Scope interpretation in Matlab

I have developed a code that takes a set of 3D coordinates and triangulates to generate a convex hull / Delaunay.

This went well and with Deluanay triangulation I can check if points are contained in a given volume using tsearchn.

Now I want to take two such 3D volumes and check if they overlap. Moreover, I would like to know what percentage of volume A is crossed by volume B.

I think I could create a gridded grid of dots that are in one of the volumes and then check them against the other using tsearchn. But I wanted to know if anyone knows a more convenient way. Or do you have recommendations for similar analyzes.

Many thanks!

EDIT ... Code example

For this example code, there shapeA

will be 50% overlap with shapeB

.
I have included a section at the end of the code that shows usability tsearchn


I know I could solve my problem by increasing the number of points for the shapes and testing them withtsearchn

% Establish shapes by coordinates
botA = [ 0 0 0 ; ...
   1 0 0;  ...
   1 1 0;  ...
   0 1 0 ];

topA = botA; topA(:,3) = 1; 
midA = [0.5 0.5 0.5];

botB = [ 0 0 0.5 ; ...
   1 0 0.5;  ...
   1 1 0.5;  ...
   0 1 0.5 ];

topB = botA; topB(:,3) = 1.5; 
midB = [0.5 0.5 1];

% Shape arrays
shapeA = [botA;midA;topA];
shapeB = [botB;midB;topB];

% Establish volume by using the delaunayn() function
dtA = delaunayn(shapeA);
dtB = delaunayn(shapeB);

% Plot the volume surfaces 
shapesurfA=tetramesh(dtA,shapeA);
set(shapesurfA,'FaceColor','b','FaceAlpha',.90,'EdgeAlpha',1);

hold on
shapesurfB=tetramesh(dtB,shapeB);
set(shapesurfB,'FaceColor','y','FaceAlpha',.90,'EdgeAlpha',1);
hold off
axis equal

%example of point in volume test
%if tsearchn output = NaN then testpoint is not in volume
testpoint1 = tsearchn(shapeA,dtA, [ 2 2 2]) % [test point [2 2 2] in volume A
testpoint2 = tsearchn(shapeA,dtA, [0.75 0.75 0.75])