Program to check whether 4 points in a 3-D plane are Coplanar - GeeksforGeeks

05 Nov, 2021
Given 4 points (x1, y1, z1), (x2, y2, z2), (x3, y3, z3), (x4, y4, z4). The task is to write a program to check whether these 4 points are coplanar or not.Note: 4 points in a 3-D plane are said to be coplanar if they lies in the same plane.  
Examples:  
Input:
x1 = 3, y1 = 2, z1 = -5
x2 = -1, y2 = 4, z2 = -3
x3 = -3, y3 = 8, z3 = -5
x4 = -3, y4 = 2, z4 = 1
Output: Coplanar

Input:
x1 = 0, y1 = -1, z1 = -1
x2 = 4, y2 = 5, z2 = 1
x3 = 3, y3 = 9, z3 = 4
x4 = -4, y4 = 4, z4 = 3
Output: Not Coplanar
 
Approach:  
To check whether 4 points are coplanar or not, first of all, find the equation of the plane passing through any three of the given points. Approach to find equation of a plane passing through 3 points.Then, check whether the 4th point satisfies the equation obtained in step 1. That is, putting the value of 4th point in the equation obtained. If it satisfies the equation then the 4 points are Coplanar otherwise not.
To check whether 4 points are coplanar or not, first of all, find the equation of the plane passing through any three of the given points. Approach to find equation of a plane passing through 3 points.
Then, check whether the 4th point satisfies the equation obtained in step 1. That is, putting the value of 4th point in the equation obtained. If it satisfies the equation then the 4 points are Coplanar otherwise not.
Below is the implementation of the above idea:  
C++
Java
Python3
C#
PHP
Javascript
// C++ program to check if 4 points// in a 3-D plane are Coplanar #include<bits/stdc++.h>using namespace std ; // Function to find equation of plane.void equation_plane(int x1,int y1,int z1,int x2,int y2,int z2,             int x3, int y3, int z3, int x, int y, int z)    {    int a1 = x2 - x1 ;    int b1 = y2 - y1 ;    int c1 = z2 - z1 ;    int a2 = x3 - x1 ;    int b2 = y3 - y1 ;    int c2 = z3 - z1 ;    int a = b1 * c2 - b2 * c1 ;    int b = a2 * c1 - a1 * c2 ;    int c = a1 * b2 - b1 * a2 ;    int d = (- a * x1 - b * y1 - c * z1) ;           // equation of plane is: a*x + b*y + c*z = 0 #           // checking if the 4th point satisfies    // the above equation    if(a * x + b * y + c * z + d == 0)        cout << "Coplanar" << endl;    else        cout << "Not Coplanar" << endl;                      }     // Driver Codeint main(){      int x1 = 3 ;int y1 = 2 ;int z1 = -5 ;int x2 = -1 ;int y2 = 4 ;int z2 = -3 ;int x3 = -3 ;int y3 = 8 ;int z3 = -5 ;int x4 = -3 ;int y4 = 2 ;int z4 = 1 ; // function callingequation_plane(x1, y1, z1, x2, y2, z2, x3,                             y3, z3, x4, y4, z4) ;                           return 0; // This code is contributed by ANKITRAI1}
//Java program to check if 4 points//in a 3-D plane are Coplanar public class GFG {     //Function to find equation of plane.    static void equation_plane(int x1,int y1,int z1,int x2,int y2,int z2,              int x3, int y3, int z3, int x, int y, int z)     {     int a1 = x2 - x1 ;     int b1 = y2 - y1 ;     int c1 = z2 - z1 ;     int a2 = x3 - x1 ;     int b2 = y3 - y1 ;     int c2 = z3 - z1 ;     int a = b1 * c2 - b2 * c1 ;     int b = a2 * c1 - a1 * c2 ;     int c = a1 * b2 - b1 * a2 ;     int d = (- a * x1 - b * y1 - c * z1) ;              // equation of plane is: a*x + b*y + c*z = 0 #              // checking if the 4th point satisfies     // the above equation     if(a * x + b * y + c * z + d == 0)         System.out.println("Coplanar");     else         System.out.println("Not Coplanar");                         }           //Driver Code    public static void main(String[] args) {                 int x1 = 3 ;        int y1 = 2 ;        int z1 = -5 ;        int x2 = -1 ;        int y2 = 4 ;        int z2 = -3 ;        int x3 = -3 ;        int y3 = 8 ;        int z3 = -5 ;        int x4 = -3 ;        int y4 = 2 ;        int z4 = 1 ;         //function calling        equation_plane(x1, y1, z1, x2, y2, z2, x3,                                  y3, z3, x4, y4, z4) ;                               }}
