Determine if a 2D point is within a quadrilateral?

Question

I'm working on a JS program which I need to have determine if points are within four corners in a coordinate system. Could somebody point me in the direction of an answer? I'm looking at what I think is called a convex quadrilateral. That is, four pretty randomly chosen corner positions with all angles smaller than 180°. Thanks.

Answer 1

Let your quadrilateral has 4 coordinates as V₁, V₂, V₃, and V₄. Also, let the given point be p = (x, y).

The trivial approach is to go around the polygon in order and for every pair of vertices V_i and V_i+1 (wrapping around to the first vertex if necessary), compute the quantity (x - x_i)⋅(y_i+1 - y_i) - (x_i+1 - x_i)⋅(y - y_i), where V_i = (x_i, y_i)

If these quantities all have the same sign, the point is inside the quadrilateral. The condition that they all have the same sign is the same as the condition that p is on the same side (left or right) of every edge.