We demonstrate that non-separable box splines deployed on body centered cubic lattices (BCC) are suitable for fast evaluation on present graphics hardware. Therefore, we develop the linear and quintic box splines using a piecewise polynomial (pp)-form as opposed to their currently known basis (B)-form. The pp-form lends itself to efficient evaluation methods such as de Boor’s algorithm for spli...

Given A spline curves and A patch surfaces that are implicitly de ned on triangles and tetrahedra we determine their NURBS representations We provide a trimmed NURBS form for A spline curves and a parametric tensor product NURBS form for A patch surfaces We concentrate on cubic A patches providing a C continuous surface that interpolates a given triangulation together with surface normals at th...

Recently, the B-spline family of reconstruction filters has been generalized for the hexagonal lattice, which is optimal for sampling 2D circularly band-limited signals. In this paper, we extend this generalization to the body-centered cubic (BCC) lattice, which is optimal for sampling spherically band-limited 3D signals. We call the obtained new reconstruction filters BCC-splines. Although the...

We show how to combine, into one unified spline complex, C2 tensorproduct bi-cubic NURBS and G2 bi-cubic rational splines. The G2 splines are capable of exactly representing basic shapes such as (pieces of) quadrics and surfaces of revolution, including tori and cyclides. The main challenge is to bridge the differing continuity. We transform the G2 splines to splines that are C2 in homogeneous ...

The space of $C^1$ cubic Clough-Tocher splines is a classical finite element approximation over triangulations for solving partial differential equations. However, such there no B-spline basis available, which preferred choice in computer aided geometric design and isogeometric analysis. A locally supported that forms convex partition unity. In this paper, we explore several alternative spline ...