Find mirror image of a point in 2-D plane in C++

In this problem, we are given a point P in a 2-D plane and the points a, b, c of the equation ax + by + c = 0. Our task is to find a mirror image of a point in 2-D plane.

Let’s take an example to understand the problem,

Input

P = (2, 1), a = 1, b = -1, c = 0

Output

(1, 2)

Explanation

The plane looks like,

Solution Approach

To solve the problem, we need to find the equation point P' with coordinates (x', y'). So, we have R, the midpoint where the line form P - P' intersects the mirror line.

The line P-R-P' is perpendicular to the mirror. Hence, the equation of line will be,

ay - by + d = 0

The points are P(x, y) ; P'(x', y') ; R(xm, ym).

The points P and R are known. So, using the equations we will find P’ as,

$$\left(\frac{??'-??}{??}\right)=\left(\frac{??'-??}{??}\right)=\left(\frac{????-????+??}{??^2+x^2}\right)$$

Program to illustrate the working of our solution,

Example

 Live Demo

#include <iostream>
using namespace std;
void findMirrorImage( double a, double b, double c, double x, double y){
   double points = -2 * (a * x + b * y + c) / (a * a + b * b);
   double xm = points * a + x;
   double ym = points * b + y;
   cout<<"("<<xm<<","<<ym<<")";
}
int main(){
   double a = -1.0;
   double b = 1.0;
   double c = 0.0;
   double x = 1.0;
   double y = 0.0;
   cout<<"Image of point ("<<x<<", "<<y<<") using mirror ("<<a<<")x + ("<<b<<")y + ("<<c<< ") = 0, is :";
   findMirrorImage(a, b, c, x, y);
   return 0;
}

Output

Image of point (1, 0) using mirror (-1)x + (1)y + (0) = 0, is :(0,1)

Sudhir sharma

Published on 12-Mar-2021 07:10:46

• Related Questions & Answers
• Validating a square in a 2-D plane in JavaScript
• Finding distance between two points in a 2-D plane using JavaScript
• Find foot of perpendicular from a point in 2D plane to a Line in C++
• C++ Program to find out the moves to read a point from another point in a 2D plane
• C++ Program to Check if a Point d lies inside or outside a circle defined by Points a, b, c in a Plane
• Print the Mirror Image of Sine-Wave Pattern in C
• Create a mirror image with CSS
• Emulating a 2-d array using 1-d array in C++
• C++ Program to check whether points in a 3-D plane are Coplanar
• Find mirror of a given node in Binary tree in C++
• Print a 2 D Array or Matrix in C#
• Find 2^(2^A) % B in C++
• Count of parallelograms in a plane in C++
• C++ Program for triangular pattern (mirror image around 0)
• Sum of the mirror image nodes of a complete binary tree in an inorder way in C++