Intersection of 3D solids，How?
It isn't clear what you are asking for.
According to the video you have three cylinders with the same radius and all three axis intersect in the same point.
Now you want to construct a single 3DSOLID that looks like the shaded result. Right?
I would start with three cylinders that are long enogh to intersect totally.
Then calculate the three bisecting planes between the axis (X,Y) / (X,Z) / (Y,Z) that run through the intersection point. Cut the cylinders at all three planes. Unite the remaining solids.
