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

Authors : Süleyman ŞENYURT, Şeyda KILIÇOGLU

Pages : 12-24

Doi:10.33434/cams.1021878

View : 27 | Download : 11

Publication Date : 2022-03-17

Article Type : Research Paper

Abstract :`How to find any $n^{th}$ order B\`{e}zier curve if we know its first, second, and third derivatives?` Hence we have examined the way to find the B\`{e}zier curve based on the control points with matrix form, while derivatives are given in $\mathbf{E}^{3}$. Further, we examined the control points of a cubic B\`{e}zier 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 $\leftinsert ignore into journalissuearticles values( n-1\right); ^{th}$ order, the $\leftinsert ignore into journalissuearticles values(n-2\right); ^{th}$ and the $\leftinsert ignore into journalissuearticles values( n-3\right); ^{th}$ Bezier curves in respective order. There is a lot of the number of B\`{e}zier curves with known the derivatives with control points. Hence to find a B\`{e}zier 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 $P_{n}$.
Keywords : Bezier curves, Cubic Bezier curves, Derivatives of Bezier curve