Draw a plane over 3d point cloud and determine the 3d point above or below that plane ?

Dear sir/ Madam

I have a 3d pont cloud in which let N are the no of points. Every point has X, Y and Z coordinate.

I want to draw a plane over this 3d point cloud which intersects this point cloud.

Next step is to determine the indices of points which are lying below or above that plane.

Please help me.

Thanks

Answer 1

[Matt J]

I would start with this,

P=[X(:),Y(:),Z(:)];

p=mean(P,1);

[~,~,V]=svd( P-p,0);

planeNormal=V(:,end);

planeEquation=[planeNormal;-dot(planeNormal,p(:))];

[Arvind Kumar Pathak]

I have tried this code for attached point cloud.

P=[radius(:,1),radius(:,2),radius(:,3)];
p=mean(P,1)
[~,~,V]=svd( P-p,0);
planeNormal=V(:,end);
planeEquation=[planeNormal;-dot(planeNormal,p)];

I am getting this error

Error using  - 
Matrix dimensions must agree.

[~,~,V]=svd( P-p,0); %%%%(in this line)

[Matt J]

If you have a non-recent Matlab version, then you modify to

[~,~,V]=svd( bsxfun(@minus,P,p) , 0);

[Arvind Kumar Pathak]

Thanks it is working.

But how to see that plane over the point cloud.

and how to get points lying above or below that plane

[Matt J]

You can find an example here for plotting a plane fit. To determine whether points are "above" or "below", you would plug the points into the plane equation. If greater than the right hand side, the point lies on one side, and on the other side if less.

[Arvind Kumar Pathak]

Dear sir

Thanks for your help. I am new for matlab environment, but I have tried this one.

But I am not able to understand it completely

P=[radius(:,1),radius(:,2),radius(:,3)];
p=mean(P,1);
% [~,~,V]=svd(P-p,0);
[~,~,V]=svd( bsxfun(@minus,P,p) , 0);
planeNormal=V(:,end);
planeEquation=[planeNormal;-dot(planeNormal,p(:))];

hold on
[xx, yy]=meshgrid(0:0.1:1,0:0.1:1); % Generating a regular grid for plotting
zz = planeEquation(1,1) * xx + planeEquation(2,1) * yy + planeEquation(3,1);
surf(xx,yy,zz) % Plotting the surface

Please guide me

[Matt J]

Thanks for your help. I am new for matlab environment

Hardly. You have been using Matlab for at least a year and a half, according to your posting history.

However, I advise you to start with this change

zz = (planeEquation(1)*xx + planeEquation(2)*yy + planeEquation(4) )./(-planeEquation(3));