Intersection of polygons

Question

There are two polygons given. how can one determine whether one polygon is inside, outside or intersecting the other polygon? Polygons can be Concave or convex.

Answer 1

Here is a simple algorithm to know if a given point is inside or outside a given polygon:

bool isInside(point a, polygon B)
{
    double angle = 0;
    for(int i = 0; i < B.nbVertices(); i++)
    {
        angle += angle(B[i],a,B[i+1]);
    }
    return (abs(angle) > pi);
}

• If a line segment of A intersects a line segment of B then the two polygons intersect each other.
• Else if all points of polygon A are inside polygon B, then A is inside B.
• Else if all points of polygon B are inside polygon A, then B is inside A.
• Else if all points of polygon A are outside polygon B, then A is outside B.
• Else the two polygons intersect each other.