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

H. Kusak Samancı, S. Çelik


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.


Bezier curve, spacelike curve, Minkowski space.

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