How to Plot Mathematical Functions in FreeCAD

This guide explains how to generate 2D and 3D mathematical function plots directly within FreeCAD. You will learn the two most effective methods: using the GUI-based Curves Workbench for parametric equations, and utilizing FreeCAD’s built-in Python console to programmatically generate precise curves and B-splines from custom mathematical formulas.

Method 1: Using the Curves Workbench (GUI Method)

The Curves Workbench provides a dedicated tool for plotting parametric equations without writing external code.

Step 1: Install the Curves Workbench

  1. Open FreeCAD.
  2. Navigate to Tools > Addon manager.
  3. In the Workbenches tab, search for Curves.
  4. Select it, click Install, and restart FreeCAD when prompted.

Step 2: Create a Parametric Curve

  1. Switch to the Curves workbench using the workbench dropdown menu.
  2. In the toolbar, click the Parametric Curve icon (a curve marked with a formula symbol).
  3. Select the created ParametricCurve object in the Model tree to inspect its Data properties in the Property View panel.
  4. Modify the properties to define your function:
    • Formula X: Enter the formula for the X coordinate as a function of parameter t (e.g., cos(t)).
    • Formula Y: Enter the formula for the Y coordinate as a function of parameter t (e.g., sin(t)).
    • Formula Z: Enter the formula for the Z coordinate (e.g., t * 0.1 for a helix, or 0 for a flat 2D plot).
    • Start: Set the minimum value for t (e.g., 0).
    • End: Set the maximum value for t (e.g., 6.28 for \(2\pi\)).
    • Number of points: Increase this value (e.g., 100 to 500) to improve curve smoothness.
  5. Press F5 or click the Recompute button to render the curve in the 3D viewport.

Method 2: Using the Python Console (Scripting Method)

For standard explicit functions (such as \(y = f(x)\)) or complex datasets, you can generate points using FreeCAD’s internal Python API and connect them with an interpolated B-spline.

Step 1: Open the Python Console

  1. Go to View > Panels.
  2. Ensure Python console is checked.

Step 2: Run the Plotting Script

Paste the following script into the console, adjusting the formula in the loop as needed:

import FreeCAD as App
import Part
import math

doc = App.activeDocument()
if not doc:
    doc = App.newDocument("MathPlot")

# Define plot bounds and resolution
x_start = -10.0
x_end = 10.0
steps = 200
step_size = (x_end - x_start) / steps

points = []
for i in range(steps + 1):
    x = x_start + i * step_size
    # Define your function here: y = f(x)
    # Example: y = sin(x) / x (Sinc function)
    y = math.sin(x) if x != 0 else 1.0
    z = 0.0
    points.append(App.Vector(x, y, z))

# Create an interpolated B-Spline curve through the generated points
curve = Part.BSplineCurve()
curve.interpolate(points)

# Create a Part feature in the document
plot_object = doc.addObject("Part::Feature", "FunctionPlot")
plot_object.Shape = curve.toShape()

doc.recompute()

Converting Plots to Usable 3D Geometry

Once your mathematical curve appears in the viewport:

  • Pad/Extrude: Switch to the Part Workbench and use the Extrude tool to turn a 2D plot into a flat sheet or wall.
  • Sweep: Create a small circular profile at one end of the curve in the Sketcher Workbench, then use the Part Sweep tool to create a solid wire, pipe, or spring along the function trajectory.