The similarities of rational space curves in 3-dimensional euclid space

Making machines that mimic people's abilities has always been an important research topic for scientists. It is tried to determine everything that can be perceived visually as objects through computers. With the help of algorithms, operations such as recognizing, distinguishing and classifying objects can be performed. If one object can be obtained by scaling and isometry of another object, these two objects are similar. Thus, although two similar objects have the same shape, their position and size may be different. Thus, similarity detection is an important area of Pattern Recognation, which has a typical database of objects and compares all elements in the database with respect to similarity. Pattern Recognation is a science that deals with the identification or classification of measured data. The structure of these curves is used to check whether the rational space curves are similar, and for positive cases the similarity between the two curves can be clearly expressed. In this study, transformations that provide similarity for two similar space curves will be introduced. In this thesis, similarity curves of rational space curves and how to express similar curves with Möbius transformation are examined.