Surface Flatness from sensor probing data

Hello,

I have the following probing data which I got through probing a 3d printer z-axis sensor. I plot the data on a surface and as can be seen that the surface is not flat, so I wanted to find from this data, the flatness of the surface. Does anyone have an Idea how can we find Surface flatness?

Note: Whenever we probe the printer it firstly does homing and set point 32 as home and then starts probing through all points and takes point 32 as a reference point.

Pos 0 1 2 3 4 5 6

0 -0.248 -0.138 -0.068 -0.028 -0.02 -0.048 -0.098

1 -0.222 -0.123 -0.062 -0.018 -0.018 -0.028 -0.078

2 -0.207 -0.11 -0.043 0.015 0.01 -0.01 -0.053

3 -0.25 -0.135 -0.068 -0.03 -0.02 -0.018 -0.083

4 -0.248 -0.162 -0.095 -0.053 -0.045 -0.043 -0.095

Answer 1

[Anurag]

Hi Hardikkumar,

I understand that you want to calculate the “straightness” of your surface, or in other words, how deviated is it from a ground truth plane. You could do it by defining a straight plane from any of a fixed coordinate and then checking for the deviation from each point or the best-fit plane.

Here are the following steps to do the same:

• Choose a reference plane. You mentioned that the point at (3, 2) is the reference point. You can consider this point as the reference plane's height.
• Calculate a best-fit plane for the entire surface. This plane should minimize the deviations from the measured points.
• You can use methods like linear regression or polynomial fitting to find the equation of the plane.
• For each point on the surface (excluding the reference point), calculate the vertical distance from the point to the best-fit plane.
• The deviation is the absolute difference between the measured height and the height predicted by the best-fit plane.
• To quantify the flatness, you can calculate statistics such as the maximum deviation, average deviation, or root mean square (RMS) deviation of all points.

Hope this helped.

Some relevant links:

• https://www.mathworks.com/help/matlab/data_analysis/linear-regression.html
• https://www.mathworks.com/help/matlab/math/polynomial-curve-fitting.html#:~:text=p%20%3D%20polyfit(x%2Cy,coordinates%20of%20the%20data%20points

Regards,

Anurag