Find Corners of Rectangle using mid points - GeeksforGeeks

11 Mar, 2022
Consider a rectangle ABCD, we’re given the co-ordinates of the mid points of side AD and BC (p and q respectively) along with their length L (AD = BC = L). Now given the parameters, we need to print the co-ordinates of the 4 points A, B, C and D. 
Examples: 
Input : p = (1, 0)
        q = (1, 2)
        L = 2
Output : (0, 0), (0, 2), (2, 2), (2, 0)
Explanation:
The printed points form a rectangle which
satisfy the input constraints.

Input : p = (1, 1)
        q = (-1, -1)
        L = 2*sqrt(2)
Output : (0, 2), (-2, 0), (0, -2), (2, 0)
From the problem statement 3 cases can arise :  
The Rectangle is horizontal i.e., AD and BC are parallel to X-axisThe Rectangle is vertical i.e., AD and BC are parallel to Y-axisThe Rectangle is inclined at a certain angle with the axes
The Rectangle is horizontal i.e., AD and BC are parallel to X-axis
The Rectangle is vertical i.e., AD and BC are parallel to Y-axis
The Rectangle is inclined at a certain angle with the axes
The first two cases are trivial and can easily be solved using basic geometry. For the third case we need to apply some mathematical concepts to find the points.
Consider the above diagram for clarity. We have the co-ordinates of p and q. Thus we can find the slope of AD and BC (As pq is perpendicular to AD). Once we have the slope of AD, we can find the equation of straight line passing through AD. Now we can apply distance formula to obtain the displacements along X and Y axes.  
If slope of AD = m, then
m = (p.x- q.x)/(q.y - p.y)

and displacement along X axis, dx =  
   L/(2*sqrt(1+m*m))

