Find a line with the highest density of points

Hi all,

I am working on a project where I have to find a square object on a patch3 object. This patch3 object is essentially a 3D mesh consisting of vertices, vertices and curvatures and I am looking for a square object on this patch3 object. I can clearly see the square when I plot my object with plot3, and I have the coordinates and curvature values of each vertex that has been used to create this patch3. The vertices that belongs to the square has higher curvature compared to other vertices, but this is not always the case. And, I know the dimensions of my square object in real life: 5 cm x 5cm.

I tried many ways to find this square object, and my current approach is to find the lower line of the square on the patch3 object.

I have an array consisting of x,y, z coordinates and the curvature value of the respective vertex. I want to find a line where the highest curvature values are dense (more than anywhere). Then I want to find the midline of this line which is essentially what I need from the square. How could I find the highest density of points which has high curvature values?

Thank you for your answers in advance.

Best, Gülce

[Jiri Hajek]

Hi, it's not really clear what is your question. Do you want to verify, whether a single patch object is a square (true/false)? Or you have a quad mesh and you want to check each face for shape quality?

[Gulce Lale]

Hi! I know for sure that in my patch3 object there is a square object and this object's vertices have higher curvature values than any place in the patch3 object. The square object on the patch consists of 4 lines, as a square would have in real life, and if I find a line on my patch3 object, then I can find the square. And since I know that the vertices forming the line have high density of points of high curvature. Therefore, I need to find the high density of points that could form a line.

I tried to find the pdist(x,y,z) between coordinates of vertices and sort them in ascending order to find the coodinates of highest density of points but I couldn't make it work because I don't know which distance corresponds to which points. Is there a way to keep that information?

highest_curvature_array = node(1:200,:) %take the first 200 highest curvature points (the node array (627x4) is already sorted in descending order)
xyz_array = node(:,1:3) %extract coordinates from the whole array (4th column is the curvature values)
distances = pdist(xyz) %gives an array of: 1x196251
sorted_distances = sort(unique(distances(:)), 'ascend');
shortest_distances = sorted_distances(1:100);

[Jiri Hajek]

I'm sorry, but this did not answer my questions... Further, it is equally not clear, what you mean by curvature, as in maths, curvature has a meaning for curves... So, you should try to reformulate your problem as clearly as possible.

[Gulce Lale]

none of your questions were defining my question, so I tried to elaborate on mine, sorry if it's still not clear.

curvature values are defined as it's defined in math. the patch3 function creates my data in 3D which uses curvature values to do that.

[Jiri Hajek]

OK, could you post a 3D plot, which you have mentioned in the original post? This could probably make it clear.

Also, you wanted to keep information about sort indices - this is possible using:

[B,I] = sort(___)

[Gulce Lale]

Unfortunately, I can't share the 3D plot since it is derived from confidential data. I appreciate your help anyways!

[Matt J]

@Gulce Lale: you do not need to rely on confidential data to provide an illustration. You could fabricate an example, preferably a small one.

Like @Jiri Hajek, I do not understand what is meant by the "curvature of a vertex", so you should also provide a reference to whatever online mathematical literature you think describes it.

Finally, the patch3 object that you are mention is not a native Matlab data type, so we have no clear picture what information that carries. You are saying you are plotting with plot3, but plot3 generates line objects as output, not patch objects, and Matlab's native patch object does not contain any properties describing "curvature".