Below is an illustration: I have an OBB in an OBB (see below for OBB2D code if needed).

What I need to determine is, what face it is in, and what direction do I point the normal? The goal is to get the OBB out of the OBB so the normal needs to face outward of the OBB.

How could I go about: Finding what face the line is penetrating given the 4 corners of the OBB and the class below:

if we define dx=x2-x1 and dy=y2-y1, then the normals are (-dy, dx) and (dy, -dx). Which normal points outward of the OBB?

Thanks

public class OBB2D
{

    // Corners of the box, where 0 is the lower left.
   private  Vector2D corner[] = new Vector2D[4];

   private Vector2D center = new Vector2D();
   private Vector2D extents = new Vector2D();

   private RectF boundingRect = new RectF();
   private float angle;

    //Two edges of the box extended away from corner[0]. 
   private  Vector2D axis[] = new Vector2D[2];

   private double origin[] = new double[2];

   public OBB2D(Vector2D center, float w, float h, float angle)
    {
       set(center,w,h,angle);
    }

   public OBB2D(float left, float top, float width, float height)
    {
       set(new Vector2D(left + (width / 2), top + (height / 2)),width,height,0.0f);
   }

   public void set(Vector2D center,float w, float h,float angle)
   {
         Vector2D X = new Vector2D( (float)Math.cos(angle), (float)Math.sin(angle));
           Vector2D Y = new Vector2D((float)-Math.sin(angle), (float)Math.cos(angle));

           X = X.multiply( w / 2);
           Y = Y.multiply( h / 2);

           corner[0] = center.subtract(X).subtract(Y);
           corner[1] = center.add(X).subtract(Y);
           corner[2] = center.add(X).add(Y);
           corner[3] = center.subtract(X).add(Y);

           computeAxes();
           extents.x = w / 2;
           extents.y = h / 2;
           computeDimensions(center,angle);
   }

   private void computeDimensions(Vector2D center,float angle)
   {
       this.center.x = center.x;
       this.center.y = center.y;   
       this.angle = angle;

       boundingRect.left = Math.min(Math.min(corner[0].x, corner[3].x), Math.min(corner[1].x, corner[2].x));
       boundingRect.top = Math.min(Math.min(corner[0].y, corner[1].y),Math.min(corner[2].y, corner[3].y));
       boundingRect.right = Math.max(Math.max(corner[1].x, corner[2].x), Math.max(corner[0].x, corner[3].x));
       boundingRect.bottom = Math.max(Math.max(corner[2].y, corner[3].y),Math.max(corner[0].y, corner[1].y)); 
   }

   public void set(RectF rect)
   {
       set(new Vector2D(rect.centerX(),rect.centerY()),rect.width(),rect.height(),0.0f);
   }

    // Returns true if other overlaps one dimension of this.
    private boolean overlaps1Way(OBB2D other)
    {
        for (int a = 0; a < axis.length; ++a) {

            double t = other.corner[0].dot(axis[a]);

            // Find the extent of box 2 on axis a
            double tMin = t;
            double tMax = t;

            for (int c = 1; c < corner.length; ++c) {
                t = other.corner[c].dot(axis[a]);

                if (t < tMin) {
                    tMin = t;
                } else if (t > tMax) {
                    tMax = t;
                }
            }

            // We have to subtract off the origin

            // See if [tMin, tMax] intersects [0, 1]
            if ((tMin > 1 + origin[a]) || (tMax < origin[a])) {
                // There was no intersection along this dimension;
                // the boxes cannot possibly overlap.
                return false;
            }
        }

        // There was no dimension along which there is no intersection.
        // Therefore the boxes overlap.
        return true;
    }


    //Updates the axes after the corners move.  Assumes the
    //corners actually form a rectangle.
    private void computeAxes()
    {
        axis[0] = corner[1].subtract(corner[0]); 
        axis[1] = corner[3].subtract(corner[0]); 

        // Make the length of each axis 1/edge length so we know any
        // dot product must be less than 1 to fall within the edge.

        for (int a = 0; a < axis.length; ++a) {
            axis[a] = axis[a].divide((axis[a].length() * axis[a].length()));
            origin[a] = corner[0].dot(axis[a]);
        }
    }

    public void moveTo(Vector2D center) 
    {
        Vector2D centroid = (corner[0].add(corner[1]).add(corner[2]).add(corner[3])).divide(4.0f);

        Vector2D translation = center.subtract(centroid);

        for (int c = 0; c < 4; ++c)
        {
            corner[c] = corner[c].add(translation);
        }

        computeAxes();
        computeDimensions(center,angle);
    }

    // Returns true if the intersection of the boxes is non-empty.
    public boolean overlaps(OBB2D other)
    {
        if(right() < other.left())
        {
            return false;
        }

        if(bottom() < other.top())
        {
            return false;
        }

        if(left() > other.right())
        {
            return false;
        }

        if(top() > other.bottom())
        {
            return false;
        }


        if(other.getAngle() == 0.0f && getAngle() == 0.0f)
        {
            return true;
        }

        return overlaps1Way(other) && other.overlaps1Way(this);
    }

    public Vector2D getCenter()
    {
        return center;
    }

    public float getWidth()
    {
        return extents.x * 2;
    }

    public float getHeight() 
    {
        return extents.y * 2;
    }

    public void setAngle(float angle)
    {
        set(center,getWidth(),getHeight(),angle);
    }

    public float getAngle()
    {
        return angle;
    }

    public void setSize(float w,float h)
    {
        set(center,w,h,angle);
    }

    public float left()
    {
        return boundingRect.left;
    }

    public float right()
    {
        return boundingRect.right;
    }

    public float bottom()
    {
        return boundingRect.bottom;
    }

    public float top()
    {
        return boundingRect.top;
    }

    public RectF getBoundingRect()
    {
        return boundingRect;
    }

    public boolean overlaps(float left, float top, float right, float bottom)
    {
        if(right() < left)
        {
            return false;
        }

        if(bottom() < top)
        {
            return false;
        }

        if(left() > right)
        {
            return false;
        }

        if(top() > bottom)
        {
            return false;
        }

        return true;
    }

};