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Approximate B-Spline Curve

In one sentence: Fit a B-spline curve to the points in a point cloud, producing a smooth parametric curve for use as a boundary or guide rail.

Overview

Workbench: Reverse Engineering
Menu: Reverse Engineering → Approximation → Approximate B-Spline Curve…
Shortcut: none

Projects all points in the selected Points::Feature onto their best-fit parametric axis (arc-length parameter), then fits a B-spline curve of specified degree and control-point count. Creates a Part::Feature containing the fitted curve. Supports open and closed curves.

Intuition

Imagine threading a smooth wire through a cloud of points so the wire passes as close as possible to each point. Approximate B-Spline Curve is that wire — it finds the smoothest curve consistent with the point data. The degree and number of control points control how flexible the wire is.

When to use it

  • You have a cross-section profile extracted from a scan and need a smooth curve from it for use in a Loft or Sweep.
  • You want to fit a guide rail curve to point data for use in the Surface workbench's Sections tool.
  • You need to approximate a scan silhouette as a B-spline for 2-D drawing.

When NOT to use it

Step-by-step

  1. Select a Points::Feature representing the curve data.
  2. Choose Reverse Engineering → Approximation → Approximate B-Spline Curve….
  3. In the task panel, set:
  4. Degree — 3 (cubic) is standard.
  5. Control points — more control points = tighter fit.
  6. Closed — check if the curve should form a loop.
  7. Click OK. A Part::Feature containing the B-spline curve is created.

Parameters

Parameter Type Default Description
Degree Integer 3 Polynomial degree. 3 (cubic) is standard.
Control points Integer 6 Number of control points. More = tighter fit to data.
Continuity Enum C2 Internal continuity: C0, C1, C2.
Closed Boolean false Whether the curve forms a closed loop.

Common mistakes and pitfalls

Curve overshoots at the ends

Cause: The end control points over-extrapolate beyond the data extent.
Fix: Reduce the degree or add more control points near the ends.

Closed curve has a kink at the join

Cause: The join continuity at the closure is C0 if the first and last control points don't satisfy the continuity condition.
Fix: Use C2 continuity and ensure the point cloud actually forms a smooth closed loop (the start and end points are close together).

Python API

import ReverseEngineering as Reen
import FreeCAD as App

doc = App.ActiveDocument
pts = doc.getObject("ProfileCloud")

result = doc.addObject("Part::Feature", "BSplineCurve")
result.Shape = Reen.approxCurve(
    Points=pts.Points,
    Degree=3,
    NbPoles=6,
    Continuity="C2",
    Closed=False   # TODO: verify exact API
)
doc.recompute()

See also