ACM Transactions on Graphics (TOG)
The NURBS book
The symmetric analogue of the polynomial power basis
ACM Transactions on Graphics (TOG)
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Curve offsetting based on Legendre series
Computer Aided Geometric Design
Convergent inversion approximations for polynomials in Bernstein form
Computer Aided Geometric Design
Applications of the polynomial s-power basis in geometry processing
ACM Transactions on Graphics (TOG)
A subdivision scheme for Poisson curves and surfaces
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Degree elevation for generalized Poisson functions
Computer Aided Geometric Design
Mathematical Methods for Curves and Surfaces
Application of Legendre--Bernstein basis transformations to degree elevation and degree reduction
Computer Aided Geometric Design
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
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Morin and Goldman [Computer Aided Geometric Design 17 (2000) 813] have recently presented a remarkable new framework, based on employing Poisson series, for describing analytic functions in CAD. We compare this Poisson formulation with s-power series, modified Newton series that can be regarded as the two-point analogue of Taylor expansions. Such s-power series yield, over finite intervals, better approximations for CAD purposes, as they are polynomial and hence expressible in the Bernstein-Bézier standard, can be pieced together in a smooth Hermitian spline and, in general, display better convergence.