如何判断一个三角形是否完全位于另一个三维空间中的三角形内部？

import java.util.Arrays;

public class TriangleInTriangle {

    public static void main(String[] args) {
        // 三角形ABC的顶点坐标
        double[][] abc = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};

        // 三角形DEF的顶点坐标
        double[][] def = {{11, 12, 13}, {14, 15, 16}, {17, 18, 19}};

        // 计算三角形DEF的法向量
        double[] n_def = crossProduct(subtractVectors(def[1], def[0]), subtractVectors(def[2], def[0]));

        // 判断共面性
        boolean isCoplanar = true;
        for (double[] point : abc) {
            if (dotProduct(subtractVectors(point, def[0]), n_def) > 0) {
                isCoplanar = false;
                break;
            }
        }

        // 判断内包关系
        boolean isInside = true;
        for (double[] point : abc) {
            double[] projected = subtractVectors(point, def[0]);
            double[] edge1 = subtractVectors(def[1], def[0]);
            double[] edge2 = subtractVectors(def[2], def[0]);
            double dot1 = dotProduct(crossProduct(projected, edge1), n_def);
            double dot2 = dotProduct(crossProduct(projected, edge2), n_def);
            if (dot1 * dot2 < 0 || dot1 == 0 || dot2 == 0) {
                isInside = false;
                break;
            }
        }

        // 输出结果
        System.out.println("三角形ABC是否在三角形DEF中：" + (isCoplanar && isInside));
    }

    private static double[] crossProduct(double[] u, double[] v) {
        return new double[]{u[1] * v[2] - u[2] * v[1], u[2] * v[0] - u[0] * v[2], u[0] * v[1] - u[1] * v[0]};
    }

    private static double dotProduct(double[] u, double[] v) {
        return Arrays.stream(u).map(c -> c * c).sum() * Arrays.stream(v).map(c -> c * c).sum();
    }

    private static double[] subtractVectors(double[] u, double[] v) {
        return new double[]{u[0] - v[0], u[1] - v[1], u[2] - v[2]};
    }
}