Overlapping Ellipses

An ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. - Wikipedia.

In this assignment you will use a Monte Carlo Simulation to estimate the overlap between two Ellipses.

Part 1: Ellipse Class

A. Write a class to capture the necessary information of an ellipse.

B. Write code to thoroughly test your implementation of the ellipse class including:

a. A constructor that accepts no variables.

b. A constructor that accepts all appropriate variables.

c. Setting and getting the appropriate variables.

d. A function that returns the area of the ellipse

e. A function that returns the circumference of the ellipse.

Part 2: Structure Chart

Using the top-down strategy discussed in class, produce a structure chart to capture the necessary steps for computing the overlap of two ellipses using the Monte Carlo Technique.

A. Each block of the chart should capture the requirements of a function.

B. Label each edge with the input and output of the function, similar to the examples given in class.

NOTE: DO NOT ATTEMPT TO IMPLEMENT YOUR SOLUTION UNTIL YOU THOROUGHLY UNDERSTAND THE PROBLEM AND HAVE MAPPED OUT YOUR SOLUTION.

Part 3: Implementation

Implement your solution described by your structure chart. Your function should accept two Ellipse objects (defined in part 1) and return the area of their overlap. Use a Monte Carlo simulation to estimate the overlap. If they do not overlap, return 0.

Part 4: Unit Testing

For this part, you will thoroughly test your implementation. For EVERY function, beginning with the lowest level functions:

A. Print the name of the function.

B. Print the doctstring of the function.

C. Print the rationale for the test (e.g. "Testing when a point falls within an Ellipse.")

D. Print the specific input used to evaluate that rationale.

E. Print the result.

F. Repeat C-E until all relevant cases are tested for that function.