From .stl to mathematical function. Is it possible?

I have a 3D object as a .stl file. I need its analytical definition ( = its mathematical function). I know importGeometry function, but its output argument is a DiscreteGeometry object and I need something more analytical like a real mathematical function. Can someone help me? Thanks

Answer 1

[Anton Semechko]

If the object is has a relatively simple geometry and you want to get a compact description of its shape, one of the following representations could work: superquadratic [1], hyperqurdaric [2], so-called "supershape" [3]. If the object isn't so simple, you can represent it in terms polynomial bases or radial basis functions. There is a vast number of other possibilities, however.

[1] Zhou & Kambhamettu, 2000, Extending superqudratics with exponent functions [2] Ohuchi & Saito, 2001, 3D shape modeling with extended hyperqudratics [3] Fougerolle et al., 2006, Rational supershapes for surface reconstruction

[Davide Bassano]

Dear Anton,

if I wanted to represent it in terms of polynomial bases or radial basis functions, how I could do? Do exist some MatLab functions and/or tools?

Thanks,

Davide

[Anton Semechko]

Here is one function I found on FEX:

https://www.mathworks.com/matlabcentral/fileexchange/44653-surface-reconstruction-using-implicit-polynomials

[Davide Bassano]

Thanks.

That function wants a triangular mesh as input. How do I get it from my 3D data set?

[Anton Semechko]

This function (also available from FEX) will generate a watertight triangular surface mesh from a 3D point cloud:

https://www.mathworks.com/matlabcentral/fileexchange/63730-surface-reconstruction-from-scattered-points-cloud