How do I find the volume between 2 point clouds?

I have 2 sets of non-uniform point cloud data from an experiment in the form of objs. One is from before an impact, the other is from after. I want to get the volume of the void space created by the impact, as well as the volume of sand now above the original surface. These two numbers should be about the same, but I still want to get them independently of each other as a check. I am having a huge amount of trouble getting those volumes.

I've tried a couple things, none of which worked. My next plan is to convert the point clouds to a gridded dataset and subtract those from each other. I'll sum all the positives and the negative values to get the void volume and the moved volume of sand.

Does anyone have a better idea?

[Image Analyst]

Not sure what you mean by volume since you forgot to attach any diagrams. Do you mean the convex hull like you'd get from convhull() (in 2-D) or convhulln() (if in 3-D)? It's kind of like if you put a rubber band or shrink wrap around your points. Is that what you mean?

numPoints = 20;
x = rand(1, numPoints)
y = rand(1, numPoints)
plot(x, y, 'b.', 'MarkerSize', 30);
hold on;
xlabel('x', 'FontSize',fontSize);
ylabel('y', 'FontSize',fontSize);
k = convhull(x, y)
% Plot convex hull
plot(x(k), y(k), 'r-', 'LineWidth', 3)
grid on;

[Joshua Knicely]

I've attached a figure to give some context. The red dots encapsulate my area of interest (not really important, just an FYI). The maroon line helps give some depth.

There's the empty space that's mostly blue; that's the void space of the crater.

Then there's the crater rim (in yellow); it's only really visible by looking at the curve in the magenta line. That volume above the originally flat surface is crater ejecta and I want to know that quantity.

convhull() sounds like it might do the job, but that involves parsing the points, which is a hassle I'd rather avoid (unless there's an easy way to do it).