1409 Submissions

[3] viXra:1409.0077 [pdf] submitted on 2014-09-11 10:00:26

Curvature of N-Dimensional Ellipsoids Embedded in R^(n+1)

Authors: Hanno Essén, Lars Hörnfeldt
Comments: 1 Page. Abstracts of contributed papers, 11th international conference on general relativity and gravitation, Stockholm, Sweden, abstract no 1:12 (supplementary volume), July 6-12 1986

The curvature tensor and scalar is computed for n up to 6 with the computer algebra system STENSOR. From that new empircal material, formulae for any n are deduced. For the special case of a sphere they coincide with wellknown results.
Category: Geometry

[2] viXra:1409.0026 [pdf] submitted on 2014-09-04 13:59:38

Moments Defined by Doo-Sabin and Loop Subdivision Surface Examples

Authors: Jan Hakenberg
Comments: 50 Pages.

Simple meshes such as the cube, tetrahedron, and tripod frequently appear in the literature to illustrate the concept of subdivision. The formulas for the volume, centroid, and inertia of the sets bounded by subdivision surfaces have only recently been derived. We specify simple meshes and state the moments of degree 0 and 1 defined by the corresponding limit surfaces. We consider the subdivision schemes Doo-Sabin, Loop, and Loop with sharp creases.

In case of Doo-Sabin, the moment of degree 2 is also available for certain simple meshes. The inertia is computed and visualized with respect to the centroid.

Category: Geometry

[1] viXra:1409.0022 [pdf] submitted on 2014-09-04 02:09:40

A Novel Trilateration Algorithm for Localization of a Transmitter/Receiver Station in a 2D Plane using Analytical Geometry

Authors: Joseph I. Thomas
Comments: 10 Pages.

Trilateration is the name given to the Algorithm used in Global Positioning System (GPS) technology to localize the position of a Transmitter/Receiver station (also called a Blind Node) in a 2D plane, using the positional knowledge of three non-linearly placed Anchor Nodes. For instance, it may be desired to locate the whereabouts of a mobile phone (Blind Node) lying somewhere within the range of three radio signal transmitting towers (Anchor Nodes). There are various Trilateration Algorithms in the literature that achieve this end using among other methods, linear algebra. This paper is a direct spin off from prior work by the same author, titled “A Mathematical Treatise on Polychronous Wavefront Computation and its Applications into Modeling Neurosensory Systems”. The Geometric Algorithm developed there was originally intended to localize the position of a special class of neurons called Coincidence Detectors in the Central Neural Field. A general outline of how the same methodology can be adapted for the purpose of Trilateration, is presented here.
Category: Geometry