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Saturday, 21 January 2017

Chapter 22 Exercise 11, Introduction to Java Programming, Tenth Edition Y. Daniel LiangY.

24.11(Geometry: Graham’s algorithm for finding a convex hull) Section  22.10.2
introduced Graham’s algorithm for finding a convex hull for a set of points.
Assume that the Java’s coordinate system is used for the points. Implement the
algorithm using the following method:

/** Return the points that form a convex hull */
public static ArrayList<MyPoint> getConvexHull(double[][] s)
MyPoint is a static inner class defined as follows:
private static class MyPoint implements Comparable<MyPoint> {
double x, y;
MyPoint rightMostLowestPoint;
MyPoint(double x, double y) {
this.x = x; this.y = y;
}
public void setRightMostLowestPoint(MyPoint p) {
rightMostLowestPoint = p;
}
@Override
public int compareTo(MyPoint o) {
// Implement it to compare this point with point o
// angularly along the x-axis with rightMostLowestPoint
// as the center, as shown in Figure 22.10b. By implementing
// the Comparable interface, you can use the Array.sort
// method to sort the points to simplify coding.
}
}

import java.util.ArrayList;
import java.util.LinkedList;
import java.util.Collections;

public class Exercise11 {

 public static void main(String[] args) {
  double[][] points = new double[100][2];
  for (int i = 0; i < points.length; i++) {
   points[i][0] = (int)(Math.random() * 1000);
   points[i][1] = (int)(Math.random() * 1000);
  }
  
  /*
  points[0][0] = 1;
  points[0][1] = 2.4;
  points[1][0] = 2.5;
  points[1][1] = 2;
  points[2][0] = 1.5;
  points[2][1] = 34.5;
  points[3][0] = 5.5;
  points[3][1] = 6;
  points[4][0] = 6;
  points[4][1] = 2.4;
  points[5][0] = 5.5;
  points[5][1] = 9;
  */
  
             
  ArrayList<MyPoint> hull = getConvexHull(points);
  System.out.println("There are " + points.length + " points:");
  for (int i = 0; i < points.length; i++) {
   System.out.print("(" + points[i][0] + ", " + points[i][1] + ")  ");
  }
  System.out.println("\nThe convex hull is:");
  for (MyPoint myPoint : hull) {
   System.out.print("(" + myPoint.x + ", " + myPoint.y + ")  ");
  }
  
  
  ArrayList<Exercise09.MyPoint> hull2 = Exercise09.getConvexHull(points);
  System.out.println("\nThe convex hull2 is:");
  for (Exercise09.MyPoint myPoint : hull2) {
   System.out.print("(" + myPoint.x + ", " + myPoint.y + ")  ");
  }
 }

 public static ArrayList<MyPoint> getConvexHull(double[][] s) {
  ArrayList<MyPoint> oldPoints = new ArrayList<>();
  for (int i = 0; i < s.length; i++) {
   oldPoints.add(new MyPoint(s[i][0], s[i][1]));
  }
  
  //first point
  MyPoint h0 = oldPoints.get(0);
  for (int i = 1; i < oldPoints.size(); i++) {
   if(oldPoints.get(i).y > h0.y) {
    h0 = oldPoints.get(i);
   } else if(oldPoints.get(i).y == h0.y) {
    if(oldPoints.get(i).x > h0.x) {
     h0 = oldPoints.get(i);
    }
   }
  }
  for (MyPoint myPoint : oldPoints) {
   myPoint.setRightMostLowestPoint(h0);
  }
  
  Collections.sort(oldPoints);  
  
  LinkedList<MyPoint> points = new LinkedList<>();
  points.add(oldPoints.get(0));
  points.add(oldPoints.get(1));
  points.add(oldPoints.get(2));
  
  
  int i = 3;
  int n = oldPoints.size();
  while (i < n) {
   MyPoint t1 = points.removeLast();
   MyPoint t2 = points.getLast();
   points.add(t1);
   MyPoint p =  oldPoints.get(i);
   if (isLeft(p, t1, t2)) {
    points.add(p);
    i++;
   } else {
    points.removeLast();
   }
  }
    
  return new ArrayList<MyPoint>(points);
 }
 
 public static boolean isLeft(MyPoint p0, MyPoint p1, MyPoint p2) {
  double position = (p1.x - p0.x) * (p2.y - p0.y) - (p2.x - p0.x) * (p1.y - p0.y);
  if (position > 0) {
   return true;
  } else {
   return false;
  }
 }
 
 public static double getAngle(MyPoint p1, MyPoint p2, MyPoint p3) {
  double a = getSide(p2, p3);
  double b = getSide(p1, p3);
  double c = getSide(p1, p2);
  return Math.toDegrees(Math.acos((a * a - b * b - c * c) / (-2 * b * c)));
 }
 
 public static double getSide(MyPoint p1, MyPoint p2) {
  return Math.sqrt((p2.x - p1.x) * (p2.x - p1.x) + (p2.y - p1.y) * (p2.y - p1.y));
 }
 
 private static class MyPoint implements Comparable<MyPoint> {
  double x, y;
  MyPoint rightMostLowestPoint;

  MyPoint(double x, double y) {
   this.x = x;
   this.y = y;
  }

  public void setRightMostLowestPoint(MyPoint p) {
   rightMostLowestPoint = p;
  }

  @Override
  public int compareTo(MyPoint o) {
   MyPoint virtualPoint = new MyPoint(rightMostLowestPoint.x + 1, rightMostLowestPoint.y);
   double a1 = getAngle(rightMostLowestPoint, virtualPoint, o);
   double a2 = getAngle(rightMostLowestPoint, virtualPoint, this);
   if(a1 > a2) {
    return -1;
   } else if(a2 > a1) {
    return 1;
   } else {
    double l1 = getSide(rightMostLowestPoint, o);
    double l2 = getSide(rightMostLowestPoint, this);
    if(l1 > l2) {
     return -1;
    } else if(l2 > l1) {
     return 1;
    } else {
     return 0;
    }
   }
  }
 }
}

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