3D 截面公式

给定 3D 中的两个坐标 (x1, y1, z1) 和 (x2, y2, z2) 以及 m 和 n，找到分割连接 (x1, y1, Z1) 和 (x2, y2, Z2) 的线的坐标) 的比率为 m:n。

例子：

Input : x1 = 2, y1 = -1, Z1 = 4, x2 = 4, y2 = 3, Z2 = 2, 
m = 2, n = 3 
Output : (2.8, .6, 3.2)
Explanation: co-ordinates (2.8, .6, 3.2) 
divides the line in ratio 2 : 3 
 

方法：
给定 3D 中的两个坐标 A(x1, y1, Z1) 和 B(x2, y2, Z2) 以及 m 和 n，我们必须找到分割连接 (x1, y1, Z1) 和 ( x2, y2, Z2) 的比率为 m:n。
让坐标为 P(x, y, z)
然后根据 3D 中的部分公式
x = (m * x2 + n * x1) / (m + n)
y = (m * y2 + n * y1) / (m + n)
z = (m * z2 + n * z1) / (m + n)

下面是上述方法的实现：

C++

// CPP program to find point that divides
// given line in given ratio in 3D.
#include 
using namespace std;
 
// Function to find the section of the line
void section(double x1, double x2, double y1,
             double y2, double z1, double z2,
             double m, double n)
{
    // Applying section formula
    double x = ((m * x2) + (n * x1)) / (m + n);
 
    double y = ((m * y2) + (n * y1)) / (m + n);
 
    double z = ((m * z2) + (n * z1)) / (m + n);
 
    // Printing result
    cout << "(" << x << ", ";
    cout << y << ", ";
    cout << z << ")" << endl;
}
 
// Driver code
int main()
{
    double x1 = 2, x2 = 4, y1 = -1,
           y2 = 3, z1 = 4, z2 = 2,
           m = 2, n = 3;
    section(x1, x2, y1, y2, z1, z2, m, n);
    return 0;
}

Java

// Java program to find point that divides
// given line in given ratio in 3D.
import java.util.*;
 
class solution
{
 
// Function to find the section of the line
static void section(double x1, double x2, double y1,
            double y2, double z1, double z2,
            double m, double n)
{
    // Applying section formula
    double x = ((m * x2) + (n * x1)) / (m + n);
 
    double y = ((m * y2) + (n * y1)) / (m + n);
 
    double z = ((m * z2) + (n * z1)) / (m + n);
 
    System.out.print( "(" +x +", ");
    System.out.print( y+ ", ");
    System.out.println(z + ")" );
 
}
 
// Driver code
public static void main(String arr[])
{
    double x1 = 2, x2 = 4, y1 = -1,
        y2 = 3, z1 = 4, z2 = 2,
        m = 2, n = 3;
    section(x1, x2, y1, y2, z1, z2, m, n);
 
}
 
}
//This code is contributed by Surendra_Gangwar

Python3

# Python 3 program to find point that divides
# given line in given ratio in 3D.
 
# Function to find the section of the line
def section(x1, x2, y1, y2, z1, z2, m, n):
    # Applying section formula
    x = ((m * x2) + (n * x1)) / (m + n)
 
    y = ((m * y2) + (n * y1)) / (m + n)
 
    z = ((m * z2) + (n * z1)) / (m + n)
 
    # Printing result
    print("(",x,",",y,",",z,")")
 
# Driver code
if __name__ == '__main__':
    x1 = 2
    x2 = 4
    y1 = -1
    y2 = 3
    z1 = 4
    z2 = 2
    m = 2
    n = 3
    section(x1, x2, y1, y2, z1, z2, m, n)
 
#This code is contributed by
# Surendra_Gangwar

C#

// C# program to find point that divides
// given line in given ratio in 3D.
using System;
 
class GFG
{
     
// Function to find the section
// of the line
static void section(double x1, double x2, double y1,
                    double y2, double z1, double z2,
                    double m, double n)
{
    // Applying section formula
    double x = ((m * x2) + (n * x1)) / (m + n);
 
    double y = ((m * y2) + (n * y1)) / (m + n);
 
    double z = ((m * z2) + (n * z1)) / (m + n);
 
    Console.Write("(" + x +", ");
    Console.Write(y + ", ");
    Console.WriteLine(z + ")" );
}
 
// Driver code
static public void Main ()
{
    double x1 = 2, x2 = 4, y1 = -1,
    y2 = 3, z1 = 4, z2 = 2,
    m = 2, n = 3;
    section(x1, x2, y1, y2, z1, z2, m, n);
}
}
 
// This code is contributed by ajit.

---

Javascript

 
// Javascript program to find point that
// divides given line in given ratio in 3D.
 
// Function to find the section
// of the line
function section(x1, x2, y1, y2, z1, z2, m, n)
{
     
    // Applying section formula
    let x = ((m * x2) + (n * x1)) / (m + n);
    let y = ((m * y2) + (n * y1)) / (m + n);
    let z = ((m * z2) + (n * z1)) / (m + n);
 
    document.write("(" + x +", ");
    document.write(y + ", ");
    document.write(z + ")" );
}
 
// Driver code
let x1 = 2, x2 = 4, y1 = -1,
y2 = 3, z1 = 4, z2 = 2,
m = 2, n = 3;
 
section(x1, x2, y1, y2, z1, z2, m, n);
 
// This code is contributed by suresh07
 

输出：

(2.8, 0.6, 3.2)