The diploma thesis addresses a special type of curve known as Pythagorean-hodograph (PH) curves. Initially, we define the basic terms and apply them in the definition of the Tschirnhausen cubic as an example of special curves. The definitions are supported by images and derivations of equations, and the procedures are illustrated with examples. The central part of the thesis focuses on cubic PH curves, their characterization, and useful properties, as well as the reasoning that leads to certain results. The main result of the thesis is the proof that every cubic PH curve can be represented as a segment of the Tschirnhausen cubic. In the final part, we use complex numbers to reach the same conclusion in a simpler way.
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