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

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Rajdeep Pawar 2020-11-5

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回答： Rahul 2025-5-14

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.

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Answer 1

Rahul 2025-5-14

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https://ww2.mathworks.cn/matlabcentral/answers/637105-how-do-we-find-the-parametric-equation-of-the-best-fit-surface-to-a-meshed-surface-stl-file-than#answer_1565183

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.