A new kind of NURBS representation for periodic curves is introduced. The method for periodic curves is extended to derive a compact and symmetric representation of the sphere or the ellipsoid using a piecewise bi-quadratic NURBS surface with only eight distinct control vertices.

The purpose of this study is the dimensioning of the cylindrical mixing chamber of a compressible fluid ejector used in particular in sugar refineries for degraded vapor re-compression at the calandria exit, during the evaporation phase. The method used, known as the “integral” or “thermodynamic model”, is based on the model of the one-dimensional isentropic flow of perfect gases with the addit...

In this article we study bases for projective monomial curves and the relationship between the basis and the set of generators for the defining ideal of the curve. We understand this relationship best for curves in P and for curves defined by an arithmetic progression. We are able to prove that the latter are set theoretic complete intersections.

Lappeenranta University of Technology Faculty of Technology Management Department of Information Technology

Article history: Received 6 May 2013 Received in revised form 21 November 2014 Accepted 4 January 2015 Available online 13 January 2015

In this paper, we propose an elaborate geometry approach to explain the group law on twisted Edwards curves which are seen as the intersection of quadric surfaces in place. Using the geometric interpretation of the group law we obtain the Miller function for Tate pairing computation on twisted Edwards curves. Then we present the explicit formulae for pairing computation on twisted Edwards curve...

Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, tota...

Non-uniform rational B-splines (NURBS) have become a de facto standard in commercial modeling systems because of their power to represent both free-form shapes and some common analytic shapes. To date, however, NURBS have been viewed as purely geometric primitives, which require the designer to interactively adjust many degrees of freedom (DOFs )-control points and associated weights-to achieve...