Booleans, and the mess they leave behind

What a boolean actually computes

Union, difference, intersection and exclusion are not shape tools. They are set operations on filled regions, and the program computes them the same way every time:

1. Find every point where the input paths intersect.
2. Split all paths at those points into segments.
3. Decide, for each segment, whether it lies on the boundary of the result.
4. Stitch the surviving segments into new closed paths.

Three consequences fall straight out of that, and they are the whole lesson.

One: every intersection becomes a node

Weld two circles and the result has the original anchors plus two new ones where the outlines crossed. Do six booleans in a row and the node count compounds. A mark that should be forty nodes arrives at three hundred, and it prints the same but cuts, stitches and enlarges badly.

Clean up after every boolean, not at the end:

• Delete nodes that sit on a straight run or in the middle of a smooth curve. Select them and press Ctrl+Delete in Illustrator (delete without breaking the path) or Ctrl+Delete in Inkscape (delete preserving shape).
• Look specifically at the new nodes at the old intersections. They almost always have handles the algorithm chose, not handles you would have chosen.
• Do not reach for Simplify. Simplify averages across the whole path and rounds off the corners you meant to keep. It is a last resort on traced artwork, not a cleanup for your own drawing.

Two: appearance is inherited, and the rule differs

Which object’s fill does the result take?

• Illustrator Pathfinder: the bottom object’s appearance for Unite, the top object’s for Intersect in some versions. This has changed across releases; test rather than trust.
• Inkscape: the bottom object’s style for Union and Difference.
• CorelDRAW Weld: the target object’s, where the target is whichever you selected last (or the bottom, if you used a marquee).

The practical habit: set the colour after the boolean, never before. You will stop losing five minutes a day to it.

Three: it is destructive, and the escapes are not equal

• Affinity Designer: hold Alt while clicking a boolean. You get a live compound whose children stay editable and movable, updating the result. This is the best implementation of the four.
• Illustrator: Alt+click a Pathfinder button makes a compound shape. Components remain editable until you press Expand. The Shape Builder tool (Shift+M) is different and better for fast work: drag across regions to merge, Alt+drag to delete a region, and you see the result as you go.
• CorelDRAW: the Shaping docker has Leave original: source / target checkboxes. Tick them and the inputs survive beside the result.
• Inkscape: no live booleans in the Path menu. The Boolean operation Live Path Effect (1.x) gets close, and otherwise you duplicate first (Ctrl+D) and stash the copy on a locked layer.

Make a layer called source, put an untouched copy of every input on it, and lock it. Thirty seconds now against an afternoon later.

Division is the underused one

Division (Illustrator’s Divide, Inkscape’s Cut Path / Division, CorelDRAW’s Simplify and Front Minus Back family) cuts every input into separate pieces along every intersection and keeps them all.

This is how you build a mark whose parts must line up exactly: draw the whole silhouette, draw the cutting lines across it, divide, then colour the pieces. The edges are shared by construction, so there is no hairline gap between them and no overlap. Trying to achieve the same result by drawing each piece separately is how you get the thin white line that shows on press.

The failure to watch for: self-intersection

A path that crosses itself, or two identical paths stacked exactly, makes the boolean solver’s job ambiguous. Symptoms: the operation does nothing, or produces a shape with a stray sliver, or produces zero-area artefacts you cannot see but a cutting plotter finds.

Before a boolean on anything traced or imported: run Union on the object with itself to clean overlaps, then check the node count. Inkscape’s Edit ▸ Select Same and the XML editor let you spot duplicate paths; Illustrator’s Document Info panel gives object counts.