Similarly, dy = m*L/(2*sqrt(1+m*m))
Now we can simply find the co-ordinates of 4 corners by simply adding and subtracting the displacements obtained accordingly. 
Below is the implementation .  
C++
Java
Python3
C#
Javascript
// C++ program to find corner points of// a rectangle using given length and middle// points.#include <bits/stdc++.h>using namespace std; // Structure to represent a co-ordinate pointstruct Point{    float x, y;    Point()    {        x = y = 0;    }    Point(float a, float b)    {        x = a, y = b;    }}; // This function receives two points and length// of the side of rectangle and prints the 4// corner points of the rectanglevoid printCorners(Point p, Point q, float l){    Point a, b, c, d;     // horizontal rectangle    if (p.x == q.x)    {        a.x = p.x - (l/2.0);        a.y = p.y;         d.x = p.x + (l/2.0);        d.y = p.y;         b.x = q.x - (l/2.0);        b.y = q.y;         c.x = q.x + (l/2.0);        c.y = q.y;    }     // vertical rectangle    else if (p.y == q.y)    {        a.y = p.y - (l/2.0);        a.x = p.x;         d.y = p.y + (l/2.0);        d.x = p.x;         b.y = q.y - (l/2.0);        b.x = q.x;         c.y = q.y + (l/2.0);        c.x = q.x;    }     // slanted rectangle    else    {        // calculate slope of the side        float m = (p.x-q.x)/float(q.y-p.y);         // calculate displacements along axes        float dx = (l /sqrt(1+(m*m))) *0.5 ;        float dy = m*dx;         a.x = p.x - dx;        a.y = p.y - dy;         d.x = p.x + dx;        d.y = p.y + dy;         b.x = q.x - dx;        b.y = q.y - dy;         c.x = q.x + dx;        c.y = q.y + dy;    }     cout << a.x << ", " << a.y << " n"         << b.x << ", " << b.y << "n";         << c.x << ", " << c.y << " n"         << d.x << ", " << d.y << "nn";} // Driver codeint main(){    Point p1(1, 0), q1(1, 2);    printCorners(p1, q1, 2);     Point p(1, 1), q(-1, -1);    printCorners(p, q, 2*sqrt(2));     return 0;}
// Java program to find corner points of// a rectangle using given length and middle// points. class GFG{     // Structure to represent a co-ordinate point    static class Point    {         float x, y;         Point()        {            x = y = 0;        }         Point(float a, float b)        {            x = a;            y = b;        }    };     // This function receives two points and length    // of the side of rectangle and prints the 4    // corner points of the rectangle    static void printCorners(Point p, Point q, float l)    {        Point a = new Point(), b = new Point(),                c = new Point(), d = new Point();         // horizontal rectangle        if (p.x == q.x)        {            a.x = (float) (p.x - (l / 2.0));            a.y = p.y;             d.x = (float) (p.x + (l / 2.0));            d.y = p.y;             b.x = (float) (q.x - (l / 2.0));            b.y = q.y;             c.x = (float) (q.x + (l / 2.0));            c.y = q.y;        }        // vertical rectangle        else if (p.y == q.y)        {            a.y = (float) (p.y - (l / 2.0));            a.x = p.x;             d.y = (float) (p.y + (l / 2.0));            d.x = p.x;             b.y = (float) (q.y - (l / 2.0));            b.x = q.x;             c.y = (float) (q.y + (l / 2.0));            c.x = q.x;        }        // slanted rectangle        else        {            // calculate slope of the side            float m = (p.x - q.x) / (q.y - p.y);             // calculate displacements along axes            float dx = (float) ((l / Math.sqrt(1 + (m * m))) * 0.5);            float dy = m * dx;             a.x = p.x - dx;            a.y = p.y - dy;             d.x = p.x + dx;            d.y = p.y + dy;             b.x = q.x - dx;            b.y = q.y - dy;             c.x = q.x + dx;            c.y = q.y + dy;        }         System.out.print((int)a.x + ", " + (int)a.y + " \n"                + (int)b.x + ", " + (int)b.y + "\n"                + (int)c.x + ", " + (int)c.y + " \n"                + (int)d.x + ", " + (int)d.y + "\n");    }     // Driver code    public static void main(String[] args)    {        Point p1 = new Point(1, 0), q1 = new Point(1, 2);        printCorners(p1, q1, 2);         Point p = new Point(1, 1), q = new Point(-1, -1);        printCorners(p, q, (float) (2 * Math.sqrt(2)));    }} // This code contributed by Rajput-Ji
# Python3 program to find corner points of# a rectangle using given length and middle# points.import math # Structure to represent a co-ordinate pointclass Point:         def __init__(self, a = 0, b = 0):                 self.x = a        self.y = b   # This function receives two points and length# of the side of rectangle and prints the 4# corner points of the rectangledef printCorners(p, q, l):         a, b, c, d = Point(), Point(), Point(), Point()         # Horizontal rectangle    if (p.x == q.x):        a.x = p.x - (l / 2.0)        a.y = p.y                 d.x = p.x + (l / 2.0)        d.y = p.y                 b.x = q.x - (l / 2.0)        b.y = q.y                 c.x = q.x + (l / 2.0)        c.y = q.y             # Vertical rectangle    else if (p.y == q.y):        a.y = p.y - (l / 2.0)        a.x = p.x                 d.y = p.y + (l / 2.0)        d.x = p.x                 b.y = q.y - (l / 2.0)        b.x = q.x                 c.y = q.y + (l / 2.0)        c.x = q.x         # Slanted rectangle    else:                 # Calculate slope of the side        m = (p.x - q.x) / (q.y - p.y)                 # Calculate displacements along axes        dx = (l / math.sqrt(1 + (m * m))) * 0.5        dy = m * dx                 a.x = p.x - dx        a.y = p.y - dy                 d.x = p.x + dx        d.y = p.y + dy                 b.x = q.x - dx        b.y = q.y - dy                 