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Where a line lies under the outline of a closed path in front of it (such as a shape an earlier merge made, which takes the place of the art in front of the lines), the planar map gave that stretch only to the closed path, so the line had no piece there. A merge or an erase across it left the line whole, and the next map split the new shape along it into two regions. - pathops: each planar edge records every input it lies on, and BuilderArrangement::lines_under holds the lines' pieces under a closed outline in front of them. lines, edges and Live Paint are unchanged. - tools: BuilderMap adds those pieces to its lines, so a merge or an erase removes the stretch between the regions it takes, as it does elsewhere. An Alt-click where a line lies under an edge hits the one in front.