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Approximate B-Spline Surface

In one sentence: Fit a free-form NURBS surface to a point cloud or mesh with adjustable degree, control-point density, and smoothing.

Overview

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

The most capable approximation tool in the workbench. Constructs a NURBS surface of user-specified degree and control-point count that minimises the distance from the surface to all input points, with a smoothing weight to trade off accuracy against fairness. The result is a Part::Spline object.

Intuition

A B-spline surface is like a sheet of flexible plastic controlled by a grid of "handles" (control points). Pulling a handle bends the sheet; adding more handles gives finer control. Approximate B-Spline Surface places those handles automatically to make the sheet conform as closely as possible to your point cloud, while the smoothing parameter prevents the sheet from following every bit of noise.

When to use it

  • You have a complex freeform mesh (car body, consumer product, organic shape) that cannot be described by analytic primitives.
  • You want a single parametric NURBS surface for subsequent use in Part or Surface workbench tools.
  • You need precise control over the accuracy/smoothness trade-off.

When NOT to use it

  • Simple quadric regions — use Approximate Polynomial Surface for planes, cylinders, and spheres; it is simpler and faster.
  • Very large meshes with millions of faces — computation time grows with point count. Downsample the mesh first with Mesh workbench → Decimating.

Step-by-step

  1. Select a Points::Feature (cloud) or Mesh::Feature.
  2. Choose Reverse Engineering → Approximation → Approximate B-Spline Surface….
  3. In the task panel, set:
  4. U degree and V degree — start with 3 (cubic).
  5. U control points and V control points — start with 6×6; increase for more detail.
  6. Iterations — 3–5 for most cases.
  7. Smoothing — higher values give a fairer surface but less accuracy.
  8. Click OK. A Part::Spline is created.

Tip

Use the minimum control-point count that gives an acceptable visual result. Too many control points with low smoothing causes oscillation (Runge's phenomenon) — the surface ripples between data points.

Parameters

Parameter Type Default Description
U degree Integer 3 Polynomial degree in U direction. 3 (cubic) is standard; higher is rarely needed.
V degree Integer 3 Polynomial degree in V direction.
U control points Integer 6 Number of control points in U. More = finer detail.
V control points Integer 6 Number of control points in V.
Iterations Integer 3 Refinement iterations. More = closer to data.
Smoothing Float 0.1 Smoothing weight. 0 = pure fit; higher = fairer surface.
Continuity Enum C2 Internal NURBS continuity: C0, C1, C2.

Parameter guidelines

Goal Settings
Smooth result, small deviations acceptable High smoothing (0.5–1.0), moderate control points
Accurate fit, data is clean Low smoothing (0.01–0.1), moderate control points
Avoid oscillation Use degree 3, start with few control points and increase
Large region, complex shape Increase U and V control points incrementally

Common mistakes and pitfalls

Surface oscillates / ripples between data points

Cause: Too many control points with too little smoothing — the solver over-fits the data including noise.
Fix: Reduce control points or increase smoothing. Degree 3 cubic is almost always better than degree 5+ for mechanical parts.

Surface is too smooth and misses sharp features

Cause: Smoothing weight is too high.
Fix: Reduce smoothing weight. For sharp feature preservation, consider post-processing with CAD tools (Part → Fillet/Chamfer).

Python API

import ReverseEngineering as Reen
import FreeCAD as App

doc = App.ActiveDocument
pts = doc.getObject("ScanCloud")   # Points::Feature or Mesh::Feature

result = doc.addObject("Part::Spline", "BSurface")
result.Shape = Reen.approxSurface(
    Points=pts.Points,
    UDegree=3,
    VDegree=3,
    NbUPoles=6,
    NbVPoles=6,
    Iterations=3,
    Smoothing=0.1,
    Continuity="C2"   # TODO: verify exact parameter names
)
doc.recompute()

See also