Preventing polygons from overlapping

Question

I'm creating a WPF application for Pixelsense where I have seven polygons. I am able to move them around using touch. Currently they overlap each other like image 1 below.

I want a shape (Shape A) to not overlap another shape (Shape B), instead it should snap into place (Shape A and Shape B end up being side by side or above and below each other) when brought near as shown below.

I have searched StackOverflow for similar problems, however, I was only able to find a few links related to checking if a point or mouse click is inside a shape. Not for complete shapes overlapping or regarding how to snap them in place.

Does anyone have any ideas regarding how I could do this? Any help will be much appreciated.

Answer 1

If we assume you use polygon, here some solutions to detect overlapping;

public static bool PointCollectionsOverlap_Slow(PointCollection area1, PointCollection area2)
{
    PathGeometry pathGeometry1 = GetPathGeometry(area1);
    PathGeometry pathGeometry2 = GetPathGeometry(area2);
    bool result = pathGeometry1.FillContainsWithDetail(pathGeometry2) != IntersectionDetail.Empty;
    return result;
}

public static PathGeometry GetPathGeometry(PointCollection polygonCorners)
{
    List<PathSegment> pathSegments = new List<PathSegment> { new PolyLineSegment(polygonCorners, true) };
    PathGeometry pathGeometry = new PathGeometry();
    pathGeometry.Figures.Add(new PathFigure(polygonCorners[0], pathSegments, true));
    return pathGeometry;
}

and a more faster one;

public static bool PointCollectionsOverlap_Fast(PointCollection area1, PointCollection area2)
{
    for (int i = 0; i < area1.Count; i++)
    {
        for (int j = 0; j < area2.Count; j++)
        {
            if (lineSegmentsIntersect(area1[i], area1[(i + 1) % area1.Count], area2[j], area2[(j + 1) % area2.Count]))
            {
                return true;
            }
        }
    }

    if (PointCollectionContainsPoint(area1, area2[0]) ||
        PointCollectionContainsPoint(area2, area1[0]))
    {
        return true;
    }

    return false;
}

public static bool PointCollectionContainsPoint(PointCollection area, Point point)
{
    Point start = new Point(-100, -100);
    int intersections = 0;

    for (int i = 0; i < area.Count; i++)
    {
        if (lineSegmentsIntersect(area[i], area[(i + 1) % area.Count], start, point))
        {
            intersections++;
        }
    }

    return (intersections % 2) == 1;
}

private static double determinant(Vector vector1, Vector vector2)
{
    return vector1.X * vector2.Y - vector1.Y * vector2.X;
}

private static bool lineSegmentsIntersect(Point _segment1_Start, Point _segment1_End, Point _segment2_Start, Point _segment2_End)
{
    double det = determinant(_segment1_End - _segment1_Start, _segment2_Start - _segment2_End);
    double t = determinant(_segment2_Start - _segment1_Start, _segment2_Start - _segment2_End) / det;
    double u = determinant(_segment1_End - _segment1_Start, _segment2_Start - _segment1_Start) / det;
    return (t >= 0) && (u >= 0) && (t <= 1) && (u <= 1);
}