The Body Centered Cubic (BCC) and Face Centered Cubic (FCC) lattices have been known to outperform the commonly-used Cartesian sampling lattice due to their improved spectral sphere packing properties. However, the Cartesian lattice has been widely used for sampling of trivariate functions with applications in areas such as biomedical imaging, scientific data visualization and computer graphics...

The inter-image flow field is often modeled by some parametric warp function. Nearly all warps in the literature are based on a linear combination of control points, as for example the Free-Form Deformation (FFD) warp which uses the tensor-product of B-splines. It has been recently shown that the FFD warp models the affine projection of a deforming surface. This is also the case for all tensorp...

In this paper, we investigate the numerical simulation of rigid particulate flows using a new moving mesh method combined with the multigrid fictitious boundary method (FBM) [9, 10]. With this approach, the mesh is dynamically relocated through a special partial differential equation to capture the region near the surface of the moving particles with high accuracy. The complete system is realiz...

A framework for the construction of stable spectral methods on arbitrary domains with unstructured grids is presented. Although most of the developments are of a general nature, an emphasis is placed on schemes for the solution of partial differential equations defined on the tetrahedron. In the first part the question of well-behaved multivariate polynomial interpolation on the tetrahedron is ...

Quantum matrices A(R) are known for every R matrix obeying the Quantum Yang-Baxter Equations. It is also known that these act on ‘vectors’ given by the corresponding Zamalodchikov algebra. We develop this interpretation in detail, distinguishing between two forms of this algebra, V (R) (vectors) and V (R) (covectors). A(R) → V (R21)⊗V (R) is an algebra homomorphism (i.e. quantum matrices are re...

The preservation of surface shape is important in geometric modelling and approximation theory. In geometric modelling one would like to manipulate the shape of the surface being modelled by the simpler task of manipulating the control points. In scattered data approximation one might wish to approximate bivariate data sampled from a function with a shape property by a spline function sharing t...