Python applications on Bèzier curves

With the development of Computer Aided Design (CAD), the importance of visualizing theoretical knowledge with computer technology is increasing and it maintains its popularity. One of the most important pioneer tools to draw curves and surfaces on computer systems is Bézier curves. The aim of this thesis is to theoretically investigate Bézier curves, which are frequently used in Computer Aided Geometric Design (CAGD), and to implement Bézier curves in the computer programming language Python 3.10, which is one of the most preferred languages in the field of Artificial Intelligence (AI) thanks to flexibility of its codes and, also being open source. Some of the presented applications are related to the curve fitting method of Machine Learning (ML) applications, known as the sub-branch of Artificial Intelligence (AI). The thesis consists of five chapters: In the first part of the thesis, motivating information is given to the reader about Machine Learning (ML) and Bézier curves. In the second chapter, basic definitions and theorems about Euclidean space, Minkowski space and Bézier curves, which will be used in the rest of the thesis, are given. In addition, the graphs of basic Bézier curves and some of their examples are plotted employing computer programming language Python 3.10 and their codes are given as an appendix at the end of the thesis. In the third and fourth chapters, proofs of Serret-Frenet frameworks of Bézier curves in three-dimensional Minkowski space and examples are presented. In the fifth chapter, the image obtained by changing the control points of Bézier curves with four different control points and the differences in the images obtained by changing the amount of increase in the given parameter range are examined drawing them in the computer programming language Python 3.10 (64 bit).