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C++ Structure Polygon Mathematical Operators

Posted May 1, 2017
By Mohamed F. Razzk
5 min read

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

Operation Action
Number_Polygons Print the number of polygons.
Total_Number_Points Print the total number of points in all polygons.
Minimum_X Print the minimum X value of all points.
Maximum_X Print the maximum X value of all points
Minimum_Y Print the minimum Y value of all points.
Maximum_Y Print the maximum Y value of all points
Enclosing_Rectangle Print the minimum Enclosing Rectangle that includes all polygons inside it
Total_Redundant_Points The number of Redundant points in all polygons
Polygon_Points n List 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 n List Polygons having more than n points excluding redundant points where n is an integer.
List_Polygons_Points Less n List Polygons having less than n points excluding redundant points where n is an integer.
List_Polygons_Points Equaln List Polygons having exactly n points excluding redundant points where n is an integer.
List_Points_Polygons More n List all Points that are in the list of more than n polygons where n is an integer.
List_Points_Polygons Less n List all Points that are in the list of less than n polygons where n is an integer.
List_Points_Polygons Equaln List all Points that are in the list of less than n polygons where n is an integer.
Polygon_Perimeter n Print the perimeter of the nth polygon.
List_Triangles List all Polygon IDs of polygons that are triangles.
List_Rectangles List all Polygon IDs of polygons that are rectangles.
List_Trapezoid List all Polygon IDs of polygons that are trapezoid.
Inside_RectangleEdge Points List all Polygon IDs of polygons that are inside the given rectangle.
Inside_Circle e.g(1,2),5 List all Polygon IDs of polygons that are inside the given Circle Center Raduis
Polygon_Area n Print the polygon area of the nth polygon
Polygons_Area_Range n1,n2 List all Polygon IDs of polygons that have area <= minArean1 and >=maxArea.n1
Polygons_Enclosing_Point p List all Polygon IDs of polygons that have the point p (1,2) inside it
Is_Intersecting i,j Print TRUE if ith polygon intersects the jth polygon
Intersecting_Group 3,5,6 Print TRUE if the list of polygon are all intersecting with each other
Largest_Intersecting_Pair Print the two IDs of polygons that are intersecting and having the largest sum of area.
Largest_Rectangle_Inside n Print the largest rectangle that can inside the nth polygon.
Largest_Circle_Inside n Print the largest circle that can inside the nth polygon.

Code - Some Funcations

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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 ;
}

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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 ;
}

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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[1000]; int col[1000];int inarc[1000];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[1000]; float y [1000]; float slope[1000];
    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[1000]; float yr[1000];
    xr[1]=x[1]; yr[1]=y[1];
    //  int repeater = 2 ;
    int re =0;

    slope[1]=((y[1+1]-y[1])/(x[1+1]-x[1]));
    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 ;
}}

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