Program to find X, Y and Z intercepts of a plane

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In this article, it is explained how to find the X, Y, and Z intercepts of a plane. There are two ways to find the intercepts:

Case 1: When the general equation of the plane is given.

Examples:

Input: A = -6, B = 5, C = -3, D = 9 
Output:
1.5 
-1.8 
3.0

Input: A = 7, B = 4, C = 5, D = -7 
Output: 
1.0 
1.75 
1.4

Approach:

The result can be computed by following the below steps:

Convert general equation of a plane Ax + By + Cz + D = 0 to Ax + By + Cz = – D
Divide by -D into both sides of the equation
So, the equation becomes x/(-D/A) + y/(-D/B) + z(-D/C) = 1
The above equation is in the intercept form of a plane. Therefore,
X intercepts will be = -D/A
Y intercepts will be = -D/B
Z intercepts will be = -D/C

Below is the implementation of the above approach:

C++

// C++ program to find the 
// X, Y and Z intercepts of a plane
#include<iostream>
using namespace std;
 
float * XandYandZintercept(float A, float B,
                            float C, float D)
{
        static float rslt[3];
         
        // For finding the x-intercept 
        // put y = 0 and z = 0 
        float x = -D / A ;
     
        // For finding the y-intercept 
        // put x = 0 and z = 0 
        float y = -D / B ;
     
        // For finding the z-intercept 
        // put x = 0 and y = 0 
        float z = -D / C ;
         
        rslt[0] = x;
        rslt[1] = y;
        rslt[2] = z;
         
        return rslt; 
}
     
// Driver code 
int main () 
{
    int A = 2 ;
    int B = 5 ;
    int C = 7;
    int D = 8 ;
         
    float *rslt = XandYandZintercept(A, B, C, D);
         
    for(int i = 0; i < 3 ; i++)
    {
        cout << rslt[i] << " ";
    }
     
}
 
// This code is contributed by ANKITKUMAR34

Java

// Java program to find the 
// X, Y and Z intercepts of a plane
class GFG 
{
     
    static float[] XandYandZintercept(float A, 
                    float B, float C, float D)
    {
        float rslt[] = new float[3];
         
        // For finding the x-intercept 
        // put y = 0 and z = 0 
        float x = -D / A ;
     
        // For finding the y-intercept 
        // put x = 0 and z = 0 
        float y = -D / B ;
     
        // For finding the z-intercept 
        // put x = 0 and y = 0 
        float z = -D / C ;
         
        rslt[0] = x;
        rslt[1] = y;
        rslt[2] = z;
         
        return rslt; 
    }
     
    // Driver code 
    public static void main (String[] args) 
    {
        int A = 2 ;
        int B = 5 ;
        int C = 7;
        int D = 8 ;
         
        float rslt[] = XandYandZintercept(A, B, C, D);
         
        for(int i = 0; i < 3 ; i++)
        {
            System.out.print(rslt[i] + " ");
        }
    }
}
 
// This code is contributed by AnkitRai01

Python3

# Python program to find the 
# X, Y and Z intercepts of a plane
 
def XandYandZintercept(A, B, C, D): 
 
    # For finding the x-intercept 
    # put y = 0 and z = 0
    x = -D / A
 
    # For finding the y-intercept 
    # put x = 0 and z = 0 
    y = -D / B 
 
    # For finding the z-intercept 
    # put x = 0 and y = 0
    z = -D / C
    return [x, y, z]
 
# Driver code
A = 2
B = 5
C = 7
D = 8
print(XandYandZintercept(A, B, C, D))

C#

// C# program to find the 
// X, Y and Z intercepts of a plane
using System;
 
class GFG 
{
     
    static float[] XandYandZintercept(float A, 
                    float B, float C, float D)
    {
        float []rslt = new float[3];
         
        // For finding the x-intercept 
        // put y = 0 and z = 0 
        float x = -D / A ;
     
        // For finding the y-intercept 
        // put x = 0 and z = 0 
        float y = -D / B ;
     
        // For finding the z-intercept 
        // put x = 0 and y = 0 
        float z = -D / C ;
         
        rslt[0] = x;
        rslt[1] = y;
        rslt[2] = z;
         
        return rslt; 
    }
     
    // Driver code 
    public static void Main() 
    {
        int A = 2 ;
        int B = 5 ;
        int C = 7;
        int D = 8 ;
         
        float []rslt = XandYandZintercept(A, B, C, D);
         
        for(int i = 0; i < 3 ; i++)
        {
            Console.Write(rslt[i] + " ");
        }
    }
}
 
// This code is contributed by AnkitRai01

Javascript

<script>
      // JavaScript program to find the
      // X, Y and Z intercepts of a plane
 
      function XandYandZintercept(A, B, C, D) {
        // For finding the x-intercept
        // put y = 0 and z = 0
        var x = -D / A;
 
        // For finding the y-intercept
        // put x = 0 and z = 0
        var y = -D / B;
 
        // For finding the z-intercept
        // put x = 0 and y = 0
        var z = -D / C;
        return [x, y, z];
      }
      function equation_plane(p, q, r) {
        var x1 = p[0];
        var y1 = p[1];
        var z1 = p[2];
        var x2 = q[0];
        var y2 = q[1];
        var z2 = q[2];
        var x3 = r[0];
        var y3 = r[1];
        var z3 = r[2];
 
        // For Finding value of A, B, C, D
        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;
 
        // Calling the first created function
 
        var [x, y, z] = XandYandZintercept(A, B, C, D);
        document.write(x + " " + y + " " + z);
      }
      // Driver Code
      var x1 = -1;
      var y1 = 2;
      var z1 = 1;
      var x2 = 0;
      var y2 = -3;
      var z2 = 2;
      var x3 = 1;
      var y3 = 1;
      var z3 = -4;
 
      var p = [x1, y1, z1];
      var q = [x2, y2, z2];
      var r = [x3, y3, z3];
 
      equation_plane(p, q, r);
    </script>

Output:

[-4.0, -1.6, -1.1428571428571428]

Time Complexity: O(1)

Auxiliary Space: O(1)

Case 2: When 3 non-collinear points are given.