Specify trimming curve in 3D space

[Andras Lasso]

Dear Onur,

Thank you very much for providing this awesome package. I could successfully use it for creating smooth, editable surface models of pediatric heart valve leaflets. While some leaflets can be represented well with a full spline surface, others would require trimming.

I have the trimming curve points specified in 3D, but geomdl.NURBS.Surface.trims require point coordinates to be in UV coordinates. I understand that in general it is a very hard problem to find closest surface point to a 3D position (invert "evaluate"), but I have a quite simple "Pringles" shape surface and the trimming points are very close to the surface, so most likely a simple iterative method could find the optimal UV coordinate.

Can you give any advice or example of how a "uv = find_closest_point_on_surface(xyz)" method could be implemented?

Thank you,

Andras Lasso

Senior Research Engineer

PerkLab, School of Computing

Queen's University, Kingston, ON, Canada

[Onur Bingol]

Hi Andras,

Some time ago, I received an email from a geomdl user who wanted to find uv from xyz (3D points on the surface or curve), and he had some success using SciPy's optimize.minimize (https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html). I am not sure how he implemented that (I don't have the code), I suppose he used the result of "evaluate_single" method somewhere in the optimization function.

I hope this helps a bit.

Thanks,

Onur

Onur R. Bingol, PhD

con...@onurbingol.net | https://onurbingol.net 

---- On Wed, 11 Nov 2020 13:04:43 -0800 Andras Lasso <andra...@gmail.com> wrote ----

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[Andras Lasso]

Hi Onur,

Thanks for your advice, based on that I was able implement surface trimming using a 3D curve (defined in xyz space). I used the code below to convert curve xyz points to uv points.

Andras

def dist(uv, surf, xyz):

    # surf.evaluate_single raises an exception if it get out of bounds values thereby

    # aborting the optimization, so we keep the optimizer away from invalid range by returning a large value

    # (probably a gradually increasing error function would be more appropriate, but this simple large value

    # seems to work well enough)

    if uv[0]<=0 or uv[0]>=1 or uv[1]<=0 or uv[1]>=1:

        return 1000

    return numpy.linalg.norm(surf.evaluate_single(uv)-xyz)

def uvFromXyz(surf, xyz):

    from scipy.optimize import minimize

    bounds = Bounds([0, 0], [1.0, 1.0])

    res = minimize(lambda uv, surf=surf, xyz=xyz: dist(uv, surf, xyz), np.array([0.5, 0.5]), method='nelder-mead')

    return res.x

[Onur Bingol]

Thanks for sharing the code, Andras!

Onur R. Bingol, PhD

con...@onurbingol.net | https://onurbingol.net 

---- On Tue, 12 Jan 2021 21:13:02 -0800 Andras Lasso <andra...@gmail.com> wrote ----

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