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++;
else
count2++;
if (crossProduct(BC, BP) > 0)
count1++;
else
count2++;
if (crossProduct(CA, CP) > 0)
count1++;
else
count2++;
// 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";
else
std::cout << "Point P is outside the triangle or on its boundary.\n";
return 0;
}