$2-$D Area Using MATLAB

Imagine that you are given a collection of $k$ boxes on the $(x,y)-$plane, assumed to have their sides aligned with the axes; an example with $k=3$ appears to the right. The goal for this problem is to compute the total area covered by the union of the boxes, without counting any overlap more than once.

Write a program to compute the area with the following syntax:

The information about the boxes are contained in the variable input$\_$box. This will consist of $k$ rows, one for each box, each with $4$ entries to describe the $4$ corners of that box: the smallest $x$ value, the largest $x$ value, the smallest $y$ value, and the largest $y$ value, respectively. For example, the data for the boxes shown above would be

$\left[\begin{array}{cccc}0& 4& 0& 2\\ 2& 6& 1& 3\\ 3& 5& -1& 1\mathrm{.}5\end{array}\right]$

for the blue, black, and red boxes, in order.

At the end of your program you should have created the solution variable my$\_$area, a scalar containing the resulting area. For the example this area is $17.$

The test files, area$\_$test$\_1.$mat and area$\_$test$\_2.$mat contain sample inputs for testing. The first of these three non$-$overlapping boxes with total area of $14$; the second has a simple overlap so that the final area is $7.$