package edu.princeton.cs.algs4.ch12;
import edu.princeton.cs.introcs.*;
/*************************************************************************
* 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 <tt>Point</tt> class is an immutable data type to encapsulate a
* two-dimensional point with real-value coordinates.
* <p>
* 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 <a href="/algs4/12oop">Section 1.2</a> of
* <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public class Point2D implements Comparable<Point2D> {
/**
* Compares two points by x-coordinate.
*/
public static final Comparator<Point2D> X_ORDER = new XOrder();
/**
* Compares two points by y-coordinate.
*/
public static final Comparator<Point2D> Y_ORDER = new YOrder();
/**
* Compares two points by polar radius.
*/
public static final Comparator<Point2D> R_ORDER = new ROrder();
/**
* Compares two points by polar angle (between 0 and 2pi) with respect to this point.
*/
public final Comparator<Point2D> POLAR_ORDER = new PolarOrder();
/**
* Compares two points by atan2() angle (between -pi and pi) with respect to this point.
*/
public final Comparator<Point2D> ATAN2_ORDER = new Atan2Order();
/**
* Compares two points by distance to this point.
*/
public final Comparator<Point2D> DISTANCE_TO_ORDER = new DistanceToOrder();
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 <tt>x</tt> or <tt>y</tt>
* is <tt>Double.NaN</tt>, <tt>Double.POSITIVE_INFINITY</tt> or
* <tt>Double.NEGATIVE_INFINITY</tt>
*/
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) x = 0.0; // convert -0.0 to +0.0
if (y == 0.0) y = 0.0; // convert -0.0 to +0.0
this.x = x;
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 coordiantes: 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 coordiantes (between -pi/2 and pi/2)
*/
public double theta() {
return Math.atan2(y, x);
}
/**
* Returns the angle between this point and that point.
* @return the angle in radians (between -pi and pi) 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);
}
/**
* Is a->b->c 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; counterclocwise } 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 this point to that point by y-coordinate, breaking ties by x-coordinate.
* @param that the other point
* @return { a negative integer, zero, a positive integer } if this point is
* { less than, equal to, greater than } that 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;
}
// 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?
* @param other the other point
* @return true if this point equals the other point; false otherwise
*/
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)
*/
public String toString() {
return "(" + x + ", " + y + ")";
}
/**
* Returns an integer hash code for this point.
* @return an integer hash code for this point
*/
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.
*/
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(.005);
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);
StdDraw.setPenRadius(.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.POLAR_ORDER);
for (int i = 0; i < N; i++) {
p.drawTo(points[i]);
StdDraw.show(100);
}
}
}
/*************************************************************************
* Copyright 2002-2012, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4-package.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4-package.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4-package.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
* You should have received a copy of the GNU General Public License
* along with algs4-package.jar. If not, see http://www.gnu.org/licenses.
*************************************************************************/