Do you mean Pick's theorem?

https://en.wikipedia.org/wiki/Pick%27s_theorem

In order to determine the points on the

convex hull, use the QHull algorithm.

Regards,

Joachim

 Hello Joachim,

thanks for your answer.

I forgot to specify in my question that the algorithm should work for 3D point cloud and the boundary can have both convex and concave regions. The Pick's theorem only applies to 2D clouds and creates the convex hull that encloses all the points.

Useful information, anyway. Thanks. 

Look for the Alpha-Shape concept.  It is a kind of convex hull generalization able to handle "holes" in the point cloud.  The CGAL C++ computational geometry has a robust implementation of it for 2D and 3D.

http://cgm.cs.mcgill.ca/~godfried/teaching/projects97/belair/alpha.html

http://doc.cgal.org/latest/Alpha_shapes_2/index.html

http://doc.cgal.org/latest/Alpha_shapes_3/

Matlab solution

https://www.mathworks.com/help/matlab/ref/alphashape.html

R programming

https://rdrr.io/cran/alphashape3d/man/ashape3d.html

C++ PCL library

http://docs.pointclouds.org/trunk/classpcl_1_1_concave_hull.html

Hello, is this your paper 'Novel algorithms for 3D surface point cloud boundary detection and edge reconstruction' which can get the performance you shown? Thank you!

Hello Rebecca,

thanks for your comment.

Indeed, I had asked the question two years ago to make sure I was not duplicating anyone else's work and my research was original. This resulted in the work you mentioned getting published in February this year. Hope you found it useful. Let me know if you need further details about it.

Kind regards,

Carmelo

Hello Carmelo Mineo ,

Thanks for your contributions.

I concern your research very much. I want to find the boundary points of the surface (points cloud data in the attached picture). My search is to enhance the accuracy of tool path generation in CAM system for free-form surface. I read your paper "Novel algorithms for 3D surface point cloud boundary detection and edge reconstruction" . Do you publish the Matlab code of your algorithm ? I don't know about the time-consuming of your algorithm applied in complex surface (the example points data in the attached file).

Thank you so much!

Dear all,

Following my original question in 2017, I developed some work to tackle the problem of detecting boundary points on a point cloud, which maps a surface. As some of you have already noticed, my work is published in this paper:

Novel algorithms for 3D surface point cloud boundary detection and edge reconstruction (https://doi.org/10.1016/j.jcde.2018.02.001)

Moreover I have recently published a compiled version of the algorithm that can be used for your applications. Here is the link to the code:

https://doi.org/10.15129/cf16c681-7971-44b5-bf74-3f47dad1ba19

Than Trong Khanh Dat , I am very sorry I have noticed your post from September 2018 just now! I will give a try to apply my algorithm to your dataset and I will let you know how it goes. Apologies for my unforgivable delay.

Kind regards,

Carmelo

You can take a look at Alphashape.