Box splines provide smooth spline spaces as shifts of a single generating function on a
lattice and so generalize tensor-product splines. Their elegant theory is laid out in classical …

B-splines are attractive basis functions for the continuous-domain representation of
biomedical images and volumes. In this paper, we prove that the extended family of box …

Abstract Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep
learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a …

Interpolation is a foundational concept in scientific computing and is at the heart of many
scientific visualization techniques. There is usually a tradeoff between the approximation …

We present a geometric framework for explicit derivation of multivariate sampling functions
(sinc) on multidimensional lattices. The approach leads to a generalization of the link …

We introduce a framework for construction of non-separable multivariate splines that are
geometrically tailored for general sampling lattices. Voronoi splines are B-spline-like …

In the literature on optimal regular volume sampling, the Body‐Centered Cubic (BCC) lattice
has been proven to be optimal for sampling spherically band‐limited signals above the …

We propose a new volume reconstruction technique based on the six-direction cubic box-
spline M 6. M 6 is C 1 continuous and possesses an approximation order of three, the same …

This paper presents an alternative box-spline filter for the body-centered cubic (BCC) lattice,
the seven-direction quartic box-spline M_7 that has the same approximation order as the …

This paper presents an efficient and accurate isosurface rendering algorithm for the natural
C1 splines on the face-centered cubic (FCC) lattice. Leveraging fast and accurate evaluation …