如何用 Java 中的行列式求四面体的体积？
给定四面体的顶点。任务是利用行列式来确定四面体的体积。
进场:
1.给定四面体的四个顶点(x1，y1，z1)，(x2，y2，z2)，(x3，y3，z3)和(x4，y4，z4)。使用这些顶点创建一个(4 × 4)矩阵，其中坐标三元组形成矩阵的列，在底部附加一个额外的行，每个值为 1。
x1 x2 x3 x4
y1 y2 y3 y4
z1 z2 z3 z4
1 1 1 1
2.对于底部有一行 1 的 4 × 4 矩阵，我们可以用给定的简化公式简化成(3 × 3)矩阵。
x1-x4 x2-x4 x3-x4
y1-y4 y2-y4 y3-y4
z1-z4 z2-z4 z3-z4
3.四面体的体积等于上述计算出的矩阵行列式绝对值的 1/6 倍。
示例:
Input: x1=9, x2=3, x3=7, x4=9, y1=5, y2=0, y3=4, y4=6, z1=1, z2=0, z3=3, z4=0
Output: Volume of the Tetrahedron Using Determinants: 3.0
Input: x1=6, x2=8, x3=5, x4=9, y1=7, y2=1, y3=7, y4=1, z1=6, z2=9, z3=2, z4=6
Output: Volume of the Tetrahedron Using Determinants: 7.0
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to find the volume of a
// tetrahedron using determinants
import java.io.*;
class VolumeOfADeterminant {
public static double determinant(double m[][], int n)
{
double dt = 0;
// if the matrix has only
// one element
if (n == 1) {
dt = m[0][0];
}
// if the matrix has 4 elements
// find determinant
else if (n == 2) {
dt = m[0][0] * m[1][1] - m[1][0] * m[0][1];
}
else {
dt = 0;
for (int j1 = 0; j1 < n; j1++) {
double[][] w = new double[n - 1][];
for (int k = 0; k < (n - 1); k++) {
w[k] = new double[n - 1];
}
for (int i = 1; i < n; i++) {
int j2 = 0;
for (int j = 0; j < n; j++) {
if (j == j1)
continue;
w[i - 1][j2] = m[i][j];
j2++;
}
}
dt += Math.pow(-1.0, 1.0 + j1 + 1.0)
* m[0][j1] * determinant(w, n - 1);
}
}
return dt;
}
public static void main(String args[])
{
// Input the vertices
int x1 = 5, x2 = 8, x3 = 1, x4 = 9, y1 = 5, y2 = 0,
y3 = 7, y4 = 8, z1 = 8, z2 = 3, z3 = 4, z4 = 1;
// create a 4 * 4 matrix
double[][] m = new double[4][4];
// Create a matrix of that vertices
m[0][0] = x1;
m[0][1] = x2;
m[0][2] = x3;
m[0][3] = x4;
m[1][0] = y1;
m[1][1] = y2;
m[1][2] = y3;
m[1][3] = y4;
m[2][0] = z1;
m[2][1] = z2;
m[2][2] = z3;
m[2][3] = z4;
m[3][0] = 1;
m[3][1] = 1;
m[3][2] = 1;
m[3][3] = 1;
// Converting the 4x4 matrix into 3x3
double[][] m1 = new double[3][3];
m1[0][0] = x1 - x4;
m1[0][1] = x2 - x4;
m1[0][2] = x3 - x4;
m1[1][0] = y1 - y4;
m1[1][1] = y2 - y4;
m1[1][2] = y3 - y4;
m1[2][0] = z1 - z4;
m1[2][1] = z2 - z4;
m1[2][2] = z3 - z4;
// find (determinant/6)
double deter = determinant(m1, 3) / 6;
// if determinant is negative
if (deter < 0)
System.out.println(
"Volume of the Tetrahedron Using Determinants: "
+ (deter * -1));
else
System.out.println(
"Volume of the Tetrahedron Using Determinants: "
+ (deter * -1));
}
}
Output
Volume of the Tetrahedron Using Determinants: 52.333333333333336
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