Algorithm for checking the complete inclusion of one polygon in another?

Question

Java

Good day! At the moment, he is concerned with finding an algorithm for checking the complete inclusion of one polygon in another. I'm interested in the fidelity of my idea:
- we check in pairs the intersections of the sides of the original polygon with the desired one. If at least 1 pair intersects, then the polygon does not lie entirely inside
+ perhaps there are ready-made implementations of the algorithm in java or at least close to it (so as not to some kind of clojure)?
Thanks in advance!

Answer 1

A polygon A lies completely inside a convex polygon B if and only if each of the vertices of A lies inside B.

Answer 2

nirvimel gave you the absolutely correct solution. And yours will not work if one polygon is completely outside the other.