Based on the construction of bivariate fractal interpolation surfaces, we introduce closed spherical fractal interpolation surfaces. The interpolation takes place in spherical coordinates and with the transformation to Cartesian coordinates a closed surface arises. We give conditions for this construction to be valid and state some useful relations about the Hausdorff and the Box counting dimen...

The ventral premotor cortex (PMv) and the primary motor cortex (MI) of monkeys participate in various sensorimotor integrations, such as the transformation of coordinates from visual to motor space, because the areas contain movement-related neuronal activity reflecting either visual or motor space. In addition to relationship to visual and motor space, laterality of the activity could indicate...

Dennis V. Perepelitsa 19 December 2006 Gerald Jay Sussman, Jack Wisdom Exercise 5.32: Hierarchical Jacobi coordinates (a) Canonical heliocentric coordinates The canonical heliocentric transformation singles out the center of mass of the system. The other coordinates are computed with respect to this coordinate. Specifically, the relationships between the elements of (x′0, . . . , x ′ n−1) and (...

A direct transformation from cartesian coordinates into hyperboloidal coordinates (considered for biaxial hyperboloids) is presented in this paper. The transformation problem is reduced to the problem of finding the smallest positive root of a fourth degree polynomial. The analysis of the polynomial’s roots is performed by an algebraically complete stratification, based on symbolic techniques (...

Advances in remote sensing technologies demonstrated the capability to acquire high quality metric information from satellite images. The IKONOS satellite image, for example, has a pixel size of one meter. The sensor model parameters are not yet released. This motivate the use of empirical transformation models to represent the relationship between image space coordinates and object space coord...

During the 88th and 96th Conferences of the Working Committee of the Surveying Authorities of the States of the Federal Republic of Germany (AdV) in 1991 and 1995 the resolution was passed to introduce the European Terrestrial Reference System 1989 (ETRS89) with the universal transversals Mercator projection (UTM) as map projection of GRS80 Ellipsoid in Germany and Europe uniformly. The task of...

Calibration of a structured light system is considered in this paper. The system consists of a projector whose output is controlled by a liquid crystal shutter, and a camera to capture the images. A sequence of patterns is projected to temporally encode 256 stripes on the visible surfaces. The transformation from 3D world coordinates to camera image plane coordinates and projector stripe ids ar...