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circles with their perimeters passing through the two points.

3. Find the length of line mc, denoted as d, which can be obtained using the Pythagorean Theorem

points are covered by each circle. Finally, return the maximum count.

This task is divided into five levels. You may submit as soon as you complete one level. There is no restriction on the number of attempts.

In the spirit of incremental coding and testing, you will need to complete ALL levels to get full credit for this lab.

Level 1

Represent a Point

The first thing we can do is to group x and y coordinates into a single data structure or class.

Design a class Point to represent a point object with each pair of x- and y- coordinates.

Define an overriding toString method to output each point. In addition, the output of each double value, say d, is to be formatted with String.format(%.3f, d);

jshell> /open Point.java

jshell> new Point(0.0, 1.0) $.. ==> point (0.000, 1.000)

jshell> /exit

Level 2

Find the mid-point and angle of line pq

Find the mid-point between two consecutive points p and q. In addition, find the angle (in radians) of line pq using the atan or atan2 Math function (refer to the Java API specifications).

Complete the midPoint and angleTo methods and include them in the Point class. You may define other helper methods to further abstract away lower-level functionalities.

Inconsistencies between your output and the actual output involving -0.000 and 0.000 can be ignored.

Level 3

Moving the point

Now we need to allow points to be moved, so that we can move point m to c. However, in the spirit of immutability, the original point is not moved. Instead, a new point is returned, which reflects the new position of the original point if it has been moved by angle and distance d.

Hint: if a point, say m, is at (x, y), then moving m at an angle and distance d, would result in the new position having the coordinates (x + d cos, y + d sin)

Level 4

Creating the Circle

Define the Circle class to allow for the creation of circle objects with a given centre and radius. You may assume that all circles created are valid.

jshell> /open Point.java

jshell> /open Circle.java

jshell> new Circle(new Point(0.0, 0.0), 1.0)

$.. ==> circle of radius 1.0 centered at point (0.000, 0.000)

jshell> new Circle(new Point(1, 1), 2)

$.. ==> circle of radius 2.0 centered at point (1.000, 1.000)

We are now ready to construct unit circles whose perimeter passes through two given points.

By using the mid-point and angle of line pq, move the mid-point to the centre of the circle of radius r whose perimeter coincides with points p and q. You will need to work out the respective angle and distance values.

Create a jshell script maxDiscCoverage.jsh and define a createUnitCircle method that takes in two points p and q and returns the unit circle created.

Notice that if the distance between points p and q is larger than 2 units, then there is no unit circle whose perimeter coincides with the points. In this level, you may assume that the two points will form a unit circle.