How do we find the parametric equation of the best fit surface, to a Meshed surface(.stl file)? Thanks in advance

I have a .stl file, which has a meshed surface with triangular mesh elements. I need to find the parametric equation of the surface that best approximates(fits) the meshed surface.

Answer 1

[Rahul]

Hi @Rajdeep Pawar,

In order to obtain the parametric equation that fits your meshed surface, consider the following:

• Read the '.stl' file using 'stlread' function.
• Obtain the vertices from the obtained data of mesh elements using the '.Points' property.
• Use the 'fit' function with appropriate 'fitType' and 'fitOptions' based on your meshed surface. This would give you the required parametric equation.
• Another way to do this while vizualising would be to use the 'Curve Fitter App' and import X, Y, Z data from the workspace which is obtained from the mesh.

The following MATLAB Answers give good informatiuon regarding this:

https://www.mathworks.com/matlabcentral/answers/547119-how-to-get-equation-of-surface

https://www.mathworks.com/matlabcentral/answers/2162315-converting-an-stl-file-to-a-3d-surface-equation

The following MathWorks documentations can be referred:

'stlread': https://www.mathworks.com/help/matlab/ref/stlread.html

'fit': https://www.mathworks.com/help/curvefit/fit.html

'Curve Fitter App': https://www.mathworks.com/help/curvefit/curvefitter-app.html

'FIt Polynomial Models' (Curve Fitter App): https://www.mathworks.com/help/releases/R2025a/curvefit/polynomial.html

Thanks.