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法学C++程序：检查三维平面上的点是否共面
给定点 (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) 和 (x4, y4, z4)，程序必须检查给定的点是否共面。如果点位于同一平面上，则称这些点为共面点；如果它们位于不同的平面上，则这些点不是共面点。
下图包含四个点，所有点都位于同一平面上（即xy平面），这意味着这些点是共面的。
下图包含四个点，它们位于不同的平面上，这表明这些点不是共面的。
示例
Input-: x1 = 2, y1 = 3, z1 = 1, x2 = 1, y2 = 9, z2 = 3, x3 = 3, y3 = 1, z3 = 5, x4 = 23, y4 = 21, z4 = 9 Output-: they are not coplanar 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-: they are coplanar
下面程序中使用的方法如下：
- 将点输入变量 (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) 和 (x4, y4, z4) 中。
- 找到平面的方程，并检查它们是否满足条件。
- 显示这些点是否共面。
算法
START Step 1-> declare function to check whether points in 3-D are coplanar or not void check_coplanar(int x1,int y1,int z1,int x2,int y2,int z2, int x3, int y3, int z3, int x, int y, int z) declare variable as int a1 = x2 - x1 declare variable as int b1 = y2 - y1 declare variable as int c1 = z2 - z1 declare variable as int a2 = x3 - x1 declare variable as int b2 = y3 - y1 declare variable as int c2 = z3 - z1 declare variable as int a = b1 * c2 - b2 * c1 declare variable as int b = a2 * c1 - a1 * c2 declare variable as int c = a1 * b2 - b1 * a2 declare variable as int d = (- a * x1 - b * y1 - c * z1) check IF(a * x + b * y + c * z + d = 0) print coplanar End Else print not coplanar End Step 2-> In main() declare and set variable int x1 = 2 , y1 = 3, z1 = 1, x2 = 1, y2 = 9, z2 = 3, x3 = 3, y3 = 1, z3 = 5, x4 = 23, y4 = 21, z4 = 9 call check_coplanar(x1, y1, z1, x2, y2, z2, x3,y3, z3, x4, y4, z4) STOP
示例
#include<bits/stdc++.h>
using namespace std ;
//calculate points in a plane are coplanar or not
void check_coplanar(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) ;
if(a * x + b * y + c * z + d == 0)
cout << "they are coplanar" << endl;
else
cout << "they are not coplanar" << endl;
}
int main() {
int x1 = 2;
int y1 = 3 ;
int z1 = 1 ;
int x2 = 1 ;
int y2 = 9 ;
int z2 = 3 ;
int x3 = 3 ;
int y3 = 1 ;
int z3 = 5 ;
int x4 = 23 ;
int y4 = 21 ;
int z4 = 9 ;
check_coplanar(x1, y1, z1, x2, y2, z2, x3,y3, z3, x4, y4, z4) ;
return 0;
}输出
如果运行上述代码，它将生成以下输出：
they are not coplanar
更新于：2019年11月20日
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