How to build a best fit plane through a cloud of points

Question

Hello I have a lot of measured points and like to create a best fit plane through these points.Does Creo provide such an option?Many thanks in advance for your help.Regards Pius

StephenW · Accepted Answer

I do not know. I would suggest contacting your VAR or PTC to understand what license would be needed and if you have it.

A google search showed the following:

To access and use the Coordinate Measuring Machine (CMM) manufacturing module in Creo Parametric, you need the optional Pro/CMM extension license (historically and internally referred to as Pro/CMM or CMM Manufacturing). [1, 2, 3, 4]

License Details

Module Name: Pro/CMM (CMM Inspection Programming)

Function: Allows you to generate associative inspection and probing programs for CMM hardware directly from your 3D models.

Requirement Type: It is an add-on option/extension that must be explicitly added to your existing locked or floating license configuration (such as Creo Design Essentials or Advanced). [1, 2]

How to Check if You Have the License

Open Creo Parametric.

Go to File > Help > System Information.

Look at the information window under Configured Option Modules to see if CMM or Pro/CMM is listed.

If it is missing, you will need to contact your software administrator or PTC representative to add the extension to your license file. [1, 2, 3]

RPN · Answer

Assume you want to create a single plane through N points of measurement you can use Least Squares because a plane is parameterized by a single equation. The result is the best fit.

import numpy as np

# Your 10 points as a (10, 3) array
points = np.array([
    [x1, y1, z1],
    [x2, y2, z2],
    # ... 10 rows total
])

# 1. Compute centroid and center the points
centroid = points.mean(axis=0)
centered = points - centroid

# 2. SVD of the centered points
U, S, Vt = np.linalg.svd(centered)

# 3. Normal vector = last row of Vt (smallest singular value)
normal = Vt[-1]
a, b, c = normal
d = -normal.dot(centroid)

print(f"Plane: {a:.4f}x + {b:.4f}y + {c:.4f}z + {d:.4f} = 0")
print(f"Normal vector: {normal}")
print(f"Point on the plane (centroid): {centroid}")

# Optional: mean squared distance as a goodness-of-fit measure
distances = centered.dot(normal)
rmse = np.sqrt(np.mean(distances**2))
print(f"RMSE (orthogonal distance): {rmse:.6f}")

Code by Claude, not tested with the SVD-Instance

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