Approximate Plane¶

In one sentence: Fit a best-fit plane to any geometric object using least-squares minimisation and create a Part::Plane aligned to the result.

Overview¶

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

Computes the plane that minimises the sum of squared distances from all input points to the plane (PlaneFit algorithm). Creates a Part::Plane positioned and sized to the bounding extent of the input, oriented with its normal along the best-fit direction. The RMS residual is reported to the Report View.

Intuition¶

If you hold a flat piece of card against a bumpy surface, it will touch in some places and float above others. The best-fit plane is the position of that card that minimises the total gap, measured in a least-squares sense. The RMS value tells you how bumpy the surface actually is relative to that ideal flat card.

When to use it¶

You have a scan of a nominally flat face and want to create the reference plane that best represents it.
You need to measure the flatness of a scanned surface (RMS = flatness error).
You want to use the fit plane as a datum for other modelling operations.

When NOT to use it¶

When the surface is not planar — the RMS will be high and the plane will not be meaningful. Use Approximate B-Spline Surface for complex shapes.
When you need a specific datum plane (not best-fit) — use the Datum Plane tools in Part Design instead.

Step-by-step¶

Select one or more geometric objects (mesh, point cloud, or solid).
Choose Reverse Engineering → Approximation → Plane.
FreeCAD fits a plane to each selected object and creates a Part::Plane.
Check the Report View (View → Panels → Report View) for the RMS value:
```
RMS value for plane fit with N points: X.XXXX
```

Parameters¶

This tool has no task panel — it runs automatically on the selected objects.

Result properties¶

Property	Description
Position	Corner of the bounding rectangle on the fit plane
Length × Width	Extent of the input projected onto the plane
Normal	Best-fit normal direction

Common mistakes and pitfalls¶

Plane is in an unexpected orientation

Cause: The least-squares normal can have two valid orientations (pointing either way along the best-fit axis). FreeCAD picks one automatically.
Fix: If the plane needs to face a specific direction, flip its placement manually in the Properties panel.

High RMS value — surface is not planar

Cause: The selected region contains curved or non-planar geometry.
Fix: Use Mesh Segmentation to isolate the planar region before fitting, or check that you selected the right object.

Python API¶

import ReverseEngineering as Reen
import FreeCAD as App

doc = App.ActiveDocument
mesh = doc.getObject("FlatFaceSegment")

# Fit plane — result is printed to Report View
# The Part::Plane object is added to the document automatically via GUI command
import FreeCADGui as Gui
Gui.doCommand("Gui.runCommand('Reen_ApproxPlane', 0)")