  Splines are one of the main methods of mathematically representing
complicated shapes, which have become the primary technique in the fields of
Computer Graphics (CG) and Computer-Aided Geometric Design (CAGD) for modeling
complex surfaces. Among all, B\'ezier and Catmull-Rom splines are the most
common in the sub-fields of engineering. In this paper, we focus on conversion
between cubic B\'ezier and Catmull-Rom curve segments, rather than going
through their properties. By deriving the conversion equations, we aim at
converting the original set of the control points of either of the Catmull-Rom
or B\'ezier cubic curves to a new set of control points, which corresponds to
approximately the same shape as the original curve, when considered as the set
of the control points of the other curve. Due to providing simple linear
transformations of control points, the method is very simple, efficient, and
easy to implement, which is further validated in this paper using some
numerical and visual examples.
