A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
Subdivision algorithms converge quadratically
Journal of Computational and Applied Mathematics
Efficient evaluation of multivariate polynomials
Computer Aided Geometric Design
Variation diminishing properties of Bernstein polynomials on triangles
Journal of Approximation Theory
Adaptive forward differencing for rendering curves and surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Algorithms for polynomials in Bernstein form
Computer Aided Geometric Design
Subdivision algorithms—recent results, some extensions and further developments
Algorithms for approximation
Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
Smooth mesh interpolation with cubic patches
Computer-Aided Design
Making the difference interpolation method for splines more stable
Journal of Computational and Applied Mathematics
On the stability of transformations between power and Bernstein polynomial forms
Computer Aided Geometric Design
Die Auswertung von Polznomen mehrerer Veränderlicher auf Punktrastern
Austrographics '88, Aktuelle Entwicklungen in der Graphischen Datenverarbeitung
Quadratic Bezier triangles as drawing primitives
HWWS '98 Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware
Localized-hierarchy surface splines (LeSS)
I3D '99 Proceedings of the 1999 symposium on Interactive 3D graphics
Evaluation algorithms for multivariate polynomials in Bernstein--Bézier form
Journal of Approximation Theory
Accurate evaluation algorithm for bivariate polynomial in Bernstein-Bézier form
Applied Numerical Mathematics
Bernstein-Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures
SIAM Journal on Scientific Computing
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Polynomials of the total degree d in m variables have a geometrically intuitive representation in the Bernstein-Be´zier form defined over an m-dimensional simplex. The two algorithms given in this article evaluate the Bernstein-Be´zier form on a large number of points corresponding to a regular partition of the simplicial domain. The first algorithm is an adaptation of isoparametric evaluation. The second is a subdivision algorithm. In contrast to de Casteljau's algorithm, both algorithms have a cost of evaluation per point that is linear in the degree regardless of the number of variables. To demonstrate practicality, implementations of both algorithms on a triangular domain are compared with generic implementations of six algorithms in the literature.