations for unconstrained optimization I. Basic transformations

In this two-part article, nonlinear coordinate transformations are discussed to simplify unconstrained global optimization problems and to test their unimodality on the basis of the analytical structure of the objective functions. If the transformed problems are quadratic in some or all the variables, then the optimum can be calculated directly, without an iterative procedure, or the number of ...