How to Find a Bezier Curve in $E^{3}$ - Şeyda Kılıçoglu; Süleyman Şenyurt (Communications in Advanced Mathematical Sciences, 2022)
"How to find any $n^{th}$ order Bézier curve if we know its first, second, and third derivatives?" Hence we have examined the way to find the Bézier 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 Bézier 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 $\left( n-1\right) ^{th}$ order, the $\left(n-2\right) ^{th}$ and the $\left( n-3\right) ^{th}$ Bezier curves in respective order. There is a lot of the number of Bézier curves with known the derivatives with control points. Hence to find a Bézier curve we have to choose any control point of any derivation\. In this study we have chosen two special points which are the initial point $P_{0}$ and the endpoint $P_{n}$.