## 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.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++) {
}

//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);

int i = 3;
int n = oldPoints.size();
while (i < n) {
MyPoint t1 = points.removeLast();
MyPoint t2 = points.getLast();
MyPoint p =  oldPoints.get(i);
if (isLeft(p, t1, t2)) {
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;
}
}
}
}
}