Bézier Triangles
When de Casteljau invented Bézier curves in 1959, he realized the need for the extension of the curve ideas to surfaces. Interestingly enough, the first surface type that he considered was what we now call Bézier triangles. This historical “first” of triangular patches is reflected by the mathematical statement that they are a more “natural” generalization of Bézier curves than are tensor product patches. We should note that although de Casteljau’s work was never published, Bézier’s was; therefore, the corresponding field now bears Bézier’s name. For the placement of triangular Bernstein-Bézier surfaces in the field of CAGD, see Barnhill [24].
Though de Casteljau’s work (established in two internal Citroën technical reports ...
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