### Paul de Faget de Casteljau

#### The 2012 Pierre Bézier Award Recipient

The award committee has chosen this year to honor the
creator of at least

three
fundamental ideas important in surface modeling. The first idea was the

use
of Bernstein polynomials as basis functions for
parametric polynomial curves

and
surfaces. The second was the use of multilinear
polynomials as a represen-

tation for these
polynomials, providing a fundamental tool for understanding,

and
working with, splines. His third contribution was using
this multilinear

form
to give an efficient and stable evaluation algorithm.

Paul de Casltejau's
contributions are less widely known than should be the

case
because he was not able to publish them until equivalent ideas had been

reinvented
independently by others, sometimes in a rather different form but

now
recognisably related. Because he was not permitted to
publish his early

work,
we now call polynomials with a Bernstein basis "Bézier
polynomials",

although
Bézier himself did not use control points but their
first difference vec-

tors as the
coefficients. We also call the multilinear
polynomials " blossoming",

following
Lyle Ramshaw who in turn credited de Casteljau with the underlying

"polar
approach" to the mathematical theory of splines.
We do call the algo-

rithm for the stable
evaluation of the Bernstein-Bezier form for polynomials "de

Casteljau algorithm"
although it is Carl de Boor's more general result applying

it
to B-splines which is now widely used in CADCAM
systems.

In
the words of Pierre Bézier himself:

There is no doubt
that Citroen was the first company in France

that paid attention to CAD, as early as 1958. Paul de Casteljau, a

highly gifted mathematician, devised a system based on
the use of

Berstein
polynomials. ... the system devised by de Casteljau
was

oriented towards translating already existing shapes
into patches,

defined in terms of numerical data. ... Due to Citroen's
policy,

the results obtained by de Casteljau
were not published until 1974,

and this excellent mathematician was deprived of part of
the well

deserved fame that his discoveries and inventions should
have earned

him.

Pierre Bézier, The first years of CAD/CAM and the UNISURF

CAD System," pp 13-26 in Fundamental Developments
of Computer-

Aided Geometric Modeling, ed
L. Piegl, 1993

The
award committee unanimously accepts this endorsement of Paul de Castel-

jau for the 2012 Bézier award and hopes this award might provide a little of

that
well-deserved fame albeit rather belatedly.