The Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989) recommends that students in elementary and middle school grades should be studying geometric properties and relationships through practical experiences with shapes and patterns, integrating mathematical experiences with their art work, and through the use of geometric computer programs. The Standards emphasize that “Ins...

A new cylindrical capacitive sensor (CCS) design for the displacement measurement of precision active magnetic bearing (AMB) spindle is presented in this paper. This research is motivated by the problem that the existing 4-segment CCS is still sensitive to the third harmonic component of the geometric errors of a rotor. The procedure of designing a new CCS starts from the modeling and error ana...

| Low-bitrate video coding receives much attention lately. Applications such as video-phone or real-time video transmissions over ATM networks or multi media have increased the interest to this challenging eld. This paper describes low-bitrate video compression based upon the characterization of the new frame as a set of geometric transformations of objects of the previous frame. Objects with m...

| Low-bitrate video coding receives much attention lately. Applications such as video-phone or real-time video transmissions over ATM networks or multi media have increased the interest to this challenging eld. This paper describes low-bitrate video compression based upon the characterization of the new frame as a set of geometric transformations of objects of the previous frame. Objects with m...

We propose a method to generate penumbrae (half shadows) in scenes that are composed of simple 3-D geometric primitives. Penumbrae occur when objects are illuminated by a light source with nite extent. Traditional methods to generate penumbrae are based either on extensive geometric reasoning or on signal processing (sampling and smoothing). In either way they have a high computational complexi...

The divergence function in information geometry, and the discrete Lagrangian in discrete geometric mechanics each induce a differential geometric structure on the product manifold Q×Q. We aim to investigate the relationship between these two objects, and the fundamental role that duality, in the form of Legendre transforms, plays in both fields. By establishing an analogy between these two appr...

We show that the geometric Hermite interpolant can be easily calculated without solving a system of nonlinear equations. In addition we give geometric conditions for the existence and uniqueness of a solution to the interpolation problem. Finally we compare geometric Hermite interpolation with standard cubic Hermite interpolation. x1 Introduction Since parametric representations of curves are n...

We recall the basic idea of an algebraic approach to learning Bayesian network (BN) structures, namely to represent every BN structure by a certain (uniquely determined) vector, called a standard imset. The main result of the paper is that the set of standard imsets is the set of vertices (= extreme points) of a certain polytope. Motivated by the geometric view, we introduce the concept of the ...