# Point2D.java

Below is the syntax highlighted version of Point2D.java from § Algorithms.

```/*************************************************************************
*  Compilation:  javac Point2D.java
*
*  Immutable point data type for points in the plane.
*
*************************************************************************/

import java.util.Arrays;
import java.util.Comparator;

public class Point2D implements Comparable<Point2D> {
public static final Comparator<Point2D> X_ORDER = new XOrder();
public static final Comparator<Point2D> Y_ORDER = new YOrder();
public static final Comparator<Point2D> R_ORDER = new ROrder();

public final Comparator<Point2D> POLAR_ORDER = new PolarOrder();
public final Comparator<Point2D> ATAN2_ORDER = new Atan2Order();
public final Comparator<Point2D> DISTANCE_TO_ORDER = new DistanceToOrder();

private final double x;    // x coordinate
private final double y;    // y coordinate

// create a new point (x, y)
public Point2D(double x, double y) {
this.x = x;
this.y = y;
}

// return the x-coorindate of this point
public double x() { return x; }

// return the y-coorindate of this point
public double y() { return y; }

// return the radius of this point in polar coordinates
public double r() { return Math.sqrt(x*x + y*y); }

// return the angle of this point in polar coordinates
// (between -pi/2 and pi/2)
public double theta() { return Math.atan2(y, x); }

// return the polar angle between this point and that point (between -pi and pi);
// (0 if two points are equal)
private double angleTo(Point2D that) {
double dx = that.x - this.x;
double dy = that.y - this.y;
return Math.atan2(dy, dx);
}

// is a->b->c a counter-clockwise turn?
// -1 if clockwise, +1 if counter-clockwise, 0 if collinear
public static int ccw(Point2D a, Point2D b, Point2D c) {
double area2 = (b.x-a.x)*(c.y-a.y) - (b.y-a.y)*(c.x-a.x);
if      (area2 < 0) return -1;
else if (area2 > 0) return +1;
else                return  0;
}

// twice signed area of a-b-c
public static double area2(Point2D a, Point2D b, Point2D c) {
return (b.x-a.x)*(c.y-a.y) - (b.y-a.y)*(c.x-a.x);
}

// return Euclidean distance between this point and that point
public double distanceTo(Point2D that) {
double dx = this.x - that.x;
double dy = this.y - that.y;
return Math.sqrt(dx*dx + dy*dy);
}

// return square of Euclidean distance between this point and that point
public double distanceSquaredTo(Point2D that) {
double dx = this.x - that.x;
double dy = this.y - that.y;
return dx*dx + dy*dy;
}

// compare by y-coordinate, breaking ties by x-coordinate
public int compareTo(Point2D that) {
if (this.y < that.y) return -1;
if (this.y > that.y) return +1;
if (this.x < that.x) return -1;
if (this.x > that.x) return +1;
return 0;
}

// compare points according to their x-coordinate
private static class XOrder implements Comparator<Point2D> {
public int compare(Point2D p, Point2D q) {
if (p.x < q.x) return -1;
if (p.x > q.x) return +1;
return 0;
}
}

// compare points according to their y-coordinate
private static class YOrder implements Comparator<Point2D> {
public int compare(Point2D p, Point2D q) {
if (p.y < q.y) return -1;
if (p.y > q.y) return +1;
return 0;
}
}

// compare points according to their polar radius
private static class ROrder implements Comparator<Point2D> {
public int compare(Point2D p, Point2D q) {
double delta = (p.x*p.x + p.y*p.y) - (q.x*q.x + q.y*q.y);
if (delta < 0) return -1;
if (delta > 0) return +1;
return 0;
}
}

// compare other points relative to atan2 angle (bewteen -pi/2 and pi/2) they make with this Point
private class Atan2Order implements Comparator<Point2D> {
public int compare(Point2D q1, Point2D q2) {
double angle1 = angleTo(q1);
double angle2 = angleTo(q2);
if      (angle1 < angle2) return -1;
else if (angle1 > angle2) return +1;
else                      return  0;
}
}

// compare other points relative to polar angle (between 0 and 2pi) they make with this Point
private class PolarOrder implements Comparator<Point2D> {
public int compare(Point2D q1, Point2D q2) {
double dx1 = q1.x - x;
double dy1 = q1.y - y;
double dx2 = q2.x - x;
double dy2 = q2.y - y;

if      (dy1 >= 0 && dy2 < 0) return -1;    // q1 above; q2 below
else if (dy2 >= 0 && dy1 < 0) return +1;    // q1 below; q2 above
else if (dy1 == 0 && dy2 == 0) {            // 3-collinear and horizontal
if      (dx1 >= 0 && dx2 < 0) return -1;
else if (dx2 >= 0 && dx1 < 0) return +1;
else                          return  0;
}
else return -ccw(Point2D.this, q1, q2);     // both above or below

// Note: ccw() recomputes dx1, dy1, dx2, and dy2
}
}

// compare points according to their distance to this point
private class DistanceToOrder implements Comparator<Point2D> {
public int compare(Point2D p, Point2D q) {
double dist1 = distanceSquaredTo(p);
double dist2 = distanceSquaredTo(q);
if      (dist1 < dist2) return -1;
else if (dist1 > dist2) return +1;
else                    return  0;
}
}

// does this point equal y?
public boolean equals(Object other) {
if (other == this) return true;
if (other == null) return false;
if (other.getClass() != this.getClass()) return false;
Point2D that = (Point2D) other;
return this.x == that.x && this.y == that.y;
}

// convert to string
public String toString() {
return "(" + x + ", " + y + ")";
}

// plot using StdDraw
public void draw() {
StdDraw.point(x, y);
}

// draw line from this point p to q using StdDraw
public void drawTo(Point2D that) {
StdDraw.line(this.x, this.y, that.x, that.y);
}

public static void main(String[] args) {
int x0 = Integer.parseInt(args[0]);
int y0 = Integer.parseInt(args[1]);
int N = Integer.parseInt(args[2]);

StdDraw.setCanvasSize(800, 800);
StdDraw.setXscale(0, 100);
StdDraw.setYscale(0, 100);
Point2D[] points = new Point2D[N];
for (int i = 0; i < N; i++) {
int x = StdRandom.uniform(100);
int y = StdRandom.uniform(100);
points[i] = new Point2D(x, y);
points[i].draw();
}

// draw p = (x0, x1) in red
Point2D p = new Point2D(x0, y0);
StdDraw.setPenColor(StdDraw.RED);
p.draw();

// draw line segments from p to each point, one at a time, in polar order