De Casteljau's algorithm

<p>In the <a href="/facts/Mathematics/pxTouaz4">mathematical</a> field of <a href="/facts/Numerical_analysis/QT9cYa9z">numerical analysis</a>, De Casteljau's algorithm is a <a href="/facts/Recursion/CxSKxJoW">recursive</a> method to evaluate polynomials in <a href="/facts/Bernstein_form/XkJFDDIB">Bernstein form</a> or <a href="/facts/B%25C3%25A9zier_curve/zJx3Uj60">Bézier curves</a>, named after its inventor <a href="/facts/Paul_de_Casteljau/TlJhEj6I">Paul de Casteljau</a>. De Casteljau's algorithm can also be used to split a single Bézier curve into two Bézier curves at an arbitrary parameter value.
</p><p>The algorithm is <a href="/facts/Numerically_stable/jRDdo8zV">numerically stable</a> when compared to direct evaluation of polynomials. The computational complexity of this algorithm is 
  
    
      
        O
        (
        d
        
          n
          
            2
          
        
        )
      
    
    {\displaystyle O(dn^{2})}
  
, where d is the number of dimensions, and n is the number of control points. There exist faster alternatives.
</p>

De Casteljau's algorithm open-in-new

De Casteljau's algorithm