Uniform cubic B-spline functions have been used for mapping functions in various areas such as image warping and morphing, 3D deformation, and volume morphing. The injectivity (one-to-one property) of a mapping function is important to obtain good results in these areas. This paper considers the local injectivity conditions of 2D and 3D uniform cubic B-spline functions. We propose a geometric i...

This paper presents a non-uniform cubic C spline framework that unifies three scenarios for incorporating data from basic curves, such as spirals and conics. In the first scenario, no parameterization of the basic curves is available, only well-spaced samples; in the second, a parameterization is available but cannot be used directly in a spline framework; only in the third scenario can pieces ...

The Gaussian kernel has long been used in the classical multiscale analysis. The purpose of the paper is to propose the uniform B-spline as an alternative for the visual modeling. A general framework for various scale-space representations is formulated using theB-spline approach. In particular, the evolution of the wavelet models can be well understood from such an approach. Most of the wavele...

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

The variation in the accuracy of the calculated natural frequencies of pre-twisted beams solved with spline collocation method is investigated in this study. The spline collocation method is used to formulate the eigenvalue problems of pre-twisted beams. Three types of boundary conditions are considered. Numerical results indicate that the accuracy of the calculated natural frequencies is signi...