Bezier curves and bezier surfaces in euclidean space

In this thesis, Bezier curves in Euclidean space are discussed. Firstly, general formula for Frenet vectors and Frenet curvatures is obtained by using the Gram-Schmidt orthonormalization method for a Bezier curve of degree n. Secondly, the strain energies of the Bezier surfaces were calculated. This thesis consists of five chapters. The first section is the introduction. In the second section, the basic definitions and theorems about curves and surfaces in E^n are given which is used in the next part of the thesis. In the third chapter, Bezier curves and Bezier surfaces are introduced in Euclidean space. The properties of a n.th degree Bezier curve are given. Similarly, the given properties are also introduced for Bezier surfaces. In the fourth chapter, the Frenet elements of the Bezier curves in the plane and in the 3 and 4-dimensional space are calculated and a method for a n.th degree Bezier curve is obtained. In addition, the strain energies of Bezier surfaces are mentioned and giving examples related to these, the state of having the appropriate strain energy has been examined. The fifth chapter is the conclusion part of the study, and with these results, open problems that may arise in the future are emphasized.