把三角形染成红色

/*
 * 思路：
 * 1. 使用 Java Stream API 处理数据。
 * 2. 与传统方法相同，使用 stream 进行点和三角形的检查。
 */

import java.util.stream.Stream;

public class Solution {
    public static void main(String[] args) {
        int[][] points = {{0, 0}, {5, 0}, {0, 5}};
        int[] pointToCheck = {2, 2};
        boolean isInside = isPointInTriangle(points, pointToCheck);
        System.out.println("The point is inside the triangle: " + isInside);
    }

    // 检查三个点是否能形成一个三角形
    public static boolean isTriangle(int[] p1, int[] p2, int[] p3) {
        return Stream.of(p1, p2, p3)
                     .distinct()
                     .count() == 3 &&
               (p2[1] - p1[1]) * (p3[0] - p1[0]) != (p3[1] - p1[1]) * (p2[0] - p1[0]);
    }

    // 计算一个点是否在三角形内部
    public static boolean isPointInTriangle(int[][] triangle, int[] point) {
        int[] p1 = triangle[0];
        int[] p2 = triangle[1];
        int[] p3 = triangle[2];

        double denominator = ((p2[1] - p3[1]) * (p1[0] - p3[0]) + (p3[0] - p2[0]) * (p1[1] - p3[1]));
        double a = ((p2[1] - p3[1]) * (point[0] - p3[0]) + (p3[0] - p2[0]) * (point[1] - p3[1])) / denominator;
        double b = ((p3[1] - p1[1]) * (point[0] - p3[0]) + (p1[0] - p3[0]) * (point[1] - p3[1])) / denominator;
        double c = 1 - a - b;

        return Stream.of(a, b, c).allMatch(coefficient -> coefficient >= 0 && coefficient <= 1);
    }
}