How much say a plate has at a sample, given how much farther it is than the nearest one and how wide the band's margin is.
One at the nearest plate, zero at the margin and past it, smooth in between. The compact support is what makes the sum finite, the continuity is what makes the whole scheme work, and the zero derivative at the far end is what lets a plate join the set without a crease. Nothing about it depends on which plate this is.
(1 − s)/(1 + s) rather than 1 − s, and the difference is the shape of a
continental margin. The plain complement blends too far into a plate's
interior: at half the margin it still gives its neighbor a third of the say,
where the two-plate blend this replaces gave a fifth. On Earth that is the
difference between a bimodal elevation histogram and a smeared one — Sarle's
coefficient reads 0.583 with this and 0.553 with the complement, against the
5/9 at which a distribution stops having two modes. This form is that
two-plate blend wherever only two plates are in range: the ratio it gives the
neighbor is (1 − s)/(1 + s), which is what mix(average, mine, s) was
spending all along. What the partition changes is the interior seams and the
triple junctions, and nothing else.
- excessnumber
- Undocumented
- widthnumber
- Undocumented