Weak to strong: | (OR), ^ (XOR), & (AND), - (difference). + is the same as |. The result is always polygons, even if an operand was edges (those are turned into polygons first). An empty operand: AND/OR/XOR with empty is empty; A - empty is A; empty - A is empty. a & b connected / not_connected keeps only result pieces whose A-shape and B-shape sit on the same (connected) or a different (not_connected) geometric net of a|b (touch/overlap = one net).
Available · yields polygons
layer u = a | bGeometric union (OR). Overlap becomes one area. Alias a + b.
Also written as: a + b
Only a shared edge (no area): the union joins when the boolean engine splits that edge; a kiss at a single point is stitched by a later merged. A hole in A that B fills disappears. More than two layers: (a | b) | c. Chains of | associate to the left.
Available · yields polygons
layer i = a & bIntersection (AND). Only area that lies in A and B.
Kissing without area overlap (edge to edge, area 0): empty (area ≤ 0.5 dbu² does not count as overlap; AND may drop a degenerate sliver). A completely inside B: result = A (after boolean clean-up). Holes: intersecting a ring can inherit the hole or cut it open.
Available · yields polygons
layer d = a - bDifference: A without B. Can split A into several polygons or into a polygon with a hole.
B covers A completely: empty. B lies completely in A and does not touch the outline: A with a hole. B only on the edge of A: often unchanged A (no area subtracted).
Available · yields polygons
layer x = a ^ bXOR: area in exactly one of the two layers. Equivalent to (a - b) | (b - a).
Identical geometry: empty. Only the overlap region disappears; the two crescents stay separate polygons until a later merged.