The conversion matrix between uniform B-spline and Bézier representations

In computer-aided design it is both convenient and practical to use the matrix form in representing parametric curves and surfaces. One of the reasons is that the matrix notation allows an easy conversion between different shape representations and provides a convenient implementation in either hardware or software with available matrix facilities. In this work we propose a very simple and efficient procedure for computing in a recursive way the conversion matrices which provide the direct transformation between uniform B-spline and Bézier representations of arbitrary degrees.