SAT collision detection - handling parallel edges

Game Mechanics
#1

Hi
I have a problem with a collision detection method I have written. I use the separating axis theorem to detect collisions and the detection is working well.
The problem is that the minimum translation vector I get from the method is sometimes wrong if there are parallel edges in the polygons.

Parallel edges, although in opposite directions, give the same overlap distance, so it’s just a matter of chance if the returned vector will point in the right direction.

How would I go about to fix this?

My code:

	/**
	 * Checks to see it there is a collision between two convex polygons. 
	 * If there is a collision it returns a vector representing the minimal 
	 * translation necessary to move 'a' so that it is not overlapping 'b', 
	 * else a vector with x and y equal to 0.
	 * 
	 * The returned vector is pointing towards the first polygon 'a'.
	 * 
	 * Uses the separating axis theorem for convex polygons.
	 * 
	 * @param a The first polygon
	 * @param b The second polygon
	 * @return The minimum translation vector directed towards the first 
	 * polygon, or a Vector with (x,y)==(0,0) if there is no overlap.
	 */
	Vector getCollisionSAT(Polygon a, Polygon b) {

		ArrayList<Vector> aVerts = new ArrayList<Vector>(a.getVertices());
		ArrayList<Vector> bVerts = new ArrayList<Vector>(b.getVertices());
		
		ArrayList<Vector> normals = new ArrayList<Vector>();
		
		// Add normals of a to the list of normals
		for (int i = 0; i < aVerts.size(); i++) {	
			Vector p1, p2;
			
			p1 = aVerts.get(i);
			p2 = aVerts.get((i + 1 == aVerts.size()) ? 0 : i + 1);
			
			Vector normal = p2.subtract(p1).perpendicularCCW();
			normal = normal.normalize();
			
			normals.add(normal);
			
		}
		
		// Add normals of b to the list normals
		for (int i = 0; i < bVerts.size(); i++) {	
			Vector p1, p2;
			
			p1 = bVerts.get(i);
			p2 = bVerts.get((i + 1 == bVerts.size()) ? 0 : i + 1);
			
			Vector normal = p2.subtract(p1).perpendicularCW();
			normal = normal.normalize();
			
			normals.add(normal);
			
		}
		
		Vector minOverlapVector = null;
		double minOverlap = Double.MAX_VALUE;
		
		for (Vector normal : normals) {
			
			double aMin = aVerts.get(0).dotProduct(normal); // some value in the range
			double aMax = aMin;
			
			// Project each vertex of a onto the current normal and save the min and max value
			for (Vector v : aVerts) {
				double dot = v.dotProduct(normal);
				if (dot < aMin) {
					aMin = dot;
				}
				else if (dot > aMax) {
					aMax = dot;
				}
			}
			
			double bMin = bVerts.get(0).dotProduct(normal); // some value in the range
			double bMax = bMin;
			
			// Do the same for b
			for (Vector v : bVerts) {
				double dot = v.dotProduct(normal);
				if (dot < bMin) {
					bMin = dot;
				}
				if (dot > bMax) {
					bMax = dot;
				}
			}
			
			
			// Compare min and max values to see if there is an overlap
			if (aMin > bMax || bMin > aMax) {
				return new Vector(0,0); // no overlap - no collision
			}
			
			else {
				double overlap = Math.min(aMax - bMin, bMax - aMin); 
				if (overlap <= minOverlap) {
					minOverlap = overlap;
					minOverlapVector = normal.scalarMultiplication(overlap);
				}
			}	
		}
		
		return minOverlapVector;
		
	}
#2

I have solved the problem with the following code right before the “return minOverlapVector”.
It checks if the vector between the two polygons is pointing in the opposite direction from the translation vector and if so reverses it.
It’s a bit of a hack though, so if anyone has any insight on how to do it properly I would appreciate it.



		// The following is not optimal but is used to find the correct 
		// direction of minOverlapVector until a better solution is found.
		Vector aMidPoint = new Vector();
		Vector bMidPoint = new Vector();
		for ( Vector v : aVerts) {
			aMidPoint = aMidPoint.add(v);
		}
		for ( Vector v : bVerts) {
			bMidPoint = bMidPoint.add(v);
		}
		aMidPoint = aMidPoint.scalarDivision(aVerts.size());
		bMidPoint = bMidPoint.scalarDivision(bVerts.size());
		
		Vector ba = aMidPoint.subtract(bMidPoint);
		
		if (ba.dotProduct(minOverlapVector) < 0) {
			minOverlapVector = minOverlapVector.scalarMultiplication(-1);
			System.out.println("switch");
		}