A MATRIX PRESENTATION OF HIGHER ORDER DERIVATIVES OF BEZIER CURVE AND SURFACE

In this study, the Bezier curves and surfaces, which have an important place in interactive design applications, are expressed in matrix form using a special matrix that gives the coefficients of the Bernstein base polynomial. The matrix forms of higher order derivatives of the Bezier curves and surfaces are obtained. It is demonstrated by numerical examples that the bidirectional transition between the control points and parametric equations of the Bezier curves and surfaces can be easily achieved using these matrix forms. In addition, it is demonstrated that this type of curve and surface, whose control points are known, its higher order derivatives can be calculated without it's parametric equations. In this study, the Bezier curves and surfaces are presented in a more easily understandable and easy to use format in algebraic form for designers.