The reason why this algorithm might not have a name is because there are a lot of cases it isn't able to handle. For example this one:
The shapes are clearly overlapping, but shape A can move around quite a lot without any of the movement paths of its vertices ever intersecting with any of the edges of B.
It is in fact even able for A to completely pass ...
Can't write a comment, so I will give you my pointers.
You should not apply that script to every object, you're basically destroying both the sword and the fruits. I think you should only place your script in the sword and only destroy the collided object. Thus, your script will change to the following :
void OnTriggerEnter(Collider other)
This is much simpler than it seems. Unity has functionality built in for this.
theButton.alphaHitTestMinimumThreshold = 0.5f;
What this does is only register hits from the raycast if the pixel hit has an alpha of 0.5 or greater.