How to Find a Bezier Curve in $\mathbf{E}^{3}$

Abstract

How to find any n th order B ézier curve if we know its first, second, and third derivatives?" Hence we have examined the way to find the B ézier curve based on the control points with matrix form, while derivatives are given in E 3 . Further, we examined the control points of a cubic B ézier curve with given derivatives as an example. In this study first we have examined how to find any n th order Bezier curve with known its first, second and third derivatives, which are inherently, the (n − 1) th order, the (n − 2) th and the (n − 3) th Bezier curves in respective order. There is a lot of the number of B ézier curves with known the derivatives with control points. Hence to find a B ézier curve we have to choose any control point of any derivation İn this study we have chosen two special points which are the initial point P 0 and the endpoint P n .

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