Paul de Casteljau
Encyclopedia
Paul de Casteljau is a French physicist and mathematician. In 1959, while working at Citroën
, he developed an algorithm
for computation of Bézier curve
s, which would later be formalized and popularized by engineer Pierre Bézier
. De Casteljau's algorithm
is widely used, with some modifications, as it is the most robust and numerically stable method for evaluating polynomials. Other methods, such as Horner's method and forward differencing, are faster for calculating single points but are less robust. De Casteljau's algorithm is still very fast for subdividing a Bézier curve
into two curve segments at an arbitrary parametric location.
Citroën
Citroën is a major French automobile manufacturer, part of the PSA Peugeot Citroën group.Founded in 1919 by French industrialist André-Gustave Citroën , Citroën was the first mass-production car company outside the USA and pioneered the modern concept of creating a sales and services network that...
, he developed an algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
for computation of Bézier curve
Bézier curve
A Bézier curve is a parametric curve frequently used in computer graphics and related fields. Generalizations of Bézier curves to higher dimensions are called Bézier surfaces, of which the Bézier triangle is a special case....
s, which would later be formalized and popularized by engineer Pierre Bézier
Pierre Bézier
Pierre Étienne Bézier was a French engineer and one of the founders of the fields of solid, geometric and physical modeling as well as in the field of representing curves, especially in CAD/CAM systems...
. De Casteljau's algorithm
De Casteljau's algorithm
In the mathematical field of numerical analysis, De Casteljau's algorithm is a recursive method to evaluate polynomials in Bernstein form or Bézier curves, named after its inventor Paul de Casteljau...
is widely used, with some modifications, as it is the most robust and numerically stable method for evaluating polynomials. Other methods, such as Horner's method and forward differencing, are faster for calculating single points but are less robust. De Casteljau's algorithm is still very fast for subdividing a Bézier curve
Bézier curve
A Bézier curve is a parametric curve frequently used in computer graphics and related fields. Generalizations of Bézier curves to higher dimensions are called Bézier surfaces, of which the Bézier triangle is a special case....
into two curve segments at an arbitrary parametric location.