Boolean operation

A Boolean operation combines two piles of shapes with and, or, and not, the way paper cutouts combine when they are stacked.

Derived layers are how rule decks think: “metal and not via hole,” “active or implant,” and “inside this outline.” You rarely type the algebra, but a checker does. The step is layer generation: two input sheets become a third. If you merge first, or fail to, the result changes. Overlap is not the same as union until you ask for union. A 0.3 micrometer enclosure ring can be “grow metal, then subtract the inner hole.” The work lives on one layer at a time, after you decide which shapes count. A hole is already a not in the interior of one polygon. A design-rule job that grows and shrinks edges is a neighbor of this idea. The output is still geometry. Running OR does not create a net; connectivity is a later story.

Left, two overlapping rectangles. Then their combined outline, the lens where they both exist, and one rectangle with a bite taken out.

Order matters. Grow then subtract is not subtract then grow. A 0.05 micrometer sliver can appear after a sequence that looked empty on screen. Run merge on inputs when the deck assumes clean outlines. Derived layers are temporary in a checker. If you save them into the stream, label them so nobody masks a derived sheet.

The three operations, the merge that feeds them, and the gap between overlap and union are covered in Boolean AND, OR, NOT, merging polygons, and overlapping is not merging.