Dados dos planos P1: a1 * x + b1 * y + c1 * z + d1 = 0 y P2: a2 * x + b2 * y + c2 * z + d2 = 0. La tarea es encontrar el ángulo entre estos dos planos en 3D
Ejemplos:
Entrada: a1 = 1, b1 = 1, c1 = 2, d1 = 1, a2 = 2, b2 = -1, c2 = 1, d2 = -4
Salida: El ángulo es de 60,0 grados
Entrada: a1 = 2, b1 = 2 , c1 = -3, d1 = -5, a2 = 3, b2 = -3, c2 = 5, d2 = -6
Salida: El ángulo es 123,696598882 grados
Enfoque: Considere las siguientes ecuaciones de dos planos dados:
P1 : a1 * x + b1 * y + c1 * z + d1 = 0 and, P2 : a2 * x + b2 * y + c2 * z + d2 = 0,
donde a1, b1, c1 y a2, b2, c2 son relaciones de dirección de la normal al plano P1 y P2.
El ángulo entre dos planos es igual al ángulo determinado por los vectores normales de los planos.
El ángulo entre estos planos se obtiene usando la siguiente fórmula:
Cos A = 
Usando la propiedad inversa, obtenemos:
A = 
A continuación se muestra la implementación de las fórmulas anteriores:
C++
// C++ program to find
// the Angle between
// two Planes in 3 D.
#include <bits/stdc++.h>
#include<math.h>
using namespace std;
// Function to find Angle
void distance(float a1, float b1,
float c1, float a2,
float b2, float c2)
{
float d = (a1 * a2 + b1 *
b2 + c1 * c2);
float e1 = sqrt(a1 * a1 + b1 *
b1 + c1 * c1);
float e2 = sqrt(a2 * a2 + b2 *
b2 + c2 * c2);
d = d / (e1 * e2);
float pi = 3.14159;
float A = (180 / pi) * (acos(d));
cout << "Angle is "
<< A << " degree";
}
// Driver Code
int main()
{
float a1 = 1;
float b1 = 1;
float c1 = 2;
float d1 = 1;
float a2 = 2;
float b2 = -1;
float c2 = 1;
float d2 = -4;
distance(a1, b1, c1,
a2, b2, c2);
return 0;
}
// This code is contributed
// by Akanksha Rai(Abby_akku)
C
// C program to find
// the Angle between
// two Planes in 3 D.
#include<stdio.h>
#include<math.h>
// Function to find Angle
void distance(float a1, float b1,
float c1, float a2,
float b2, float c2)
{
float d = (a1 * a2 + b1 *
b2 + c1 * c2);
float e1 = sqrt(a1 * a1 + b1 *
b1 + c1 * c1);
float e2 = sqrt(a2 * a2 + b2 *
b2 + c2 * c2);
d = d / (e1 * e2);
float pi = 3.14159;
float A = (180 / pi) * (acos(d));
printf("Angle is %.2f degree", A);
}
// Driver Code
int main()
{
float a1 = 1;
float b1 = 1;
float c1 = 2;
float d1 = 1;
float a2 = 2;
float b2 = -1;
float c2 = 1;
float d2 = -4;
distance(a1, b1, c1,
a2, b2, c2);
return 0;
}
// This code is contributed
// by Amber_Saxena.
Java
// Java program to find
// the Angle between
// two Planes in 3 D.
import java .io.*;
import java.lang.Math;
class GFG
{
// Function to find Angle
static void distance(float a1, float b1,
float c1, float a2,
float b2, float c2)
{
float d = (a1 * a2 + b1 *
b2 + c1 * c2);
float e1 = (float)Math.sqrt(a1 * a1 + b1 *
b1 + c1 * c1);
float e2 = (float)Math.sqrt(a2 * a2 + b2 *
b2 + c2 * c2);
d = d / (e1 * e2);
float pi = (float)3.14159;
float A = (180 / pi) * (float)(Math.acos(d));
System.out.println("Angle is "+ A +" degree");
}
// Driver code
public static void main(String[] args)
{
float a1 = 1;
float b1 = 1;
float c1 = 2;
float d1 = 1;
float a2 = 2;
float b2 = -1;
float c2 = 1;
float d2 = -4;
distance(a1, b1, c1,
a2, b2, c2);
}
}
// This code is contributed
// by Amber_Saxena.
