Boolean Operation

Theory

Boolean operations originate from set theory and are applied in 3D modeling to combine solids. Union (A∪B) merges two bodies into one. Difference (A−B) subtracts B from A, creating a cavity or cutout. Intersection (A∩B) retains only the overlapping volume. These operations are fundamental to constructive solid geometry (CSG) and are the basis for most CAD feature modeling workflows.

Application

In FDM part design, boolean difference creates holes, pockets, and channels in a single operation. Boolean union joins separately modeled components into one printable body, eliminating internal interfaces that could cause slicing artefacts. Most CAD tools (Fusion 360, FreeCAD, OpenSCAD) expose these as core commands. OpenSCAD is entirely expression-based on CSG booleans.

Common mistakes

Boolean operations on mesh-based geometry (Blender, Meshmixer) can fail when meshes are non-manifold or have coincident (zero-thickness) faces. Always ensure both operands are watertight before attempting. In parametric CAD, boolean failures often indicate sketch under-constraint or overlapping references: check the feature tree history first.

Related terms: Manifold Geometry, Watertight Mesh, B-rep