# Python program to check if 4 points# in a 3-D plane are Coplanar # Function to find equation of plane.def equation_plane(x1, y1, z1, x2, y2, z2, x3,                                y3, z3, x, y, z):         a1 = x2 - x1    b1 = y2 - y1    c1 = z2 - z1    a2 = x3 - x1    b2 = y3 - y1    c2 = z3 - z1    a = b1 * c2 - b2 * c1    b = a2 * c1 - a1 * c2    c = a1 * b2 - b1 * a2    d = (- a * x1 - b * y1 - c * z1)         # equation of plane is: a*x + b*y + c*z = 0 #         # checking if the 4th point satisfies    # the above equation    if(a * x + b * y + c * z + d == 0):        print("Coplanar")    else:        print("Not Coplanar")          # Driver Codex1 = 3y1 = 2z1 = -5x2 = -1y2 = 4z2 = -3x3 = -3y3 = 8z3 = -5x4 = -3y4 = 2z4 = 1equation_plane(x1, y1, z1, x2, y2, z2, x3,                            y3, z3, x4, y4, z4)
// C# program to check if 4 points// in a 3-D plane are Coplanarusing System; class GFG{ // Function to find equation of plane.static void equation_plane(int x1, int y1, int z1,                           int x2, int y2, int z2,                           int x3, int y3, int z3,                           int x, int y, int z){    int a1 = x2 - x1 ;    int b1 = y2 - y1 ;    int c1 = z2 - z1 ;    int a2 = x3 - x1 ;    int b2 = y3 - y1 ;    int c2 = z3 - z1 ;    int a = b1 * c2 - b2 * c1 ;    int b = a2 * c1 - a1 * c2 ;    int c = a1 * b2 - b1 * a2 ;    int d = (- a * x1 - b * y1 - c * z1) ;             // equation of plane is: a*x + b*y + c*z = 0 #             // checking if the 4th point satisfies    // the above equation    if(a * x + b * y + c * z + d == 0)        Console.WriteLine("Coplanar");    else        Console.WriteLine("Not Coplanar");                     }     // Driver Codestatic public void Main (){    int x1 = 3 ;    int y1 = 2 ;    int z1 = -5 ;    int x2 = -1 ;    int y2 = 4 ;    int z2 = -3 ;    int x3 = -3 ;    int y3 = 8 ;    int z3 = -5 ;    int x4 = -3 ;    int y4 = 2 ;    int z4 = 1 ;     //function calling    equation_plane(x1, y1, z1, x2, y2, z2,                   x3, y3, z3, x4, y4, z4);                        }} // This code is contributed by jit_t
<?php// PHP program to check if 4 points// in a 3-D plane are Coplanar // Function to find equation of plane.function equation_plane($x1, $y1, $z1, $x2,                        $y2, $z2, $x3, $y3,                        $z3, $x, $y, $z){    $a1 = $x2 - $x1;    $b1 = $y2 - $y1;    $c1 = $z2 - $z1;    $a2 = $x3 - $x1;    $b2 = $y3 - $y1;    $c2 = $z3 - $z1;    $a = $b1 * $c2 - $b2 * $c1;    $b = $a2 * $c1 - $a1 * $c2;    $c = $a1 * $b2 - $b1 * $a2;    $d = (- $a * $x1 - $b *            $y1 - $c * $z1);         // equation of plane is:    // a*x + b*y + c*z = 0 #         // checking if the 4th point     // satisfies the above equation    if($a * $x + $b * $y +       $c * $z + $d == 0)        echo ("Coplanar");    else        echo ("Not Coplanar");}     // Driver Code$x1 = 3; $y1 = 2; $z1 = -5;$x2 = -1; $y2 = 4; $z2 = -3;$x3 = -3; $y3 = 8; $z3 = -5;$x4 = -3; $y4 = 2; $z4 = 1; // function callingequation_plane($x1, $y1, $z1,               $x2, $y2, $z2,               $x3, $y3, $z3,               $x4, $y4, $z4);                     // This code is contributed// by Shivi_Aggarwal?>
<script>//javascript program to check if 4 points//in a 3-D plane are Coplanar     // Function to find equation of plane.    function equation_plane(x1 , y1 , z1 , x2 , y2 , z2    , x3 , y3 , z3 , x , y, z)    {        var a1 = x2 - x1;        var b1 = y2 - y1;        var c1 = z2 - z1;        var a2 = x3 - x1;        var b2 = y3 - y1;        var c2 = z3 - z1;        var a = b1 * c2 - b2 * c1;        var b = a2 * c1 - a1 * c2;        var c = a1 * b2 - b1 * a2;        var d = (-a * x1 - b * y1 - c * z1);         // equation of plane is: a*x + b*y + c*z = 0 #         // checking if the 4th point satisfies        // the above equation        if (a * x + b * y + c * z + d == 0)            document.write("Coplanar");        else            document.write("Not Coplanar");     }     // Driver Code        var x1 = 3;        var y1 = 2;        var z1 = -5;        var x2 = -1;        var y2 = 4;        var z2 = -3;        var x3 = -3;        var y3 = 8;        var z3 = -5;        var x4 = -3;        var y4 = 2;        var z4 = 1;         // function calling        equation_plane(x1, y1, z1, x2, y2, z2,        x3, y3, z3, x4, y4, z4);  // This code is contributed by Rajput-Ji</script>
Coplanar
 
ankthon
ukasp
Shivi_Aggarwal
jit_t
Rajput-Ji
arorakashish0911
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