Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
Orthogonal polynomials on the hexagon
SIAM Journal on Applied Mathematics
On the numerical condition of polynomials in Berstein form
Computer Aided Geometric Design
Algorithms for polynomials in Bernstein form
Computer Aided Geometric Design
Chebyshev economization for parametric surfaces
Computer Aided Geometric Design
On multivariate orthogonal polynomials
SIAM Journal on Mathematical Analysis
Recurrence formulas for multivariate orthogonal polynomials
Mathematics of Computation
On the optimal stability of the Bernstein basis
Mathematics of Computation
Convergent inversion approximations for polynomials in Bernstein form
Computer Aided Geometric Design
Legendre-Bernstein basis transformations
Journal of Computational and Applied Mathematics - Special issue/Dedicated to Prof. Larry L. Schumaker on the occasion of his 60th birthday
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
On the Bernstein-Bézier form of Jacobi polynomials on a simplex
Journal of Approximation Theory
Connections between two-variable Bernstein and Jacobi polynomials on the triangle
Journal of Computational and Applied Mathematics
Jacobi polynomials in Bernstein form
Journal of Computational and Applied Mathematics - Special issue: Special functions in harmonic analysis and applications
Constrained degree reduction of polynomials in Bernstein-Bézier form over simplex domain
Journal of Computational and Applied Mathematics
Bivariate orthogonal polynomials on triangular domains
Mathematics and Computers in Simulation
Geometric applications of bivariate q-Bernstein and q-orthogonal polynomials
MATH'08 Proceedings of the American Conference on Applied Mathematics
Gauss-Lobatto to Bernstein polynomials transformation
Journal of Computational and Applied Mathematics
On the Bernstein--Bézier form of Jacobi polynomials on a simplex
Journal of Approximation Theory
A vertex-based hierarchical slope limiter for p-adaptive discontinuous Galerkin methods
Journal of Computational and Applied Mathematics
Approximate implicitization of triangular Bézier surfaces
Proceedings of the 26th Spring Conference on Computer Graphics
Legendre-like orthogonal basis for spline space
Computer-Aided Design
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A scheme for constructing orthogonal systems of bivariate polynomials in the Bernstein-Bézier form over triangular domains is formulated. The orthogonal basis functions have a hierarchical ordering by degree, facilitating computation of least-squares approximations of increasing degree (with permanence of coefficients) until the approximation error is subdued below a prescribed tolerance. The orthogonal polynomials reduce to the usual Legendre polynomials along one edge of the domain triangle, and within each fixed degree are characterized by vanishing Bernstein coefficients on successive rows parallel to that edge. Closed-form expressions and recursive algorithms for computing the Bernstein coefficients of these orthogonal bivariate polynomials are derived, and their application to surface smoothing problems is sketched. Finally, an extension of the scheme to the construction of orthogonal bases for polynomials over higher-dimensional simplexes is also presented.