Translate 3D coordinates on a known surface

Hi. I would like to know if there is a way to translate each 3D coordinate (blue dots) such that they lie on a known red surface.

Below is the code:

Nodes_XFix = load("Nodes_XFix.mat");
Nodes_XFix = Nodes_XFix.Nodes_XFix;
Faces_XFix = load("Faces_XFix.mat");
Faces_XFix = Faces_XFix.Faces_XFix;
coord_XMov = load("coord_XMov.mat");
coord_XMov = coord_XMov.coord_XMov;

figure
plot3(Nodes_XFix(:,1), Nodes_XFix(:,2), Nodes_XFix(:,3),'r.','Markersize',12)
hold on
trimesh(Faces_XFix(:,:),Nodes_XFix(:,1),Nodes_XFix(:,2),Nodes_XFix(:,3),'EdgeColor','r','Linewidth',1,'Facecolor','w')
plot3(coord_XMov(:,1), coord_XMov(:,2), coord_XMov(:,3),'b.','Markersize',12)
hold off
grid off
axis equal
xlabel('x')
ylabel('y')
zlabel('z')
view([15,50,30])

[Image Analyst]

I know I've told you this before but, if you have any more questions, then attach your data and code to read it in with the paperclip icon after you read this:

TUTORIAL: How to ask a question (on Answers) and get a fast answer

We'll check back later for your attached data and screenshots of your plot(s).

[Alberto Acri]

Sorry! I forgot to attach the files!

[Star Strider]

What do you want to do with them?

LD1 = load(websave('','https://www.mathworks.com/matlabcentral/answers/uploaded_files/1263470/Nodes_XFix.mat'));
Nodes_XFix = LD1.Nodes_XFix;
LD2 = load(websave('','https://www.mathworks.com/matlabcentral/answers/uploaded_files/1263465/Faces_XFix.mat'));
Faces_XFix = LD2.Faces_XFix;
LD3 = load(websave('','https://www.mathworks.com/matlabcentral/answers/uploaded_files/1263475/coord_XMov.mat'));
coord_XMov = LD3.coord_XMov;

figure
scatter3(Nodes_XFix(:,1), Nodes_XFix(:,2), Nodes_XFix(:,3), 50, 'r.', 'MarkerFaceAlpha',0.5)
hold on
trimesh(Faces_XFix(:,:),Nodes_XFix(:,1),Nodes_XFix(:,2),Nodes_XFix(:,3),'EdgeColor','r','Linewidth',1,'Facecolor','w')
plot3(coord_XMov(:,1), coord_XMov(:,2), coord_XMov(:,3),'b.','Markersize',12)
hold off
grid off
axis equal
xlabel('x')
ylabel('y')
zlabel('z')
view([15,50,30])

.

[Alberto Acri]

I would like the blue coordinates to be positioned on the red triangular surface.

[Matt J]

Hi. I would like to know if there is a way to translate each 3D coordinate (blue dots) such that they lie on a known red surface.

Do all the blue points have to translate as a single rigid body, or do they all translate independently of each other? If the latter, which point on the red surface should a blue point move to? The closest point?

[Alberto Acri]

Do all the blue points have to translate as a single rigid body, or do they all translate independently of each other?

Each blue dot must move independently of each other.

If the latter, which point on the red surface should a blue point move to? The closest point?

Yes, each blue dot must move across the red surface to the nearest point.

[Matt J]

In future, please consolidate your variables into a single .mat file, as I have done here. This reduces the amount of work needed for us to download and import all your variables.

Answer 1

[Matt J]

This FEX download seems to do what you want. I haven't used it myself, though.

https://www.mathworks.com/matlabcentral/fileexchange/52882-point2trimesh-distance-between-point-and-triangulated-surface

[Alberto Acri]

Hi! Thank you for your reply.

I tried using this code, but I am not sure if the input data is correct. Could you please check the code below?

Nodes_XFix = load("Nodes_XFix.mat");
Nodes_XFix = Nodes_XFix.Nodes_XFix;
Faces_XFix = load("Faces_XFix.mat");
Faces_XFix = Faces_XFix.Faces_XFix;
coord_XMov = load("coord_XMov.mat");
coord_XMov = coord_XMov.coord_XMov;

[faces2, vertices2] = point2trimesh(Faces_XFix, Nodes_XFix, 'QueryPoints', coord_XMov);

figure
plot3(Nodes_XFix(:,1), Nodes_XFix(:,2), Nodes_XFix(:,3),'r.','Markersize',12)
hold on
trimesh(Faces_XFix(:,:),Nodes_XFix(:,1),Nodes_XFix(:,2),Nodes_XFix(:,3),'EdgeColor','r','Linewidth',1,'Facecolor','w')
plot3(vertices2(:,1), vertices2(:,2), vertices2(:,3),'b.','Markersize',30)
hold off
grid off
axis equal
xlabel('x')
ylabel('y')
zlabel('z')
view([15,50,30])

because I am getting the following error:

Error using point2trimesh
Expected a string scalar or character vector for the parameter name.
Error in point2trimesh (line 127)
parser.parse(varargin{:});

[Matt J]

I think it should be,

[faces2, vertices2] = point2trimesh('Faces',Faces_XFix,...
                                   'Vertices',Nodes_XFix,...
                                   'QueryPoints', coord_XMov);

[Alberto Acri]

Yes it works!

I also tried with another dataset (closed surface) however it gives me the following "warning":

Warning: Some input points are not referenced by the triangulation. 

Do you have any idea how to solve it?

[Matt J]

I don't. Like I said, I've never used it before. It might help to see the complete warning message, though.

Answer 2

[Matt J]

[~,I]=pdist2( Nodes_XFix, coord_XMov,'euc','Smallest',1)


coord_XMov = Nodes_XFix(I,:);

[Alberto Acri]

Thank you for your reply @Matt J! I observed that each blue point moves to the nearest red point.

Is there a possibility to move the blue points also on the surface of the triangles (red mesh) and not only on the vertices ? See, for example, the green dots in the figure below:

[Matt J]

It's going to be a lot more computation. Are you sure you need a rigorous projection? Obviously as the mesh gets finer, the difference diminishes.