Open Access Open Access  Restricted Access Subscription or Fee Access

The Curvatures of the Spacelike Bezier Curve with a Spacelike Principal Normal in Minkowski-3 Space

H. Kusak Samancı, S. Çelik

Abstract



Bezier curves are parametric curves which are commonly used in Computer Aided Geometric Design. Many applications of the Bezier curves took place in the automobile industry, robotics, computer animations etc. This curve is defined by its endpoints. In order to investigate some geometric properties of the Bezier curve, the calculations of the geometric properties of the endpoints are sufficient. In recent years, it has been realized that the Bezier curve provide useful tools for Minkowski space. Therefore the aim of this paper is to investigate the spacelike Bezier curve with a spacelike principal normal for endpoints. Firstly, we obtained Serret-Frenet frame at the starting point of this kind of curves for three special conditions. Secondly, we calculated the curvatures and torsions for all conditions. Thirdly, we found the derivation formulas of Serret-Frenet formulas. Finally, we gave an example for the starting point of the curve.

Keywords


Bezier curve, spacelike curve, Minkowski space.

Full Text:

PDF


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.