Before revision:  The second variant, the multi-boundary resistar (or m-resistar) addresses this problem by defining several simplex stars in a cube or in its faces when necessary, which is shown to increase the local classification performance. With both s-resistars and m-resistars, classifying a point  requires only a small number  of simple tests without explicitly computing the simplices.
After revision:  The second variant, the approximation is defined in these simplices from the boundary points computed on their edges, with the same principle. Both the approximation in cubes and in simplices define a separating surface on the whole grid and classifying a point requires only a small number of simple tests without explicitly computing the simplices.