Editing De Casteljau's algorithm (section)

{{Short description|Method to evaluate polynomials in Bernstein form}}
In the [[mathematics|mathematical]] field of [[numerical analysis]], '''De Casteljau's algorithm''' is a [[Recursion|recursive]] method to evaluate polynomials in [[Bernstein form]] or [[Bézier curve]]s, named after its inventor [[Paul de Casteljau]]. De Casteljau's algorithm can also be used to split a single Bézier curve into two Bézier curves at an arbitrary parameter value.

The algorithm is [[numerically stable]]<ref>{{Cite journal |last1=Delgado |first1=J. |last2=Mainar |first2=E. |last3=Peña |first3=J. M. |date=2023-10-01 |title=On the accuracy of de Casteljau-type algorithms and Bernstein representations |url=https://www.sciencedirect.com/science/article/pii/S0167839623000754 |journal=Computer Aided Geometric Design |volume=106 |pages=102243 |doi=10.1016/j.cagd.2023.102243 |issn=0167-8396|doi-access=free }}</ref> when compared to direct evaluation of polynomials. The computational complexity of this algorithm is <math>O(d n^2)</math>, where d is the number of dimensions, and n is the number of control points. There exist faster alternatives.<ref>{{Cite journal |last1=Woźny |first1=Paweł |last2=Chudy |first2=Filip |date=2020-01-01 |title=Linear-time geometric algorithm for evaluating Bézier curves |url=https://www.sciencedirect.com/science/article/abs/pii/S0010448518301234 |journal=Computer-Aided Design |volume=118 |pages=102760 |doi=10.1016/j.cad.2019.102760 |issn=0010-4485|arxiv=1803.06843 }}</ref><ref>{{Cite journal |last1=Fuda |first1=Chiara |last2=Ramanantoanina |first2=Andriamahenina |last3=Hormann |first3=Kai |date=2024 |title=A comprehensive comparison of algorithms for evaluating rational Bézier curves |url=https://drna.padovauniversitypress.it/2024/3/9 |journal=Dolomites Research Notes on Approximation |volume=17 |issue=9/2024 |pages=56–78 |doi=10.14658/PUPJ-DRNA-2024-3-9 |issn=2035-6803}}</ref>