Find intersection between two data sets

Question

I am generating two arrays similar to this:

[x,y,z] = sphere;
A=[x,y,z]
B=[x+0.5,y+0.5,z+0.5]

The second array is at an offset to the first.

I would like to find the intersection space of both of these arrays A and B.

I have used the sphere function in this case but can this be done for any two data arrays not necessarily spherical. Is there a way to do this?

I am including an image for what I am looking for. I want to find the intersection between these two areas. But the values are not necessarily going to be the same as you can see.

If I have an equation for the limits of each of the spaces, would that make the problem easier?

Answer 1

I stated in the comments that one could use convhull and inpolygon to solve this problem, only inpolygon doesn't seem to apply to 3D polygons. We'll use delaunayTriangulation and pointLocation in order to get to the result

Full code :

[x,y,z] = sphere;
A=[x(:),y(:),z(:)];
B=[x(:)+0.5,y(:)+0.5,z(:)+0.5];

tess1=delaunayTriangulation(A); % delaunay Triangulation of points set A
tess2=delaunayTriangulation(B); % delaunay Triangulation of points set B

Tmp=[A;B];

% Point location searches for the triangles in the given delaunay     
% triangulation that contain the points specified in Tmp, here Tmp is 
% the reunion of sets A and B and we check for both triangulations
ids1=~isnan(pointLocation(tess1,Tmp));
ids2=~isnan(pointLocation(tess2,Tmp));

% ids1&ids2 is a logical array indicating which points
% in Tmp are in the intersection
IntersectPoints=Tmp(ids1&ids2,:);


plot3(A(:,1),A(:,2),A(:,3),'+b'); hold on
plot3(B(:,1),B(:,2),B(:,3),'+g');
plot3(IntersectPoints(:,1),IntersectPoints(:,2),IntersectPoints(:,3),'*r')

Output :

EDIT - A 2D example :

[x,y,z] = sphere;
A=[x(:),y(:)];
B=[x(:)+0.5,y(:)+0.5];

tess1=delaunayTriangulation(A); % delaunay Triangulation of points set A
tess2=delaunayTriangulation(B); % delaunay Triangulation of points set B

Tmp=[A;B];

% Point location searches for the triangles in the given delaunay     
% triangulation that contain the points specified in Tmp, here Tmp is 
% the reunion of sets A and B and we check for both triangulations
ids1=~isnan(pointLocation(tess1,Tmp));
ids2=~isnan(pointLocation(tess2,Tmp));

% ids1&ids2 is a logical array indicating which points
% in Tmp are in the intersection
IntersectPoints=Tmp(ids1&ids2,:);


plot(A(:,1),A(:,2),'+b'); hold on
plot(B(:,1),B(:,2),'+g');
plot(IntersectPoints(:,1),IntersectPoints(:,2),'*r');

Output :

Edit 2 :

If you want your code to adapt to either 2D or 3D arrays automatically, you just really need to modify the plot calls. Just write an if statement that will check the number of columns in A and B