In this contribution, a new algorithm is described. It basically follows the splitting box approach, but now bilinear interpolation on grid faces and trilinear interpolation on grid cubes are used. It turns out that the new approach is conceptionally easier to describe and to implement than the originial splitting box algorithm. Experimental investigations on diffferent data sets however showed that the data reduction is inferior compared with the splitting box algorithm. For an analysis of the causes an improvement of both algorithms is derived.
Further investigations show that the results of the splitting box algorithm are almost optimal.
The problem of deforming a given spatial shape is treated. Our solution warps the space surrounding the given shape with the effect of deforming the embedded shape, too, with a function derived with scattered data interpolation methods from the displacements of a finite set of control points that can be placed arbitrarily and adaptively. We present algorithms implementing this idea on parametric surfaces and rasterized volume data. In this work, deformation methods based on scattered data interpolation methods are developed. These allow the specification of deformations through arbitrary geometric constraints.