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Boolean XOR

In one sentence: Keep only the material that is in one shape but not both — the symmetric difference — discarding the shared overlapping region.

Overview

Workbench: Part
Menu: Part → Split → Boolean XOR
Shortcut: none

Computes the symmetric difference of two shapes: keeps only the material that belongs exclusively to one shape or the other, and removes the region where they overlap. XOR = Fuse − Common.

Intuition

Think of a Venn diagram: Boolean Fuse is both circles; Boolean Common is only the overlap; Boolean XOR is both circles with the overlap cut out — just the unique parts of each.

Use XOR to isolate the engagement region between two mating parts, or to visualise the material that would be removed or added to make one design match another.

When to use it

  • Cutting out the engagement region between two mating parts to see what interferences exist.
  • Visualising the non-overlapping material when checking part fits for assembly.
  • Generating the "difference region" for tolerance analysis or design comparison.
  • Removing the common material from two overlapping decorative elements.

When NOT to use it

  • Don't use it when shapes don't overlap — XOR of non-overlapping shapes is equivalent to Fuse, which is rarely what you want from XOR semantics.
  • Don't use it when you want to keep the overlap — use Boolean Common to extract only the shared region.

Step-by-step

  1. Select the first shape.
  2. Ctrl+click the second shape.
  3. Choose Part → Split → Boolean XOR.
  4. A compound appears with the two non-overlapping fragments.

Parameters

Parameter Description
Objects The two shapes to compute XOR on

Common mistakes and pitfalls

Non-overlapping shapes produce a Fuse equivalent

When two shapes do not share any volume, XOR returns both shapes unchanged (same result as Fuse). This is mathematically correct but rarely useful. Verify the shapes actually overlap before using this tool.

Result is a compound of two fragments

The output is a compound containing the two exclusive regions. Use Part → Explode Compound to work with them independently.

XOR of identical shapes is empty

If both shapes are identical, the XOR result has zero volume (all material is in the "common" region that gets removed). This is correct behaviour.

Python API

import FreeCAD as App
import BOPTools.SplitFeatures as SF

doc = App.newDocument()

s1 = doc.addObject("Part::Box", "Shape1")
s1.Length = 20; s1.Width = 20; s1.Height = 20

s2 = doc.addObject("Part::Box", "Shape2")
s2.Length = 20; s2.Width = 20; s2.Height = 20
s2.Placement = App.Placement(App.Vector(10, 0, 0), App.Rotation())
doc.recompute()

xor = SF.makeXOR(name="XOR")
xor.Objects = [s1, s2]
xor.Proxy.execute(xor)
doc.recompute()

print(f"XOR result solids: {len(xor.Shape.Solids)}")   # 2

See also