Symmetric box-splines on the An* lattice

Minho Kim, Jörg Peters

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Sampling and reconstruction of generic multivariate functions is more efficient on non-Cartesian root lattices, such as the BCC (Body-Centered Cubic) lattice, than on the Cartesian lattice. We introduce a new n×n generator matrix A* that enables, in n variables, efficient reconstruction on the non-Cartesian root lattice An* by a symmetric box-spline family Mr*. A2* is the hexagonal lattice and A3* is the BCC lattice. We point out the similarities and differences of Mr* with respect to the popular Cartesian-shifted box-spline family Mr, document the main properties of Mr* and the partition induced by its knot planes and construct, in n variables, the optimal quasi-interpolant of M2*.

Original languageEnglish
Pages (from-to)1607-1630
Number of pages24
JournalJournal of Approximation Theory
Issue number9
StatePublished - Sep 2010


Dive into the research topics of 'Symmetric box-splines on the An* lattice'. Together they form a unique fingerprint.

Cite this