In general you can check if any Intersection exist between your two polygon (even non-convex) as below.

Problem: Given n line segments; Report all(as k in algorithms) Intersections.

You can implement any of these two algorithm in your desire language and use them. they take your line segments as input and return if any intersection ( Collision in your case) exists.

---

Solution 1: Sweep Algorithm (Bentley, Ottmann '79)

Time Complexity: O(n*lg(n)+k)

Space Complexity: O(n+k)

Pseudo Code:

ReportIntersections() { Initialize event queue EQ = all segment endpoints; Sort EQ by increasing x and y; Initialize sweep line SL to be empty; Initialize output intersection list IL to be empty; While (EQ is nonempty) { Let E = the next event from EQ; If (E is a left endpoint) { Let segE = E's segment; Add segE to SL; Let segA = the segment Above segE in SL; Let segB = the segment Below segE in SL; If (I = Intersect( segE with segA) exists) Insert I into EQ; If (I = Intersect( segE with segB) exists) Insert I into EQ; } Else If (E is a right endpoint) { Let segE = E's segment; Let segA = the segment Above segE in SL; Let segB = the segment Below segE in SL; Delete segE from SL; If (I = Intersect( segA with segB) exists) If (I is not in EQ already) Insert I into EQ; } Else { // E is an intersection event Add E’s intersect point to the output list IL; Let segE1 above segE2 be E's intersecting segments in SL; Swap their positions so that segE2 is now above segE1; Let segA = the segment above segE2 in SL; Let segB = the segment below segE1 in SL; If (I = Intersect(segE2 with segA) exists) If (I is not in EQ already) Insert I into EQ; If (I = Intersect(segE1 with segB) exists) If (I is not in EQ already) Insert I into EQ; } remove E from EQ; } return IL; } 

---

Solution 2: Divide & Conquer Algorithm (Balaban '95)

Complexity: O(n*lg(n)+k)

Space Complexity: O(n)