ACM Transactions on Graphics (TOG)
The NURBS book
The symmetric analogue of the polynomial power basis
ACM Transactions on Graphics (TOG)
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
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
Hermite approximation for free-form deformation of curves and surfaces
Computer-Aided Design
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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-Bezier standard, can be pieced together in a smooth Hermitian spline and, in general, display better convergence.