/******************************************************************************
* Compilation: javac Point2D.java
* Execution: java Point2D x0 y0 n
* Dependencies: StdDraw.java StdRandom.java
*
* Immutable point data type for points in the plane.
*
******************************************************************************/
import java.util.Arrays;
import java.util.Comparator;
/**
* The {@code Point} class is an immutable data type to encapsulate a
* two-dimensional point with real-value coordinates.
*
* Note: in order to deal with the difference behavior of double and
* Double with respect to -0.0 and +0.0, the Point2D constructor converts
* any coordinates that are -0.0 to +0.0.
*
* For additional documentation,
* see Section 1.2 of
* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public final class Point2D implements Comparable {
/**
* Compares two points by x-coordinate.
*/
public static final Comparator X_ORDER = new XOrder();
/**
* Compares two points by y-coordinate.
*/
public static final Comparator Y_ORDER = new YOrder();
/**
* Compares two points by polar radius.
*/
public static final Comparator R_ORDER = new ROrder();
private final double x; // x coordinate
private final double y; // y coordinate
/**
* Initializes a new point (x, y).
* @param x the x-coordinate
* @param y the y-coordinate
* @throws IllegalArgumentException if either {@code x} or {@code y}
* is {@code Double.NaN}, {@code Double.POSITIVE_INFINITY} or
* {@code Double.NEGATIVE_INFINITY}
*/
public Point2D(double x, double y) {
if (Double.isInfinite(x) || Double.isInfinite(y))
throw new IllegalArgumentException("Coordinates must be finite");
if (Double.isNaN(x) || Double.isNaN(y))
throw new IllegalArgumentException("Coordinates cannot be NaN");
if (x == 0.0) this.x = 0.0; // convert -0.0 to +0.0
else this.x = x;
if (y == 0.0) this.y = 0.0; // convert -0.0 to +0.0
else this.y = y;
}
/**
* Returns the x-coordinate.
* @return the x-coordinate
*/
public double x() {
return x;
}
/**
* Returns the y-coordinate.
* @return the y-coordinate
*/
public double y() {
return y;
}
/**
* Returns the polar radius of this point.
* @return the polar radius of this point in polar coordinates: sqrt(x*x + y*y)
*/
public double r() {
return Math.sqrt(x*x + y*y);
}
/**
* Returns the angle of this point in polar coordinates.
* @return the angle (in radians) of this point in polar coordinates (between –π and π)
*/
public double theta() {
return Math.atan2(y, x);
}
/**
* Returns the angle between this point and that point.
* @return the angle in radians (between –π and π) between this point and that point (0 if equal)
*/
private double angleTo(Point2D that) {
double dx = that.x - this.x;
double dy = that.y - this.y;
return Math.atan2(dy, dx);
}
/**
* Returns true if a→b→c is a counterclockwise turn.
* @param a first point
* @param b second point
* @param c third point
* @return { -1, 0, +1 } if a→b→c is a { clockwise, collinear; counterclockwise } turn.
*/
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;
}
/**
* Returns twice the signed area of the triangle a-b-c.
* @param a first point
* @param b second point
* @param c third point
* @return twice the signed area of the triangle 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);
}
/**
* Returns the Euclidean distance between this point and that point.
* @param that the other point
* @return the 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);
}
/**
* Returns the square of the Euclidean distance between this point and that point.
* @param that the other point
* @return the square of the 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;
}
/**
* Compares two points by y-coordinate, breaking ties by x-coordinate.
* Formally, the invoking point (x0, y0) is less than the argument point (x1, y1)
* if and only if either {@code y0 < y1} or if {@code y0 == y1} and {@code x0 < x1}.
*
* @param that the other point
* @return the value {@code 0} if this string is equal to the argument
* string (precisely when {@code equals()} returns {@code true});
* a negative integer if this point is less than the argument
* point; and a positive integer if this point is greater than the
* argument point
*/
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;
}
/**
* Compares two points by polar angle (between 0 and 2π) with respect to this point.
*
* @return the comparator
*/
public Comparator polarOrder() {
return new PolarOrder();
}
/**
* Compares two points by atan2() angle (between –π and π) with respect to this point.
*
* @return the comparator
*/
public Comparator atan2Order() {
return new Atan2Order();
}
/**
* Compares two points by distance to this point.
*
* @return the comparator
*/
public Comparator distanceToOrder() {
return new DistanceToOrder();
}
// compare points according to their x-coordinate
private static class XOrder implements Comparator {
public int compare(Point2D p, Point2D q) {
return Double.compare(p.x, q.x);
}
}
// compare points according to their y-coordinate
private static class YOrder implements Comparator {
public int compare(Point2D p, Point2D q) {
return Double.compare(p.y, q.y);
}
}
// compare points according to their polar radius
private static class ROrder implements Comparator {
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);
return Double.compare(delta, 0);
}
}
// compare other points relative to atan2 angle (between -pi/2 and pi/2) they make with this Point
private class Atan2Order implements Comparator {
public int compare(Point2D q1, Point2D q2) {
double angle1 = angleTo(q1);
double angle2 = angleTo(q2);
return Double.compare(angle1, angle2);
}
}
// compare other points relative to polar angle (between 0 and 2pi) they make with this Point
private class PolarOrder implements Comparator {
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 {
public int compare(Point2D p, Point2D q) {
double dist1 = distanceSquaredTo(p);
double dist2 = distanceSquaredTo(q);
return Double.compare(dist1, dist2);
}
}
/**
* Compares this point to the specified point.
*
* @param other the other point
* @return {@code true} if this point equals {@code other};
* {@code false} otherwise
*/
@Override
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;
}
/**
* Return a string representation of this point.
* @return a string representation of this point in the format (x, y)
*/
@Override
public String toString() {
return "(" + x + ", " + y + ")";
}
/**
* Returns an integer hash code for this point.
* @return an integer hash code for this point
*/
@Override
public int hashCode() {
int hashX = ((Double) x).hashCode();
int hashY = ((Double) y).hashCode();
return 31*hashX + hashY;
}
/**
* Plot this point using standard draw.
*/
public void draw() {
StdDraw.point(x, y);
}
/**
* Plot a line from this point to that point using standard draw.
* @param that the other point
*/
public void drawTo(Point2D that) {
StdDraw.line(this.x, this.y, that.x, that.y);
}
/**
* Unit tests the point data type.
*
* @param args the command-line arguments
*/
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);
StdDraw.setPenRadius(0.005);
StdDraw.enableDoubleBuffering();
Point2D[] points = new Point2D[n];
for (int i = 0; i < n; i++) {
int x = StdRandom.uniformInt(100);
int y = StdRandom.uniformInt(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);
StdDraw.setPenRadius(0.02);
p.draw();
// draw line segments from p to each point, one at a time, in polar order
StdDraw.setPenRadius();
StdDraw.setPenColor(StdDraw.BLUE);
Arrays.sort(points, p.polarOrder());
for (int i = 0; i < n; i++) {
p.drawTo(points[i]);
StdDraw.show();
StdDraw.pause(100);
}
}
}