In this work, we will be dealing with obtaining suitable parametrizations of curved planar domains with prescribed boundaries. As the main tool, we will take a closer look at Bézier curves and surfaces, where in addition to the basic definitions, we will also list some nice properties of them, as well as look at some examples. Later we will focus on the parametrizations themselves - we will look at some ways we can generate a parametrization in a closed form, either by using an algorithm, or by solving a matrix equation, and in the end we will investigate how the parametrization can be obtained through the process of minimization of certain functionals.
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