Question

i just need the Polygon class

Shapes

In this lab you will create an interface, and then implement that interface in three derived classes.

Your interface will be called Shape, and will define the following functions:

Return Type Name Parameters Description

double area none computes the area of the shape

double perimeter none computes the perimeter of the shape

Point2d center none computes the center of the shape

You will then create 3 implementations of this interface: Rectangle, Circle, and Polygon. Each one will need to provide implementations of area, perimeter, and center. (I have provided an implementation of Square in case you need to reference it.)

Here are the signatures of the constructors for Rectangle, Circle, and Polygon:

// Create a rectangle with p1 and p2 as opposite corners

public Rectangle(Point2d p1, Point2d p2)

// Create a circle with center 'c' and radius 'r'

public Circle(Point2d c, double r)

// Create a polygon with the given points.

public Polygon(Point2d[] pts)

Your classes will need to delare and initialize the necessary instance data to store the necessary data for each class.

Note that I have supplied a Point2d class for you. As you'll see below, this has some functions in it that you may find useful.

I assume you know from HS geometry how to computer the area, perimeter, and center of a rectangle and a circle. It may help to know that the Java library defines pi as Math.pi.

The Polygon class is a bit more complicated:

For the center of the polygon, you can simply average all the x coordinates, and all the y coordinates, then create a point with those averages as the x and y coordinates of the point.

For the perimeter, just use the distance() function in Point2d to compute the length of each edge, and add them.

For the area, I've provided a function in the Point2d class that computes the area of a triangle, given the three points. You can use this function along with the formula Area of a polygon to compute the area of the polygon.

There is one more gotcha in the Polygon class. The Point2d class is immutable (that is, a Point2d object, once created, cannot be modified), but an array is not. One of the tests will fail if you do not take this into account.

I would advise that you use incremental development here. I suggest doing things in this order:

Create the Shape interface. You'll know the Shape interface is correct when the first test passes. (None of the other test will even compile at this point.)

Create the Rectangle class. You'll know this is done correctly when the second test passes. (The other tests will still not even compile.)

Create the Circle and Polygon classes, and have them just pass back dummy data. Once this is done correctly, all the tests should compile, though they will not pass.

Finish the Circle class.

Finish the Polygon class.

// the shape interface with methods which will be implimented in the circle,

//rectangle and polygon class

public interface Shape {

public double area();

public double perimeter();

public Point2d center();

}

public class Point2d {

// NOTE: Point2d is immutable. It is safe to store a reference

// and rely on it not changing.

private double x;

private double y;

public Point2d(double x, double y) {

this.x = x;

this.y = y;

}

public double getX() {

return x;

}

public double getY() {

return y;

}

public double distance(Point2d pt) {

double dx = pt.x - x;

double dy = pt.y - y;

return Math.sqrt(dx*dx + dy*dy);

}

public static double area(Point2d a, Point2d b, Point2d c) {

return ((b.x - a.x) * (c.y - a.y) - (c.x - a.x) * (b.y - a.y)) / 2;

}

public String toString() {

return String.format("[%.4f,%.4f]", x, y);

}

public static void main(String[] args) {

// Test distance

{

Point2d p1 = new Point2d(1.0, 1.0);

Point2d p2 = new Point2d(5.0, 4.0);

System.out.println(p1.distance(p2));

System.out.println(p2.distance(p1));

}

// Test area2

{

Point2d p1 = new Point2d(1.0, 1.0);

Point2d p2a = new Point2d(5.0, 1.0);

Point2d p2b = new Point2d(1.0, 4.0);

Point2d p3 = new Point2d(5.0, 4.0);

System.out.println(area(p1, p2a, p3));

System.out.println(area(p1, p2b, p3));

}

}

}

i

Answer 1

Below is the code for all three classes implementing the Shape interface.

Note: I have put all the classes including Point2d in the package named "shapes".

1. Shape.java

package shapes;

interface Shape {

    double area();

    double perimeter();

    Point2d center();

}

2. Rectangle.java

package shapes;

public class Rectangle implements Shape {
    private double length;
    private double breadth;
    private Point2d p1;
    private Point2d p2;

    public Rectangle(Point2d p1, Point2d p2) {
        this.p1 = p1;
        this.p2 = p2;
        this.length = this.p2.getX() - this.p1.getX();
        this.breadth = this.p2.getY() - this.p1.getY();
    }

    public double area() {
        return getLength() * getBreadth();
    }

    public double perimeter() {
        return 2 * (getLength() + getBreadth());
    }

    public Point2d center() {
        double xCenter = (this.p1.getX() + this.p2.getX()) / 2;
        double yCenter = (this.p1.getY() + this.p2.getY()) / 2;
        return new Point2d(xCenter, yCenter);
    }

    public double getLength() {
        return length;
    }

    public double getBreadth() {
        return breadth;
    }

    public void setLength(double length) {
        this.length = length;
    }

    public void setBreadth(double breadth) {
        this.breadth = breadth;
    }
}

3. Circle.java

package shapes;

public class Circle implements Shape {
    private Point2d center;
    private double radius;

    public Circle(Point2d c, double r) {
        this.center = c;
        this.radius = r;
    }

    public double area() {
        return Math.PI * getRadius() * getRadius();
    }

    public double perimeter() {
        return 2 * Math.PI * getRadius();
    }

    public Point2d center() {
        return center;
    }

    public Point2d getCenter() {
        return center;
    }

    public double getRadius() {
        return radius;
    }

    public void setCenter(Point2d center) {
        this.center = center;
    }

    public void setRadius(double radius) {
        this.radius = radius;
    }
}

4. Polygon.java

package shapes;

public class Polygon implements Shape {
    private Point2d[] points;

    public Polygon(Point2d[] pts) {
        this.points = new Point2d[pts.length];
        System.arraycopy(pts, 0, this.points, 0, pts.length); // this method copies the pts array into the points field
                                                              // of the class
    }

    public double area() {

        /*
         * I have used the Shoelace Formula to calculate the area of the polygon
         */
        double xCoordinates[] = new double[points.length];
        double yCoordinates[] = new double[points.length];

        double area = 0.0;

        int j = points.length - 1;
        for (int i = 0; i < points.length; i++) {
            area += (xCoordinates[j] + xCoordinates[i]) * (yCoordinates[j] - yCoordinates[i]);
            j = i;
        }

        return Math.abs(area / 2.0);
    }

    public double perimeter() {
        double perimeter = 0.0;
        for (Point2d pt : points) {
            perimeter += pt.distance(pt);
        }
        return perimeter;
    }

    public Point2d center() {
        double xAvg = 0.0, yAvg = 0.0;
        for (Point2d pt : points) {
            xAvg += pt.getX();
            yAvg += pt.getY();
        }
        double xCenter = xAvg / points.length;
        double yCenter = yAvg / points.length;
        return new Point2d(xCenter, yCenter);
    }
}

NOTE: It would be better if you could provide the test cases for the program. If you can please provide the test cases in the comment to this answer and I will update the answer by running your test cases.
Try to run this program against your test cases and if there is any problem, I will update the answer accordingly.