We will define basic parametric planar curve properties, like tangent vector, curvature, normal vector and offset. Then, we will describe polynomials in the Bernstein basis and use that concept for defining Bézier curves and control polygon. Interpolation with cubic Bézier will follow. We will define pythagorean-hodograph (PH) curves, describe their main properties and calculate control points. We will interpolate given data with the PH quintics and show a criteria for choosing the best solution. We will construct PH quintic splines and compare them to the ordinary cubic splines. We will finish with constructing offset curves and describe trimming procedure.