On the numerical condition of polynomials in Berstein form
Computer Aided Geometric Design
Algorithms for polynomials in Bernstein form
Computer Aided Geometric Design
Degree reduction of Be´zier curves
Computer-Aided Design
Chebyshev economization for parametric surfaces
Computer Aided Geometric Design
The numerical problem of using Be´zier curves and surfaces in the power basis
Computer Aided Geometric Design
A generalized Ball curve and its recursive algorithm
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
On the stability of transformations between power and Bernstein polynomial forms
Computer Aided Geometric Design
Shape preserving properties of the generalised Ball basis
Computer Aided Geometric Design
Mathematica: a system for doing mathematics by computer (2nd ed.)
Mathematica: a system for doing mathematics by computer (2nd ed.)
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Degree reduction of Be´zier curves
Selected papers of the international symposium on Free-form curves and free-form surfaces
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Point and tangent computation of tensor product rational Be´zier surfaces
Computer Aided Geometric Design
Applications of the polynomial s-power basis in geometry processing
ACM Transactions on Graphics (TOG)
s-power series: an alternative to Poisson expansions for representing analytic functions
Computer Aided Geometric Design
ISTASC'04 Proceedings of the 4th WSEAS International Conference on Systems Theory and Scientific Computation
s-power series: an alternative to Poisson expansions for representing analytic functions
Computer Aided Geometric Design
Hermite approximation for free-form deformation of curves and surfaces
Computer-Aided Design
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A new polynomial basis over the unit interval t∈0,1 is proposed. The work is motivation by the fact that the monomial (power) form is not suitable in CAGD, as it suffers from serious numerical problems, and the monomial coefficients have no geometric meaning. The new form is the symmetric analogue of the power form, because it can be regarded as an “Hermite two-point expansion” instead of a Taylor expansion. This form enjoys good numerical properties and admits a Horner-like evaluation algorithm that is almost as fast as that of the power form. In a ddition, the symmetric power coeddicients convey a geometric meaning, and therefore they can be used as shape handles. A polynomial expressed in the symmetric power basis is decomposed into linear, cubic, quintic, and successive components. In consequence, this basis is better suited to handle polynomials of different degrees than the Bernstein basis, and those algorithms involving degree operations have extremely simple formulations. The minimum degree of a polynomial is immediately obtained by inspecting its coefficients. Degree reduction of a curve or surface reduces to drooping the desired high degree terms.