给定一个点(x1,y1,z1)和一个平面a * x + b * y + c * z + d =0。任务是找到该点与给定平面之间的垂直(最短)距离。
例子 :
Input: x1 = 4, y1 = -4, z1 = 3, a = 2, b = -2, c = 5, d = 8
Output: Perpendicular distance is 6.78902858227
Input: x1 = 2, y1 = 8, z1 = 5, a = 1, b = -2, c = -2, d = -1
Output: Perpendicular distance is 8.33333333333
方法:从给定点到平面的垂直距离(即最短距离)是从该点到给定平面的垂直距离。设给定点的坐标为(x1,y1,z1)
平面方程由方程a * x + b * y + c * z + d = 0给出,其中a,b和c为实常数。
3-D中点与平面之间的距离的公式由下式给出:
Distance = (| a*x1 + b*y1 + c*z1 + d |) / (sqrt( a*a + b*b + c*c))
下面是上述公式的实现:
C++
// C++ program to find the
// Perpendicular(shortest)
// distance between a point
// and a Plane in 3 D.
#include
#include
using namespace std;
// Function to find distance
void shortest_distance(float x1, float y1,
float z1, float a,
float b, float c,
float d)
{
d = fabs((a * x1 + b * y1 +
c * z1 + d));
float e = sqrt(a * a + b *
b + c * c);
cout << "Perpendicular distance is "
<< (d / e);
return;
}
// Driver Code
int main()
{
float x1 = 4;
float y1 = -4;
float z1 = 3;
float a = 2;
float b = -2;
float c = 5;
float d = 8;
// Function call
shortest_distance(x1, y1, z1,
a, b, c, d);
}
// This code is contributed
// by Akanksha Rai(Abby_akku)
C
// C program to find the Perpendicular(shortest)
// distance between a point and a Plane in 3 D.
#include
#include
// Function to find distance
void shortest_distance(float x1, float y1, float z1,
float a, float b, float c, float d)
{
d = fabs((a * x1 + b * y1 + c * z1 + d));
float e = sqrt(a * a + b * b + c * c);
printf("Perpendicular distance is %f", d/e);
return;
}
// Driver Code
int main()
{
float x1 = 4;
float y1 = -4;
float z1 = 3;
float a = 2;
float b = -2;
float c = 5;
float d = 8;
// Function call
shortest_distance(x1, y1, z1, a, b, c, d);
}
// This code is contributed
// by Amber_Saxena.
Java
// Java program to find the
// Perpendicular(shortest)
// distance between a point
// and a Plane in 3 D.
import java .io.*;
class GFG
{
// Function to find distance
static void shortest_distance(float x1, float y1,
float z1, float a,
float b, float c,
float d)
{
d = Math.abs((a * x1 + b *
y1 + c * z1 + d));
float e = (float)Math.sqrt(a * a + b *
b + c * c);
System.out.println("Perpendicular distance " +
"is " + d / e);
}
// Driver code
public static void main(String[] args)
{
float x1 = 4;
float y1 = -4;
float z1 = 3;
float a = 2;
float b = -2;
float c = 5;
float d = 8;
// Function call
shortest_distance(x1, y1, z1,
a, b, c, d);
}
}
// This code is contributed
// by Amber_Saxena.
Python
# Python program to find the Perpendicular(shortest)
# distance between a point and a Plane in 3 D.
import math
# Function to find distance
def shortest_distance(x1, y1, z1, a, b, c, d):
d = abs((a * x1 + b * y1 + c * z1 + d))
e = (math.sqrt(a * a + b * b + c * c))
print("Perpendicular distance is"), d/e
# Driver Code
x1 = 4
y1 = -4
z1 = 3
a = 2
b = -2
c = 5
d = 8
# Function call
shortest_distance(x1, y1, z1, a, b, c, d)
C#
// C# program to find the
// Perpendicular(shortest)
// distance between a point
// and a Plane in 3 D.
using System;
class GFG
{
// Function to find distance
static void shortest_distance(float x1, float y1,
float z1, float a,
float b, float c,
float d)
{
d = Math.Abs((a * x1 + b *
y1 + c * z1 + d));
float e = (float)Math.Sqrt(a * a + b *
b + c * c);
Console.Write("Perpendicular distance " +
"is " + d / e);
}
// Driver code
public static void Main()
{
float x1 = 4;
float y1 = -4;
float z1 = 3;
float a = 2;
float b = -2;
float c = 5;
float d = 8;
// Function call
shortest_distance(x1, y1, z1,
a, b, c, d);
}
}
// This code is contributed
// by ChitraNayal
PHP
输出:
Perpendicular distance is 6.78902858227