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Approximate Sphere

In one sentence: Fit a best-fit sphere to a mesh segment and create a Part::Sphere at the estimated centre and radius.

Overview

Workbench: Reverse Engineering
Menu: Reverse Engineering → Approximation → Sphere
Shortcut: none

Fits a sphere to the selected mesh using a least-squares algorithm. Creates a Part::Sphere placed at the fit centroid with the best-fit radius.

Intuition

Just as Approximate Plane finds the flattest surface through a cloud of points, Approximate Sphere finds the spherical surface that all the input points lie closest to. It computes the centre and radius of that sphere.

When to use it

  • You have a scan of a spherical joint, ball bearing, or ball-end feature and need its centre position and radius.
  • You want to measure the roundness deviation of a scanned sphere.
  • You need the sphere centre as a reference point for assembly alignment.

When NOT to use it

  • Hemispheres or partial spheres — the algorithm works best with more than half the sphere covered by the scan. Thin caps may produce unstable fits.
  • Non-spherical regions — isolate just the spherical segment first.

Step-by-step

  1. Isolate the spherical region using Mesh Segmentation.
  2. Select the spherical Mesh::Feature.
  3. Choose Reverse Engineering → Approximation → Sphere.
  4. FreeCAD creates a Part::Sphere.

Parameters

No task panel — the fit runs automatically.

Result properties

Property Description
Radius Best-fit sphere radius
Placement Centre of the fit sphere

Common mistakes and pitfalls

Sphere centred at wrong location

Cause: The scan covers less than a hemisphere — the under-constrained fit can produce an unstable centre estimate.
Fix: Ensure at least a hemisphere is included in the scan segment.

Python API

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

See also