1.问题
判断点是否在三角形内部。
2.思路
计算向量AB和AP的叉积、向量BC和BP的叉积、向量CA和CP的叉积，如果所有的叉积符号相同，则点在三角形内部。
3.代码实现和注释
#include <iostream>
#include <vector>// 计算两个二维向量的叉积
double crossProduct(const std::vector<double>& v1, const std::vector<double>& v2) {return v1[0] * v2[1] - v1[1] * v2[0];
}// 判断点P是否在三角形ABC内部
bool isPointInsideTriangle(double ax, double ay,double bx, double by,double cx, double cy,double px, double py) {// 将点和顶点表示为向量std::vector<double> AB = {bx - ax, by - ay};std::vector<double> AP = {px - ax, py - ay};std::vector<double> BC = {cx - bx, cy - by};std::vector<double> BP = {px - bx, py - by};std::vector<double> CA = {ax - cx, ay - cy};std::vector<double> CP = {px - cx, py - cy};// 计算叉积int count1 = 0, count2 = 0;if (crossProduct(AB, AP) > 0)count1++;elsecount2++;if (crossProduct(BC, BP) > 0)count1++;elsecount2++;if (crossProduct(CA, CP) > 0)count1++;elsecount2++;// 如果计数为3，点在三角形内部printf("count1 = %d, count2 = %d\n", count1, count2);return count1 == 3 || count2 == 3;
}int main() {double ax, ay, bx, by, cx, cy, px, py;std::cout << "Enter triangle vertices (A(x, y), B(x, y), C(x, y)):\n";std::cin >> ax >> ay >> bx >> by >> cx >> cy;std::cout << "Enter point P(x, y):\n";std::cin >> px >> py;bool result = isPointInsideTriangle(ax, ay, bx, by, cx, cy, px, py);if (result)std::cout << "Point P is inside the triangle.\n";elsestd::cout << "Point P is outside the triangle or on its boundary.\n";return 0;
}
