Code:
import java.util.Random;
public class Volume_Tetrahedron_Determinants
{
public static double determinant(double A[][], int N)
{
double det = 0;
if (N == 1)
{
det = A[0][0];
} else if (N == 2)
{
det = A[0][0] * A[1][1] - A[1][0] * A[0][1];
} else
{
det = 0;
for (int j1 = 0; j1 < N; j1++)
{
double[][] m = new double[N - 1][];
for (int k = 0; k < (N - 1); k++)
{
m[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;
m[i - 1][j2] = A[i][j];
j2++;
}
}
det += Math.pow(-1.0, 1.0 + j1 + 1.0) * A[0][j1]
* determinant(m, N - 1);
}
}
return det;
}
public static void main(String args[])
{
Random random = new Random();
int x1, x2, x3, x4, y1, y2, y3, y4, z1, z2, z3, z4;
x1 = random.nextInt(10);
x2 = random.nextInt(10);
x3 = random.nextInt(10);
x4 = random.nextInt(10);
y1 = random.nextInt(10);
y2 = random.nextInt(10);
y3 = random.nextInt(10);
y4 = random.nextInt(10);
z1 = random.nextInt(10);
z2 = random.nextInt(10);
z3 = random.nextInt(10);
z4 = random.nextInt(10);
double[][] mat = new double[4][4];
mat[0][0] = x1;
mat[0][1] = x2;
mat[0][2] = x3;
mat[0][3] = x4;
mat[1][0] = y1;
mat[1][1] = y2;
mat[1][2] = y3;
mat[1][3] = y4;
mat[2][0] = z1;
mat[2][1] = z2;
mat[2][2] = z3;
mat[2][3] = z4;
mat[3][0] = 1;
mat[3][1] = 1;
mat[3][2] = 1;
mat[3][3] = 1;
System.out
.println("The matrix formed by the coordinates of the tetrahedron is: ");
for (int i = 0; i < 4; i++)
{
for (int j = 0; j < 4; j++)
System.out.print(mat[i][j] + " ");
System.out.println();
}
double[][] matrix = new double[3][3];
matrix[0][0] = x1 - x4;
matrix[0][1] = x2 - x4;
matrix[0][2] = x3 - x4;
matrix[1][0] = y1 - y4;
matrix[1][1] = y2 - y4;
matrix[1][2] = y3 - y4;
matrix[2][0] = z1 - z4;
matrix[2][1] = z2 - z4;
matrix[2][2] = z3 - z4;
System.out.println("Matrix after simplification: ");
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
System.out.print(matrix[i][j] + " ");
System.out.println();
}
double det = determinant(matrix, 3) / 6;
if (det < 0)
System.out.println("The Area of the tetrahedron formed by (" + x1
+ "," + y1 + "," + z1 + "),(" + x2 + "," + y2 + "," + z2
+ "),(" + x3 + "," + y3 + "," + z3 + "), = " + (det * -1));
else
System.out.println("The Area of the tetrahedron formed by (" + x1
+ "," + y1 + "," + z1 + "),(" + x2 + "," + y2 + "," + z2
+ "),(" + x3 + "," + y3 + "," + z3 + "), = " + (det * -1));
}
}
Output:
The matrix formed by the coordinates of the tetrahedron is:
0.0 9.0 6.0 0.0
4.0 2.0 1.0 1.0
3.0 4.0 7.0 5.0
1.0 1.0 1.0 1.0
Matrix after simplification:
0.0 9.0 6.0
3.0 1.0 0.0
-2.0 -1.0 2.0
The Area of the tetrahedron formed by (0,4,3),(9,2,4),(6,1,7), = 10.0
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