Question

 c programming 
Objectives:
Learn about conditional statements and Boolean operators.
Problem:
Let R and S be two rectangles in the xy-plane whose sides are parallel to the coordinate axes. Each rectangle is described by its center and its height and width. Determine if R and S overlap.
Example:
1) Suppose R is the rectangle centered at the origin height and width equal to one and S is the rectangle centered at the point (1,1) with a height equal to 2 and width equal to 3. Then L and S overlap.

2) Suppose R is the rectangle centered at the origin height and width equal to one and S is the rectangle centered at the point (100,100) with a height equal to 2 and width equal to 3. Then L and S do not overlap.

Bonus:
If two given rectangles as described above overlap, their intersection forms a new rectangle. Further determine its center, height, and width

Answer 1

• If two rectangles touch each other, they are not considered as overlapped.

CODE :

#include
#include

struct Rect
{
    float x;
    float y; // x,y co-ordinate of its center
    float h; // height
    float w; // width
};

int is_overlap(struct Rect a, struct Rect b)
// checks whether the two rectangles overlap or not
// by checking whether the farthest points on the rectangle cross each other or not
{
    if ( a.x - a.w/2 >= b.x + b.w/2 )    // a is on the right side of b
        return 0;

    if ( a.x + a.w/2 <= b.x - b.w/2 )    // a is on the left side of b
        return 0;

    if ( a.y - a.h/2 >= b.y + b.h/2 )    // a is above b
        return 0;

    if ( a.y + a.h/2 <= b.y - b.h/2 )    // a is below b
        return 0;

    return 1;
}

float max(float a, float b)
{
    if(a>b)
        return a;
    else
        return b;
}

float min(float a, float b)
{
    if(a         return a;
    else
        return b;
}

void print_overlap(struct Rect a, struct Rect b)
{
    float left = max(a.x - a.w/2, b.x - b.w/2);     // left is the x co-ordinate of the left most point of the rectangle
    float down = max(a.y - a.h/2, b.y - b.h/2);     // down is the y co-ordinate of the lowest most point of the rectangle
    float right = min(a.x + a.w/2, b.x + b.w/2 );   // right is the x co-ordinate of the right most point of the rectangle
    float top = min(a.y + a.h/2, b.y + b.h/2);      // top is the y co-ordinate of the top most point of the rectangle

    struct Rect c;      // overlap rectangle
    c.x = (left + right)/2;
    c.y = (top + down)/2;
    c.h = top - down;
    c.w = right - left;
    printf("\n\nOverLapped Rectangle : ");
    printf("\nCenter : %.2f %.2f\n", c.x, c.y);
    printf("Height : %.2f\nWidth : %.2f", c.h, c.w);
}

int main()
{
    struct Rect a;
    struct Rect b;
    printf("Enter the center, the height, the width of first rectangle : ");
    scanf("%f %f %f %f", &(a.x), &(a.y), &(a.h), &(a.w));
    printf("Enter the center, the height, the width of second rectangle : ");
    scanf("%f %f %f %f", &(b.x), &(b.y), &(b.h), &(b.w));
    if(is_overlap(a,b) == 1)
    {
        printf("\nBoth the rectangles overlap");
        print_overlap(a,b);
    }
    else
    {
        printf("\nBoth the rectangles don't overlap");
    }
    return 0;
}

Output :