I posted the below on StackOverflow but was directed here as this may be more mathematical problem but I was looking to implement an algorithm....
I have a discrete set of points.
From this set of point I need to find the 4 points that make up a Quadrilateral with the largest area.
To begin I have already used a Gift Wrapping algorithm to establish the points that make up the convex hull as the 4 points of the Quad will be on the hull.
I am now looking at what would be the best way to establish if the convex hull consists of more than 4 points how to narrow this down to only 4 points that make up that Quad.
I can only think of a brute force method of checking the area or perimeter of each combination of 4 points to then pick up the set with the largest but as the number of points on the convex hull is not predetermined I want to hopefully find a more efficient method.
I don't mind using brute force but was hoping someone could think up something a little more elegant to implement.
Found this entry:
to produce list of all quadrilaterals that I can use to test the area.