programming-examples/java/Computational_Geometry_Problems/Java Program to Implement Quick Hull Algorithm to Find Convex Hull.java

/*This is a Java Program to implement Quick Hull Algorithm to find convex hull. Here we’ll talk about the Quick Hull algorithm, which is one of the easiest to implement and has a reasonable expected running time of O(n log n).*/

import java.util.ArrayList;
import java.util.Scanner;

public class QuickHull
{
    public ArrayList<Point> quickHull(ArrayList<Point> points)
    {
        ArrayList<Point> convexHull = new ArrayList<Point>();
        if (points.size() < 3)
            return (ArrayList) points.clone();
        int minPoint = -1, maxPoint = -1;
        int minX = Integer.MAX_VALUE;
        int maxX = Integer.MIN_VALUE;
        for (int i = 0; i < points.size(); i++)
            {
                if (points.get(i).x < minX)
                    {
                        minX = points.get(i).x;
                        minPoint = i;
                    }
                if (points.get(i).x > maxX)
                    {
                        maxX = points.get(i).x;
                        maxPoint = i;
                    }
            }
        Point A = points.get(minPoint);
        Point B = points.get(maxPoint);
        convexHull.add(A);
        convexHull.add(B);
        points.remove(A);
        points.remove(B);
        ArrayList<Point> leftSet = new ArrayList<Point>();
        ArrayList<Point> rightSet = new ArrayList<Point>();
        for (int i = 0; i < points.size(); i++)
            {
                Point p = points.get(i);
                if (pointLocation(A, B, p) == -1)
                    leftSet.add(p);
                else if (pointLocation(A, B, p) == 1)
                    rightSet.add(p);
            }
        hullSet(A, B, rightSet, convexHull);
        hullSet(B, A, leftSet, convexHull);
        return convexHull;
    }

    public int distance(Point A, Point B, Point C)
    {
        int ABx = B.x - A.x;
        int ABy = B.y - A.y;
        int num = ABx * (A.y - C.y) - ABy * (A.x - C.x);
        if (num < 0)
            num = -num;
        return num;
    }

    public void hullSet(Point A, Point B, ArrayList<Point> set,
                        ArrayList<Point> hull)
    {
        int insertPosition = hull.indexOf(B);
        if (set.size() == 0)
            return;
        if (set.size() == 1)
            {
                Point p = set.get(0);
                set.remove(p);
                hull.add(insertPosition, p);
                return;
            }
        int dist = Integer.MIN_VALUE;
        int furthestPoint = -1;
        for (int i = 0; i < set.size(); i++)
            {
                Point p = set.get(i);
                int distance = distance(A, B, p);
                if (distance > dist)
                    {
                        dist = distance;
                        furthestPoint = i;
                    }
            }
        Point P = set.get(furthestPoint);
        set.remove(furthestPoint);
        hull.add(insertPosition, P);
        // Determine who's to the left of AP
        ArrayList<Point> leftSetAP = new ArrayList<Point>();
        for (int i = 0; i < set.size(); i++)
            {
                Point M = set.get(i);
                if (pointLocation(A, P, M) == 1)
                    {
                        leftSetAP.add(M);
                    }
            }
        // Determine who's to the left of PB
        ArrayList<Point> leftSetPB = new ArrayList<Point>();
        for (int i = 0; i < set.size(); i++)
            {
                Point M = set.get(i);
                if (pointLocation(P, B, M) == 1)
                    {
                        leftSetPB.add(M);
                    }
            }
        hullSet(A, P, leftSetAP, hull);
        hullSet(P, B, leftSetPB, hull);
    }

    public int pointLocation(Point A, Point B, Point P)
    {
        int cp1 = (B.x - A.x) * (P.y - A.y) - (B.y - A.y) * (P.x - A.x);
        if (cp1 > 0)
            return 1;
        else if (cp1 == 0)
            return 0;
        else
            return -1;
    }

    public static void main(String args[])
    {
        System.out.println("Quick Hull Test");
        Scanner sc = new Scanner(System.in);
        System.out.println("Enter the number of points");
        int N = sc.nextInt();
        ArrayList<Point> points = new ArrayList<Point>();
        System.out.println("Enter the coordinates of each points: <x> <y>");
        for (int i = 0; i < N; i++)
            {
                int x = sc.nextInt();
                int y = sc.nextInt();
                Point e = new Point(x, y);
                points.add(i, e);
            }
        QuickHull qh = new QuickHull();
        ArrayList<Point> p = qh.quickHull(points);
        System.out
        .println("The points in the Convex hull using Quick Hull are: ");
        for (int i = 0; i < p.size(); i++)
            System.out.println("(" + p.get(i).x + ", " + p.get(i).y + ")");
        sc.close();
    }
}

/*
Quick Hull Test
Enter the number of points
4
Enter the coordinates of each points: <x> <y>
12 32
45 98
65 12
10 30
The points in the Convex hull using Quick Hull are:
(10, 30)
(45, 98)
(65, 12)