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dotCooCoo
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Auto Grouping compared the box of every traced path with the box of every path that can hold something, and with Overlapping it also compared each grouped path with every path below it. On a 1400 x 1400 px noise image traced with Limited 8, Overlapping (18,653 paths), parents() made 442,998,298 box tests and took 3.0 s in a release build. parents() now keeps the holders and, for stacked traces, the paths below in a grid of about one cell per path. A path's candidates are the holders in the cell of its box center, smallest first, and the paths below it come from the cells its box reaches. When a box reaches more cells or entries than there are paths below it, the old scan is used. The cells grow larger when the boxes would otherwise be listed in more than 32 cells each on average. The same trace now takes 142,289 box tests and 0.08 s, and every parent is the same as before. The 20,000-path limit is unchanged. The tests compare parents() with the pairwise version on rings, faces and noise traced Abutting and Overlapping, check that a dense trace takes at most 64 box tests per path while the pairwise version takes more, check that 300 nested discs take no more box tests than the pairwise version, and check that boxes covering the whole image make the cells larger.