Python
# Python program to find the Angle between
# two Planes in 3 D.
import math
# Function to find Angle
def distance(a1, b1, c1, a2, b2, c2):
d = ( a1 * a2 + b1 * b2 + c1 * c2 )
e1 = math.sqrt( a1 * a1 + b1 * b1 + c1 * c1)
e2 = math.sqrt( a2 * a2 + b2 * b2 + c2 * c2)
d = d / (e1 * e2)
A = math.degrees(math.acos(d))
print("Angle is"), A, ("degree")
# Driver Code
a1 = 1
b1 = 1
c1 = 2
d1 = 1
a2 = 2
b2 = -1
c2 = 1
d2 = -4
distance(a1, b1, c1, a2, b2, c2)
C#
// C# program to find
// the Angle between
// two Planes in 3 D.
using System;
class GFG
{
// Function to find Angle
static void distance(float a1, float b1,
float c1, float a2,
float b2, float c2)
{
float d = (a1 * a2 + b1 *
b2 + c1 * c2);
float e1 = (float)Math.Sqrt(a1 * a1 + b1 *
b1 + c1 * c1);
float e2 = (float)Math.Sqrt(a2 * a2 + b2 *
b2 + c2 * c2);
d = d / (e1 * e2);
float pi = (float)3.14159;
float A = (180 / pi) * (float)(Math.Acos(d));
Console.Write("Angle is "+ A +" degree");
}
// Driver code
public static void Main()
{
float a1 = 1;
float b1 = 1;
float c1 = 2;
float a2 = 2;
float b2 = -1;
float c2 = 1;
distance(a1, b1, c1,
a2, b2, c2);
}
}
// This code is contributed
// by ChitraNayal
PHP
<?php
// PHP program to find the Angle
// between two Planes in 3 D.
// Function to find Angle
function distance($a1, $b1,
$c1, $a2,
$b2, $c2)
{
$d = ($a1 * $a2 + $b1 *
$b2 + $c1 * $c2);
$e1 = sqrt($a1 * $a1 + $b1 *
$b1 + $c1 * $c1);
$e2 = sqrt($a2 * $a2 + $b2 *
$b2 + $c2 * $c2);
$d = $d / ($e1 * $e2);
$pi = 3.14159;
$A = (180 / $pi) * (acos($d));
echo sprintf("Angle is %.2f degree", $A);
}
// Driver Code
$a1 = 1;
$b1 = 1;
$c1 = 2;
$d1 = 1;
$a2 = 2;
$b2 = -1;
$c2 = 1;
$d2 = -4;
distance($a1, $b1, $c1,
$a2, $b2, $c2);
// This code is contributed
// by Amber_Saxena.
?>
Javascript
<script>
// JavaScript program to find
// the Angle between
// two Planes in 3 D.
// Function to find Angle
function distance(a1, b1, c1, a2, b2, c2)
{
var d = a1 * a2 + b1 * b2 + c1 * c2;
var e1 = Math.sqrt(a1 * a1 + b1 * b1 + c1 * c1);
var e2 = Math.sqrt(a2 * a2 + b2 * b2 + c2 * c2);
d = parseFloat(d / (e1 * e2));
var pi = 3.14159;
var A = (180 / pi) * Math.acos(d);
document.write("Angle is " + A.toFixed(1) + " degree");
}
// Driver Code
var a1 = 1;
var b1 = 1;
var c1 = 2;
var d1 = 1;
var a2 = 2;
var b2 = -1;
var c2 = 1;
var d2 = -4;
distance(a1, b1, c1, a2, b2, c2);
</script>
Producción:
Angle is 60.0 degree
Publicación traducida automáticamente
Artículo escrito por anamika9988 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA