347 lines
11 KiB
Java
347 lines
11 KiB
Java
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/*************************************************************************
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* Compilation: javac Point2D.java
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*
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* Immutable point data type for points in the plane.
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*
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*************************************************************************/
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import java.util.Arrays;
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import java.util.Comparator;
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import edu.princeton.cs.introcs.StdDraw;
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import edu.princeton.cs.introcs.StdRandom;
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/**
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* The Point class is an immutable data type to encapsulate a
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* two-dimensional point with real-value coordinates.
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*
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* Note: in order to deal with the difference behavior of double and
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* Double with respect to -0.0 and +0.0, the Point2D constructor converts
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* any coordinates that are -0.0 to +0.0.
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*
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* For additional documentation, see <a href="/algs4/12oop">Section 1.2</a> of
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* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
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*
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* @author Robert Sedgewick
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* @author Kevin Wayne
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*/
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public class Point2D implements Comparable<Point2D> {
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/**
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* Compares two points by x-coordinate.
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*/
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public static final Comparator<Point2D> X_ORDER = new XOrder();
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/**
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* Compares two points by y-coordinate.
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*/
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public static final Comparator<Point2D> Y_ORDER = new YOrder();
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/**
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* Compares two points by polar radius.
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*/
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public static final Comparator<Point2D> R_ORDER = new ROrder();
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/**
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* Compares two points by polar angle (between 0 and 2pi) with respect to this point.
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*/
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public final Comparator<Point2D> POLAR_ORDER = new PolarOrder();
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/**
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* Compares two points by atan2() angle (between -pi and pi) with respect to this point.
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*/
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public final Comparator<Point2D> ATAN2_ORDER = new Atan2Order();
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/**
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* Compares two points by distance to this point.
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*/
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public final Comparator<Point2D> DISTANCE_TO_ORDER = new DistanceToOrder();
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private final double x; // x coordinate
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private final double y; // y coordinate
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/**
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* Initializes a new point (x, y).
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* @param x the x-coordinate
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* @param y the y-coordinate
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* @throws IllegalArgumentException if either x or y
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* is Double.NaN , Double.POSITIVE_INFINITY or
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* Double.NEGATIVE_INFINITY
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*/
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public Point2D(double x, double y) {
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if (Double.isInfinite(x) || Double.isInfinite(y))
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throw new IllegalArgumentException("Coordinates must be finite");
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if (Double.isNaN(x) || Double.isNaN(y))
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throw new IllegalArgumentException("Coordinates cannot be NaN");
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if (x == 0.0) x = 0.0; // convert -0.0 to +0.0
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if (y == 0.0) y = 0.0; // convert -0.0 to +0.0
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this.x = x;
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this.y = y;
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}
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/**
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* Returns the x-coordinate.
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* @return the x-coordinate
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*/
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public double x() {
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return x;
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}
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/**
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* Returns the y-coordinate.
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* @return the y-coordinate
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*/
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public double y() {
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return y;
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}
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/**
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* Returns the polar radius of this point.
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* @return the polar radius of this point in polar coordiantes: sqrt(x*x + y*y)
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*/
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public double r() {
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return Math.sqrt(x*x + y*y);
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}
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/**
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* Returns the angle of this point in polar coordinates.
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* @return the angle (in radians) of this point in polar coordiantes (between -pi/2 and pi/2)
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*/
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public double theta() {
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return Math.atan2(y, x);
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}
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/**
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* Returns the angle between this point and that point.
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* @return the angle in radians (between -pi and pi) between this point and that point (0 if equal)
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*/
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private double angleTo(Point2D that) {
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double dx = that.x - this.x;
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double dy = that.y - this.y;
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return Math.atan2(dy, dx);
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}
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/**
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* Is a->b->c a counterclockwise turn?
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* @param a first point
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* @param b second point
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* @param c third point
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* @return { -1, 0, +1 } if a->b->c is a { clockwise, collinear; counterclocwise } turn.
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*/
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public static int ccw(Point2D a, Point2D b, Point2D c) {
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double area2 = (b.x-a.x)*(c.y-a.y) - (b.y-a.y)*(c.x-a.x);
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if (area2 < 0) return -1;
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else if (area2 > 0) return +1;
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else return 0;
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}
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/**
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* Returns twice the signed area of the triangle a-b-c.
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* @param a first point
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* @param b second point
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* @param c third point
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* @return twice the signed area of the triangle a-b-c
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*/
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public static double area2(Point2D a, Point2D b, Point2D c) {
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return (b.x-a.x)*(c.y-a.y) - (b.y-a.y)*(c.x-a.x);
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}
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/**
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* Returns the Euclidean distance between this point and that point.
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* @param that the other point
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* @return the Euclidean distance between this point and that point
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*/
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public double distanceTo(Point2D that) {
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double dx = this.x - that.x;
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double dy = this.y - that.y;
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return Math.sqrt(dx*dx + dy*dy);
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}
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/**
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* Returns the square of the Euclidean distance between this point and that point.
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* @param that the other point
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* @return the square of the Euclidean distance between this point and that point
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*/
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public double distanceSquaredTo(Point2D that) {
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double dx = this.x - that.x;
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double dy = this.y - that.y;
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return dx*dx + dy*dy;
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}
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/**
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* Compares this point to that point by y-coordinate, breaking ties by x-coordinate.
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* @param that the other point
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* @return { a negative integer, zero, a positive integer } if this point is
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* { less than, equal to, greater than } that point
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*/
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public int compareTo(Point2D that) {
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if (this.y < that.y) return -1;
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if (this.y > that.y) return +1;
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if (this.x < that.x) return -1;
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if (this.x > that.x) return +1;
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return 0;
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}
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// compare points according to their x-coordinate
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private static class XOrder implements Comparator<Point2D> {
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public int compare(Point2D p, Point2D q) {
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if (p.x < q.x) return -1;
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if (p.x > q.x) return +1;
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return 0;
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}
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}
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// compare points according to their y-coordinate
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private static class YOrder implements Comparator<Point2D> {
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public int compare(Point2D p, Point2D q) {
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if (p.y < q.y) return -1;
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if (p.y > q.y) return +1;
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return 0;
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}
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}
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// compare points according to their polar radius
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private static class ROrder implements Comparator<Point2D> {
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public int compare(Point2D p, Point2D q) {
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double delta = (p.x*p.x + p.y*p.y) - (q.x*q.x + q.y*q.y);
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if (delta < 0) return -1;
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if (delta > 0) return +1;
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return 0;
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}
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}
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// compare other points relative to atan2 angle (bewteen -pi/2 and pi/2) they make with this Point
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private class Atan2Order implements Comparator<Point2D> {
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public int compare(Point2D q1, Point2D q2) {
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double angle1 = angleTo(q1);
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double angle2 = angleTo(q2);
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if (angle1 < angle2) return -1;
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else if (angle1 > angle2) return +1;
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else return 0;
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}
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}
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// compare other points relative to polar angle (between 0 and 2pi) they make with this Point
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private class PolarOrder implements Comparator<Point2D> {
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public int compare(Point2D q1, Point2D q2) {
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double dx1 = q1.x - x;
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double dy1 = q1.y - y;
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double dx2 = q2.x - x;
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double dy2 = q2.y - y;
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if (dy1 >= 0 && dy2 < 0) return -1; // q1 above; q2 below
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else if (dy2 >= 0 && dy1 < 0) return +1; // q1 below; q2 above
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else if (dy1 == 0 && dy2 == 0) { // 3-collinear and horizontal
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if (dx1 >= 0 && dx2 < 0) return -1;
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else if (dx2 >= 0 && dx1 < 0) return +1;
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else return 0;
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}
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else return -ccw(Point2D.this, q1, q2); // both above or below
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// Note: ccw() recomputes dx1, dy1, dx2, and dy2
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}
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}
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// compare points according to their distance to this point
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private class DistanceToOrder implements Comparator<Point2D> {
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public int compare(Point2D p, Point2D q) {
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double dist1 = distanceSquaredTo(p);
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double dist2 = distanceSquaredTo(q);
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if (dist1 < dist2) return -1;
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else if (dist1 > dist2) return +1;
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else return 0;
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}
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}
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/**
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* Does this point equal y?
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* @param other the other point
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* @return true if this point equals the other point; false otherwise
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*/
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@Override
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public boolean equals(Object other) {
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if (other == this) return true;
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if (other == null) return false;
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if (other.getClass() != this.getClass()) return false;
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Point2D that = (Point2D) other;
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return this.x == that.x && this.y == that.y;
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}
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/**
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* Return a string representation of this point.
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* @return a string representation of this point in the format (x, y)
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*/
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@Override
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public String toString() {
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return "(" + x + ", " + y + ")";
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}
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/**
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* Returns an integer hash code for this point.
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* @return an integer hash code for this point
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*/
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@Override
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public int hashCode() {
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int hashX = ((Double) x).hashCode();
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int hashY = ((Double) y).hashCode();
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return 31*hashX + hashY;
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}
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/**
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* Plot this point using standard draw.
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*/
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public void draw() {
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StdDraw.point(x, y);
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}
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/**
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* Plot a line from this point to that point using standard draw.
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* @param that the other point
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*/
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public void drawTo(Point2D that) {
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StdDraw.line(this.x, this.y, that.x, that.y);
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}
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/**
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* Unit tests the point data type.
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*/
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public static void main(String[] args) {
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int x0 = Integer.parseInt(args[0]);
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int y0 = Integer.parseInt(args[1]);
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int N = Integer.parseInt(args[2]);
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StdDraw.setCanvasSize(800, 800);
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StdDraw.setXscale(0, 100);
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StdDraw.setYscale(0, 100);
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StdDraw.setPenRadius(.005);
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Point2D[] points = new Point2D[N];
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for (int i = 0; i < N; i++) {
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int x = StdRandom.uniform(100);
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int y = StdRandom.uniform(100);
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points[i] = new Point2D(x, y);
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points[i].draw();
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}
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// draw p = (x0, x1) in red
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Point2D p = new Point2D(x0, y0);
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StdDraw.setPenColor(StdDraw.RED);
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StdDraw.setPenRadius(.02);
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p.draw();
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// draw line segments from p to each point, one at a time, in polar order
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StdDraw.setPenRadius();
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StdDraw.setPenColor(StdDraw.BLUE);
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Arrays.sort(points, p.POLAR_ORDER);
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for (int i = 0; i < N; i++) {
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p.drawTo(points[i]);
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StdDraw.show(100);
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}
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}
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}
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