Skip to content

Minkowski Sum

In one sentence: Compute the Minkowski sum of the selected objects using OpenSCAD's CGAL engine — most commonly used to create rounded offsets of shapes.

Overview

Workbench: OpenSCAD
Menu: OpenSCAD → Minkowski Sum
Requires: OpenSCAD binary installed
Shortcut: none

Passes all selected objects to OpenSCAD as a minkowski() call and imports the result as a Part object. All inputs are hidden.

Intuition

The Minkowski sum of shape A and shape B is the set of all points you can reach by placing shape B at each point of shape A and taking the union. Practically:

  • Minkowski(solid, sphere of radius r) = the solid expanded uniformly by radius r in all directions, with perfectly rounded corners and edges.
  • Minkowski(shape, small cube) = the shape expanded with flat-corner offsets.

This is one of the most powerful morphological operations in computational geometry. It can create rounded offsets that are impossible with simple face offsetting.

When to use it

  • You need to expand a solid by a uniform radius with fully rounded convex corners (a "blob offset").
  • You are computing the swept volume of a tool or end-effector.
  • You need a Minkowski sum for CNC clearance analysis.

When NOT to use it

  • For simple face offsets — use Part → Offset 3D Surface, which is faster and produces B-rep output.
  • Without OpenSCAD installed — requires the OpenSCAD binary.
  • On complex shapes — Minkowski sum is computationally expensive; it can time out on high-polygon-count geometry.

Step-by-step

  1. Select two objects (typically the shape to expand and the structuring element, e.g. a small sphere).
  2. Choose OpenSCAD → Minkowski Sum.
  3. FreeCAD hides the inputs and creates a Part object with the result.

Common mistakes and pitfalls

Operation times out on complex geometry

Cause: The Minkowski sum algorithm is O(n × m) in the number of faces of both inputs. High-resolution meshes make this extremely slow.
Fix: Reduce mesh resolution before applying. Use Mesh workbench → Decimating to reduce polygon count first.

Python API

import FreeCADGui as Gui
Gui.doCommand("Gui.runCommand('OpenSCAD_Minkowski', 0)")

See also