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| 1 | +import java.util.*; |
| 2 | + |
| 3 | +public class JarvisMarch { |
| 4 | + |
| 5 | + static class Point { |
| 6 | + private double x; |
| 7 | + private double y; |
| 8 | + |
| 9 | + public Point(double a, double b) { |
| 10 | + x = a; |
| 11 | + y = b; |
| 12 | + } |
| 13 | + |
| 14 | + public double getX() { |
| 15 | + return x; |
| 16 | + } |
| 17 | + public double getY() { |
| 18 | + return y; |
| 19 | + } |
| 20 | + |
| 21 | + public boolean equals(Point p) { |
| 22 | + if (p.getX() == x && p.getY() == y) { |
| 23 | + return true; |
| 24 | + } else { |
| 25 | + return false; |
| 26 | + } |
| 27 | + } |
| 28 | + public double magnitude() { |
| 29 | + return Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2)); |
| 30 | + } |
| 31 | + } |
| 32 | + |
| 33 | + //find the angle by creating two vectors and then using a property of dot products |
| 34 | + private static double angle(Point a, Point b, Point c) { |
| 35 | + Point ab = new Point(b.getX() - a.getX(), b.getY() - a.getY()); |
| 36 | + Point bc = new Point(c.getX() - b.getX(), c.getY() - b.getY()); |
| 37 | + return Math.acos(-1 * ((ab.getX() * bc.getX()) + (ab.getY() * bc.getY())) / |
| 38 | + (ab.magnitude() * bc.magnitude())); |
| 39 | + } |
| 40 | + |
| 41 | + public static ArrayList<Point> jarvisMarch(ArrayList<Point> arr) { |
| 42 | + ArrayList<Point> hull = new ArrayList<Point>(); |
| 43 | + Point pointOnHull = new Point(Double.MAX_VALUE, 0); |
| 44 | + |
| 45 | + //find leftmost point |
| 46 | + for (Point p: arr) { |
| 47 | + if (p.getX() < pointOnHull.getX()) { |
| 48 | + pointOnHull = p; |
| 49 | + } |
| 50 | + } |
| 51 | + hull.add(pointOnHull); |
| 52 | + |
| 53 | + //look for the rest of the points on the hull |
| 54 | + Point ref; |
| 55 | + while (true) { |
| 56 | + if (hull.size() == 1) { |
| 57 | + ref = new Point(pointOnHull.getX(), pointOnHull.getY() + 1); //finds a third point to use in calculating the angle |
| 58 | + } else { |
| 59 | + ref = hull.get(hull.size() - 2); |
| 60 | + } |
| 61 | + Point endpoint = arr.get(0); //initial canidate for next point in hull |
| 62 | + for (Point p: arr) { |
| 63 | + if (angle(p, pointOnHull, ref) > angle(endpoint, pointOnHull, ref)) { //found a point that makes a greater angle |
| 64 | + endpoint = p; |
| 65 | + } |
| 66 | + } |
| 67 | + pointOnHull = endpoint; |
| 68 | + if (pointOnHull.equals(hull.get(0))) { //add next point to hull if not equal to the leftmost point |
| 69 | + break; |
| 70 | + } else { |
| 71 | + hull.add(pointOnHull); |
| 72 | + } |
| 73 | + } |
| 74 | + return hull; |
| 75 | + } |
| 76 | + |
| 77 | + public static void main(String[] args) { |
| 78 | + |
| 79 | + //test array setup |
| 80 | + ArrayList<Point> gift = new ArrayList<Point>(); |
| 81 | + gift.add(new Point(-5, 2)); |
| 82 | + gift.add(new Point(5, 7)); |
| 83 | + gift.add(new Point(-6, -12)); |
| 84 | + gift.add(new Point(-14, -14)); |
| 85 | + gift.add(new Point(9, 9)); |
| 86 | + gift.add(new Point(-1, -1)); |
| 87 | + gift.add(new Point(-10, 11)); |
| 88 | + gift.add(new Point(-6, 15)); |
| 89 | + gift.add(new Point(-6, -8)); |
| 90 | + gift.add(new Point(15, -9)); |
| 91 | + gift.add(new Point(7, -7)); |
| 92 | + gift.add(new Point(-2, -9)); |
| 93 | + gift.add(new Point(6, -5)); |
| 94 | + gift.add(new Point(0, 14)); |
| 95 | + gift.add(new Point(2, 8)); |
| 96 | + |
| 97 | + //print initial array of points |
| 98 | + System.out.println("Gift:"); |
| 99 | + for (Point p: gift) { |
| 100 | + System.out.println("[" + p.getX() + ", " + p.getY() + "]"); |
| 101 | + } |
| 102 | + |
| 103 | + //find and print the array of points in the hull |
| 104 | + ArrayList<Point> hull = jarvisMarch(gift); |
| 105 | + System.out.println("Wrapping:"); |
| 106 | + for (Point p: hull) { |
| 107 | + System.out.println("[" + p.getX() + ", " + p.getY() + "]"); |
| 108 | + } |
| 109 | + } |
| 110 | + |
| 111 | +} |
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