Lab 15.1 IrregularPolygon

Background

Polygons are closed two-dimensional shapes bounded by line segments. The segments meet in pairs at corners called vertices. A polygon is irregular if not all its sides are equal in length. The figure below shows examples of irregular polygons:

Assignment

1. Implement a class IrregularPolygon that contains an array list of Point2D.Double objects.

2. The Point2D.Double class defines a point specified in double precision representing a location in (x, y) coordinate space. For example, Point2D.Double(2.5, 3.1) constructs and initializes a point at coordinates (2.5, 3.1).

3. Use the following declarations as a starting point for your lab work.

   import  java.awt.geom.*; // for Point2D.Double  
   import  java.util.ArrayList; // for ArrayList  
   import  gpdraw.*; // for DrawingTool
   
   public class  IrregularPolygon{  
   private  ArrayList <Point2D.Double> myPolygon;  
   
   // constructors  
   public  IrregularPolygon() { }  
   
   // public methods  
   public void  add(Point2D.Double aPoint) { }
   
   public void  draw() { }
   
   public double  perimeter() { }
   
   public double  area() { }  
   }
   

4. The program should use the Drawing Tool to draw the polygon by joining adjacent points with a line segment, and then closing it up by joining the end and start points.

5. Write methods that compute the perimeter and the area of a polygon. To compute the perimeter, compute the distance between adjacent points, and total up the distances. The area of a polygon with corners is the absolute value of:

   Note: add n products, then subtract n products, then divide by 2. The result will be negative or positive depending on the order in which the products are taken, i.e., which products are subtracted and which are added. Here is an explanation and proof of the formula, if you want to know more.

6. As a test case, the parallelogram formed by the following coordinates has a perimeter of 174.1 units and an area of 1700 square units: (20, 10), (70, 20), (50, 50), (0, 40). For more cases to practice with, see these slides.

7. For the normal lab, assume that the points are entered in either clockwise or counterclockwise order.

All classes must be named with your name and period. For example, P3_Wang_Michael_IrregularPolygon

Gold Challenge: As an optional challenge, make the program automatically arrange the points in clockwise or counterclockwise order, such that a valid polygon is drawn from any set of at least three non-linear points. Throw an error if draw, area, or perimeter is called on a polygon when its points cannot form a valid polygon (i.e. there are not at least three non-linear points).

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