Specify limits to a plane's dimension, depending on data dimensions, so it exactly overlaps data

I am plotting a plane which should overlap with 3D data available. In certain cases (as shown below), the plane's dimension becomes too large. How can I specify the dimensions of the plane so that it more or less overlaps with my data and does not appear very huge?

Is it in the meshgrid function? What should the input be? This dimension should adapt to all my other (but similar) data.

I have attached the functions here .

This is how you can use the functions:

DisplayReconstructedScene( PointCloud3D, J1 ); hold on
load('n,V and p.mat')
[ n,V,p,x,y,z ] = Display_Plane(n, V, p);

Answer 1

[Thorsten]

Determine the minimum and maximum values of your data and then use patch to draw a plane below the data.

[Meghana Dinesh]

Could you please expand what you said..??

[Thorsten]

First you have to determine the extension of your point cloud in X,Y and Z. I assume that you can somehow compute xmin, xmax, ymin, ymax, zmin, zmax, such that all x-values fall between xmin, xmax etc.

Then you can plot a patch in 3D space by specifying the coordinates of its corners

 z = zmin - 0.1*(zmax-zmin); % 10% below smallest z-value
 col = [0.5 0.5 0.5]; % sample color of the plane
 patch([xmin xmax xmax xmin], [ymin ymin ymax ymax], [z z z z], col)

[Meghana Dinesh]

Right. I can compute the max and min for each of the three axes. What should I do with this patch? How can I plot a plane in 3D which overlaps with my data?

[Thorsten]

The patch function then plots the plane in 3D, that has the size of your data in x and y is is 10% below the smallest z value. I thought that something like this is what your're asking for.

[Meghana Dinesh]

Well, not really. All I want is to plot a plane with the given properties (normal vector, passing through the point "p"), etc (which is attached on dropbox). I am able to plot this plane as required. The only trivial point which I am seeking for help is to plot this plane such that it looks neat over my point cloud. In the figure I have displayed above, for example, the plane is very huge and exceeds the dimensions of point cloud data. I want it to have the same dimensions (or maybe a lil more) as the point cloud just so that it looks neat. And is aligned well. (in the displayed figure above, the plane is shifted to one corner).

First, please plot the point cloud. Look at the figure, the size of the 3 axes. When you plot the plane over this, the axes increase a lot. How can I trim the dimensions of this plane to overlap and be accommodated within the allocated space? I DO NOT want to change the properties of the plane.

I hope I am clear enough.