## Inroduction

Structure Polygons shaps calculators writen in c++ can do multiple operation on multiple polygon given by points on one string .

## Project Description

a program to do operations on polygons data. The program use a defined string format to represent polygons. All polygons will be in one line input. For example: Polygons=[(1,1),(4,1),(4,5),(1,5);(3,4),(6,4),(6,12),(3,12)]

## Polygons Data

The Polygons line contains a list of polygons data separated by ‘;’. Fields of a Polygon is represented by a set of points separated by ‘,’. The number of polygons are up to 1000 polygon. Each polygon has up to 100 points.

### Definition of Redundant Point

A redundant point is a point of the polygon points that can be deleted without change in the polygon shape. Like

• Examples of Redundant Point
• (1,1),(2,1),(4,1),(4,3),(1,3)
• (1,2),(4,2),(4,2),(4,8),(1,8)
• (1,2),(4,2),(4,2),(4,2),(4,8),(1,8)

In the second case two neighbor identical points any one of them can be redundant (you should select only the second one). If more than two points are identical and follow each other, all of them are redundant except the first point of them.

### Intersecting Polygons

Intersecting Polygons are polygons sharing common area, side, or point(s).

### Connected Polygons

Two Connected Polygons are polygons that are intersecting or polygons which have path from one to the other through intersecting polygons.

## Operations

When the program start, the user enters one Polygons Line in the defined above format then followed by one or more operations from the below table (each operation in a line). The program ends when it reads Quit operation.

### Operations Table

OperationAction
Number_PolygonsPrint the number of polygons.
Total_Number_PointsPrint the total number of points in all polygons.
Minimum_XPrint the minimum X value of all points.
Maximum_XPrint the maximum X value of all points
Minimum_YPrint the minimum Y value of all points.
Maximum_YPrint the maximum Y value of all points
Enclosing_RectanglePrint the minimum Enclosing Rectangle that includes all polygons inside it
Total_Redundant_PointsThe number of Redundant points in all polygons
Polygon_Points nList all points of the nth polygon (neglecting redundant points) n start from 1
Point_Polygons (2,1)List all polygons IDs(ID is 1 for the first polygon, 2 for the second polygon,…)
List_Polygons_Points More nList Polygons having more than n points excluding redundant points where n is an integer.
List_Polygons_Points Less nList Polygons having less than n points excluding redundant points where n is an integer.
List_Polygons_Points EqualnList Polygons having exactly n points excluding redundant points where n is an integer.
List_Points_Polygons More nList all Points that are in the list of more than n polygons where n is an integer.
List_Points_Polygons Less nList all Points that are in the list of less than n polygons where n is an integer.
List_Points_Polygons EqualnList all Points that are in the list of less than n polygons where n is an integer.
Polygon_Perimeter nPrint the perimeter of the nth polygon.
List_TrianglesList all Polygon IDs of polygons that are triangles.
List_RectanglesList all Polygon IDs of polygons that are rectangles.
List_TrapezoidList all Polygon IDs of polygons that are trapezoid.
Inside_RectangleEdge PointsList all Polygon IDs of polygons that are inside the given rectangle.
Inside_Circle e.g(1,2),5List all Polygon IDs of polygons that are inside the given Circle Center Raduis
Polygon_Area nPrint the polygon area of the nth polygon
Polygons_Area_Range n1,n2List all Polygon IDs of polygons that have area <= minArean1 and >=maxArea.n1
Polygons_Enclosing_Point pList all Polygon IDs of polygons that have the point p (1,2) inside it
Is_Intersecting i,jPrint TRUE if ith polygon intersects the jth polygon
Intersecting_Group 3,5,6Print TRUE if the list of polygon are all intersecting with each other
Largest_Intersecting_PairPrint the two IDs of polygons that are intersecting and having the largest sum of area.
Largest_Rectangle_Inside nPrint the largest rectangle that can inside the nth polygon.
Largest_Circle_Inside nPrint the largest circle that can inside the nth polygon.

## Code - Some Funcations

1 2 3 4 5 6 7 8 9 10 11 12 13 int Number_Polygons (string input , int input_length) //function to get polygons number { int polygon_numbers = 0 ; for (int i=0 ; i <= input_length ; i++ ) { if ( input [i]== ';') { polygon_numbers = polygon_numbers +1 ; } } return polygon_numbers+1 ; } 
1 2 3 4 5 6 7 8 9 10 11 12 int Total_Number_Points (string input , int input_length) //function to get total number of points { int number_point = 0 ; for (int i = 0 ; i <= input_length ; i++ ) { if (input[i]=='(') { number_point = number_point + 1 ; } } return number_point ; } 
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 int Total_Number_Points (string input , int input_length) //function to get total number of points { int Redundant_points (string points , int number ) // function to number of redundant at polygon { int arc; int col;int inarc;int counter1= 0;int counter2= 0 ;int counter3 = 0 ;int colrep = 1 ; for (int i =0 ; i<= points.length() ;i++ ) //getting place of that "(" and ")" and "," { if (points[i]== '('){counter1=counter1+1; arc[counter1]=i ;} if (points[i]== ','){counter2=counter2+1; col[counter2]=i ;} if (points[i]== ')'){counter3=counter3+1;inarc[counter3]=i ;} } float x; float y ; float slope; for (int i = 1 ; i <=number ; i++){ x[i]=atof(points.substr(arc[i]+1,col[colrep]-arc[i]-1).c_str()) ; y[i]=atof(points.substr(col[colrep]+1,inarc[i]-col[colrep]-1).c_str()) ; colrep +=2 ; } float xr; float yr; xr=x; yr=y; // int repeater = 2 ; int re =0; slope=((y[1+1]-y)/(x[1+1]-x)); for (int i = 2 ; i<=number ; i++) { slope[i]=((y[i+1]-y[i])/(x[i+1]-x[i])); for (int p =2 ; p <=number ;p++){ if (x[i-1]==x[i] && y[i-1]==y[i]) { re +=1 ; break; } // get redundant of dip point if(x[i+1]-x[i] !=0 && slope[i]==slope[i-1]) { re +=1 ;break; } // getting redundant point of slope if (x[i+1]-x[i]==0 && y[i+1]-y[i]!=0 && x[i]-x[i-1]==0 && y[i]-y[i-1]!=0 ){ re+=1; ; break; }// get redundant of x-x =0 // xr[repeater] = x[i];yr[repeater] =y[i];repeater +=1 ; break ; }} //for (int i=1 ;i<repeater ; i++) { cout << "X = " << xr[i] << endl;cout << "y = " << yr[i] << endl; } return re ; }}