Program Design Course Your job is to write specifications (with Liskov’s style) for the problem and implement them based on the specifications you wrote. Things that can help include thinking through your implementation before you start coding, coding in the way that eliminates errors before you test, doing rigorous testing so that errors are found early, and paying careful attention to modularity so that when eoors are discovered, they can corrected with minimal impact on the program as a whole.The picture below shows two polygons, one is a pentagon and the other is a triangle. Their intersection consists of the two dark regions.
Your task is to write the part of the program that deals with polygon intersections. You delay work on the user interface and focus only on the geometric representations of the intersections.A polygon in the Cartesian plane can be represented by a sequence of points that are its vertices. The vertices in the sequence appear in the order in which they are visited when traveling clockwise around the polygonís boundary; so any two adjacent vertices in the sequence are the endpoints of a line segment that is one of the polygonís sides. The last and the first vertices in the sequence are also endpoints of a side. Vertices are identified by their x- and y-coordinates. Assume the following about each polygon.· No point will occur as a vertex (on the same polygon) more than once.
· Two sides can intersect only at a common endpoint (vertex).
· The angle between any two sides with a common vertex has a measure that is greater than 0 and less than 360.
· The polygon has at least 3 vertices.The intersection of two polygons consists of 0 or more connected regions. Your problem is to take two polygons and determine the regions of their intersection that are polygons satisfying the criteria above.InputThe input contains several data sets, each consisting of two polygons. Each polygon appears as a sequence of numbers:n x1 y1 x2 y2 ... xn ynwhere the integer n is the number of vertices of the polygon, and the real coordinates (x1,y1) through (xn, yn) are the boundary vertices. OutputFor each data set, your program should output its number (Data set 1, Data set 2, etc.), and the number of regions in the intersection of its two polygons. Label each region in the data set (Region 1, Region 2, etc.) and list its vertices in the order they appear when they are visited going either clockwise or counterclockwise around the boundary of the region. The first vertex printed should be the vertex with the smallest x-coordinate (to break ties, use the smallest y-coordinate). No region may include degenerate parts (consisting of adjacent sides whose angle of intersection is 0). If the three endpoints of two adjacent sides are collinear, the two sides should be merged into a single side. Print each vertex in the standard form ( x,y), where x and y have two digits to the right of the decimal. The following sample input contains exactly one data set. (The data set corresponds to the illustration at the beginning of this problem description.)Sample Input
3 2 1 0.5 3.5 8 5
5 1.5 3 2 7 6.5 6.5 6.5 3.25 4 4.5Output for the Sample Input
Data Set 1
Number of intersection regions: 2
Region 1:(1.50,3.00)(1.59,3.72)(3.25,4.05)
Region 2:(4.43,4.29)(6.50,4.70)(6.50,4.00)(5.86,3.57)
Your task is to write the part of the program that deals with polygon intersections. You delay work on the user interface and focus only on the geometric representations of the intersections.A polygon in the Cartesian plane can be represented by a sequence of points that are its vertices. The vertices in the sequence appear in the order in which they are visited when traveling clockwise around the polygonís boundary; so any two adjacent vertices in the sequence are the endpoints of a line segment that is one of the polygonís sides. The last and the first vertices in the sequence are also endpoints of a side. Vertices are identified by their x- and y-coordinates. Assume the following about each polygon.· No point will occur as a vertex (on the same polygon) more than once.
· Two sides can intersect only at a common endpoint (vertex).
· The angle between any two sides with a common vertex has a measure that is greater than 0 and less than 360.
· The polygon has at least 3 vertices.The intersection of two polygons consists of 0 or more connected regions. Your problem is to take two polygons and determine the regions of their intersection that are polygons satisfying the criteria above.InputThe input contains several data sets, each consisting of two polygons. Each polygon appears as a sequence of numbers:n x1 y1 x2 y2 ... xn ynwhere the integer n is the number of vertices of the polygon, and the real coordinates (x1,y1) through (xn, yn) are the boundary vertices. OutputFor each data set, your program should output its number (Data set 1, Data set 2, etc.), and the number of regions in the intersection of its two polygons. Label each region in the data set (Region 1, Region 2, etc.) and list its vertices in the order they appear when they are visited going either clockwise or counterclockwise around the boundary of the region. The first vertex printed should be the vertex with the smallest x-coordinate (to break ties, use the smallest y-coordinate). No region may include degenerate parts (consisting of adjacent sides whose angle of intersection is 0). If the three endpoints of two adjacent sides are collinear, the two sides should be merged into a single side. Print each vertex in the standard form ( x,y), where x and y have two digits to the right of the decimal. The following sample input contains exactly one data set. (The data set corresponds to the illustration at the beginning of this problem description.)Sample Input
3 2 1 0.5 3.5 8 5
5 1.5 3 2 7 6.5 6.5 6.5 3.25 4 4.5Output for the Sample Input
Data Set 1
Number of intersection regions: 2
Region 1:(1.50,3.00)(1.59,3.72)(3.25,4.05)
Region 2:(4.43,4.29)(6.50,4.70)(6.50,4.00)(5.86,3.57)
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