Question

I have an array of points, as well as two more points (A and B). The last two points form a line, and I’m trying to find which of the points in my array are furthest from the line. How would I do this in Java?

I’m wondering if it’s something along the lines of finding the distance from A and B, but that doesn’t sit well in my head.

Additional info:
I think it’s a line segment. Given this is QuickHull, I don’t know if it makes a difference.
I’ve never been the greatest when it comes to math and formulas, so more explanation is better. Thanks!

Answer 1

Note that each 3 points [a,b,p] for each p in the array form a trianle, whose area is denoted by: (ab) * h /2 [where h is the distance from p to ab]

You can compute the area these trianles create, and select the minimal. Since ab is constant for all – it guarantees that the trianle with the minimal area will also have the minimal h.

You can find it [the area of each triangle] using

T=(1/2)* abs((x_a - x_p) * (y_b-y_a) - (x_a - x_b)* (y_p - y_a))

[where x_a,x_b,x_p and y_a,y_b,y_p are the x,y coordinates of a,b,p respectively].

• Though I find this method very elegant, I believe there are better
  ways to do it.