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1 | 1 | package ch_22; |
2 | 2 |
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| 3 | +import javafx.geometry.Point2D; |
| 4 | + |
| 5 | +import java.util.ArrayList; |
| 6 | +import java.util.Arrays; |
| 7 | +import java.util.List; |
| 8 | +import java.util.Scanner; |
| 9 | +import java.util.stream.Collectors; |
| 10 | + |
3 | 11 | /** |
4 | 12 | * **22.9 (Geometry: gift-wrapping algorithm for finding a convex hull) Section 22.10.1 |
5 | 13 | * introduced the gift-wrapping algorithm for finding a convex hull for a set of |
6 | | - * points. Assume that the Java’s coordinate system is used for the points. Implement the algorithm using the following method: |
| 14 | + * points. Assume that the Java’s coordinate system is used for the points. |
| 15 | + * Implement the algorithm using the following method: |
7 | 16 | * // Return the points that form a convex hull |
8 | 17 | * public static ArrayList<Point2D> getConvexHull(double[][]s) |
9 | 18 | * Point2D is defined in Section 9.6. |
10 | 19 | * Write a test program that prompts the user to enter the set size and the points |
11 | | - * and displays the points that form a convex hull.Here is a sample run: |
| 20 | + * and displays the points that form a convex hull. |
| 21 | + * Here is a sample run: |
| 22 | + * <p> |
| 23 | + * How many points are in the set? 6 |
| 24 | + * Enter 6 points: 1 2.4 2.5 2 1.5 34.5 5.5 6 6 2.4 5.5 9 |
| 25 | + * The convex hull is |
| 26 | + * (1.5, 34.5) (5.5, 9.0) (6.0, 2.4) (2.5, 2.0) (1.0, 2.4) |
12 | 27 | */ |
13 | 28 | public class Exercise22_09 { |
| 29 | + public static void main(String[] args) { |
| 30 | + Scanner scanner = new Scanner(System.in); |
| 31 | + System.out.print("How many points are in the set? "); |
| 32 | + int numPoints = scanner.nextInt(); |
| 33 | + System.out.print("Enter " + numPoints + " points: "); |
| 34 | + |
| 35 | + double[][] points = new double[numPoints][2]; |
| 36 | + |
| 37 | + for (int i = 0; i < points.length; i++) { |
| 38 | + for (int j = 0; j < 2; j++) { |
| 39 | + points[i][j] = scanner.nextDouble(); |
| 40 | + } |
| 41 | + } |
| 42 | + scanner.close(); |
| 43 | + System.out.println("The convex hull is " + getConvexHull(points)); |
| 44 | + |
| 45 | + } |
| 46 | + |
| 47 | + |
| 48 | + public static ArrayList<Point2D> getConvexHull(double[][] s) { |
| 49 | + int n = s.length; |
| 50 | + // map matrix into List of Point2D's |
| 51 | + List<Point2D> S = Arrays.stream(s).map(points -> new Point2D(points[0], points[1])).collect(Collectors.toList()); |
| 52 | + // Created list to hold the points in the convex hull |
| 53 | + ArrayList<Point2D> H = new ArrayList<>(); |
| 54 | + // Find the leftmost point |
| 55 | + int l = 0; |
| 56 | + for (int i = 1; i < n; i++) |
| 57 | + if (S.get(i).getX() < S.get(l).getX()) { |
| 58 | + l = i; |
| 59 | + } |
| 60 | + |
| 61 | + int p = l, q; |
| 62 | + do { |
| 63 | + H.add(S.get(p)); |
| 64 | + |
| 65 | + q = (p + 1) % n; |
| 66 | + |
| 67 | + for (int i = 0; i < n; i++) { |
| 68 | + if (getOrientation(S.get(p), S.get(i), S.get(q)) == -1) { |
| 69 | + q = i; |
| 70 | + } |
| 71 | + } |
| 72 | + p = q; |
| 73 | + |
| 74 | + } while (p != l); |
| 75 | + |
| 76 | + return H; |
| 77 | + } |
| 78 | + |
| 79 | + public static int getOrientation(Point2D p, Point2D q, Point2D r) { |
| 80 | + double val = (q.getY() - p.getY()) * (r.getX() - q.getX()) - (q.getX() - p.getX()) * (r.getY() - q.getY()); |
| 81 | + |
| 82 | + if (val == 0) return 0; |
| 83 | + return (val > 0) ? 1 : -1; |
| 84 | + } |
14 | 85 | } |
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