If the intersection is on center and at 90 to the target tube you will get an "oval" shape. Otherwise, you get all sorts of other shapes. Like the following:
This is from a program I wrote about a hundred years ago or so. Notice that there are TWO intersections, one on the outside and one on the inside. If he is inserting a tube then welding he may actually need the INSIDE intersection, not the outer. Here is why:
BTW, the program was for rotary axis cutting on a laser. Normally a LOT more segments are generated, but I cut it down so we could see what is going on.
Low Profile CNC Router Vise