c.x = q.x + dx        c.y = q.y + dy             print(int(a.x), ", ", int(a.y), sep = "")    print(int(b.x), ", ", int(b.y), sep = "")    print(int(c.x), ", ", int(c.y), sep = "")    print(int(d.x), ", ", int(d.y), sep = "")    print()     # Driver codep1 = Point(1, 0)q1 = Point(1, 2)printCorners(p1, q1, 2) p = Point(1, 1)q = Point(-1, -1)printCorners(p, q, 2 * math.sqrt(2)) # This code is contributed by shubhamsingh10
// C# program to find corner points of// a rectangle using given length and middle// points.using System; class GFG{     // Structure to represent a co-ordinate point    public class Point    {         public float x, y;         public Point()        {            x = y = 0;        }         public Point(float a, float b)        {            x = a;            y = b;        }    };     // This function receives two points and length    // of the side of rectangle and prints the 4    // corner points of the rectangle    static void printCorners(Point p, Point q, float l)    {        Point a = new Point(), b = new Point(),                c = new Point(), d = new Point();         // horizontal rectangle        if (p.x == q.x)        {            a.x = (float) (p.x - (l / 2.0));            a.y = p.y;             d.x = (float) (p.x + (l / 2.0));            d.y = p.y;             b.x = (float) (q.x - (l / 2.0));            b.y = q.y;             c.x = (float) (q.x + (l / 2.0));            c.y = q.y;        }                 // vertical rectangle        else if (p.y == q.y)        {            a.y = (float) (p.y - (l / 2.0));            a.x = p.x;             d.y = (float) (p.y + (l / 2.0));            d.x = p.x;             b.y = (float) (q.y - (l / 2.0));            b.x = q.x;             c.y = (float) (q.y + (l / 2.0));            c.x = q.x;        }                 // slanted rectangle        else        {            // calculate slope of the side            float m = (p.x - q.x) / (q.y - p.y);             // calculate displacements along axes            float dx = (float) ((l / Math.Sqrt(1 + (m * m))) * 0.5);            float dy = m * dx;             a.x = p.x - dx;            a.y = p.y - dy;             d.x = p.x + dx;            d.y = p.y + dy;             b.x = q.x - dx;            b.y = q.y - dy;             c.x = q.x + dx;            c.y = q.y + dy;        }         Console.Write((int)a.x + ", " + (int)a.y + " \n"                + (int)b.x + ", " + (int)b.y + "\n"                + (int)c.x + ", " + (int)c.y + " \n"                + (int)d.x + ", " + (int)d.y + "\n");    }     // Driver code    public static void Main(String[] args)    {        Point p1 = new Point(1, 0), q1 = new Point(1, 2);        printCorners(p1, q1, 2);         Point p = new Point(1, 1), q = new Point(-1, -1);        printCorners(p, q, (float) (2 * Math.Sqrt(2)));    }} // This code has been contributed by 29AjayKumar
<script>// Javascript program to find corner points of// a rectangle using given length and middle// points. // Structure to represent a co-ordinate pointclass Point{    constructor(a,b)    {        this.x=a;        this.y=b;    }} // This function receives two points and length    // of the side of rectangle and prints the 4    // corner points of the rectanglefunction printCorners(p,q,l){    let a = new Point(), b = new Point(),                c = new Point(), d = new Point();           // horizontal rectangle        if (p.x == q.x)        {            a.x =  (p.x - (l / 2.0));            a.y = p.y;               d.x =  (p.x + (l / 2.0));            d.y = p.y;               b.x =  (q.x - (l / 2.0));            b.y = q.y;               c.x =  (q.x + (l / 2.0));            c.y = q.y;        }        // vertical rectangle        else if (p.y == q.y)        {            a.y = (p.y - (l / 2.0));            a.x = p.x;               d.y = (p.y + (l / 2.0));            d.x = p.x;               b.y = (q.y - (l / 2.0));            b.x = q.x;               c.y = (q.y + (l / 2.0));            c.x = q.x;        }        // slanted rectangle        else        {            // calculate slope of the side            let m = (p.x - q.x) / (q.y - p.y);               // calculate displacements along axes            let dx =  ((l / Math.sqrt(1 + (m * m))) * 0.5);            let dy = m * dx;               a.x = p.x - dx;            a.y = p.y - dy;               d.x = p.x + dx;            d.y = p.y + dy;               b.x = q.x - dx;            b.y = q.y - dy;               c.x = q.x + dx;            c.y = q.y + dy;        }           document.write(a.x + ", " + a.y + " <br>"                + b.x + ", " + b.y + "<br>"                + c.x + ", " + c.y + " <br>"                + d.x + ", " + d.y + "<br>");} // Driver codelet p1 = new Point(1, 0), q1 = new Point(1, 2);printCorners(p1, q1, 2); let p = new Point(1, 1), q = new Point(-1, -1);printCorners(p, q,  (2 * Math.sqrt(2))); // This code is contributed by rag2127</script>
Output: 
0, 0 
0, 2
2, 2 
2, 0

0, 2 
-2, 0
0, -2 
2, 0
Reference: StackOverflowThis article is contributed by Ashutosh Kumar  If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 
Rajput-Ji
29AjayKumar
rag2127
SHUBHAMSINGH10
simmytarika5
square-rectangle
Geometric
Geometric
Writing code in comment?
Please use ide.geeksforgeeks.org,
generate link and share the link here.
Haversine formula to find distance between two points on a sphere
Program to find slope of a line
Equation of circle when three points on the circle are given
Program to find line passing through 2 Points
Maximum Manhattan distance between a distinct pair from N coordinates
Orientation of 3 ordered points
Minimum Cost Polygon Triangulation
Check if a line touches or intersects a circle
Quickhull Algorithm for Convex Hull
Program to find area of a circle