Fast and Stable Evaluation of Box-splines via BB-form

level set of 6-directional tri-variate box-spline (click the image for animation)

level set of 7-directional tri-variate box-spline (click the image for animation)

isosurface of a quasi-interpolated spline generated by 6-directional tri-variate box-spline with input data on FCC (Face-Centered Cubic) lattice (click the image for animation)

Selected References

Giulio Casciola, Elena Franchini and Lucia Romani, The mixed directional difference-summation algorithm for generating the Bézier net of a trivariate four-direction Box-spline Numerical Algorithms, 43 2006 1 1017--1398
Charles K. Chui and Ming-Jun Lai, Algorithms for Generating B-nets and Graphically Displaying Spline Surfaces on Three- and Four- Directional Meshes Computer Aided Geometric Design 8 1991 6 479--493
Carl de Boor, On the evaluation of box splines Numerical Algorithms 5 1993 1--4 5--23
Leif Kobbelt, Stable evaluation of box-splines Numerical Algorithms 14 1997 4 377--382
Ming-Jun Lai, Fortran Subroutines for B-nets of Box Splines on Three- and Four-Directional Meshes Numerical Algorithms 2 1992 1 33--38

last updated 18 Nov. 2007, Minho Kim