Approximation by GP box-splines on a four-direction mesh

Authors:
Costanza Conti;Laura Gori;Francesca Pitolli;Paul Sablonnière
Affiliations:
Universití di Firenze, Italy;Universití di Roma La Sapienza, Italy;Universití di Roma La Sapienza, Italy;INSA de Rennes, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 4
Cited 2

Box splines

Box splines
The Discrete Cosine Transform

SIAM Review
Refinable functions and positive operators

Applied Numerical Mathematics - Special issue: Applied scientific computing - Grid generation, approximated solutions and visualization
Shape-preserving C1 Hermite interpolants generated by a Gori-Pitolli subdivision scheme

Journal of Computational and Applied Mathematics

Stationary and nonstationary affine combination of subdivision masks

Mathematics and Computers in Simulation
Scalar multivariate subdivision schemes and box splines

Computer Aided Geometric Design

Quantified Score

Hi-index	7.29

Visualization

Abstract

On a four-directional uniform mesh of the plane, we define and study C^0 Gori-Pitolli (abbreviated as GP) quadratics and C^1 GP quartics generated by integer translates of GP box-splines generalizing respectively the classical C^1 quadratic box-spline and one of the C^2 quartic box-splines. More specifically, we study the approximation of a bivariate function f by some quasi-interpolants and interpolants with values in these generalized spline spaces.