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

"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 t...

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Xehetasun bibliografikoak
Egile Nagusiak: Şeyda Kılıçoglu, Süleyman Şenyurt
Formatua: Artikulua
Hizkuntza:English
Argitaratua: Emrah Evren KARA 2022-03-01
Saila:Communications in Advanced Mathematical Sciences
Gaiak:
Sarrera elektronikoa:https://dergipark.org.tr/tr/download/article-file/2074739
Deskribapena
Gaia:"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 $\left( n-1\right) ^{th}$ 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 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 $P_{n}$.
ISSN:2651-4001