判断两点是否在直线的同侧C++代码

在C++中判断两点A(x1, y1)和B(x2, y2)是否位于直线l的同侧，通常需要考虑三点共线的情况，因为如果点在线上，也视为在同一侧。直线l可以用两个点P(x0, y0)和Q(x0', y0')来代表，斜率为(m = (y0 - y0') / (x0 - x0'))，截距(b = y0 - m * x0)。对于任意一点R(x, y)，我们有公式判断其在直线上方、下方还是两侧：

1. 如果m * (x - x0) + b > y - y0，点R在直线下方；
2. 如果m * (x - x0) + b < y - y0，点R在直线上方；
3. 否则，点R在直线上。

下面是C++代码实现：

#include <cmath>

bool arePointsOnSameSide(double x1, double y1, double x2, double y2,
                          double x0, double y0, double x0p, double y0p) {
    double slope = (y0p - y0) / (x0p - x0);
    double intercept = y0 - slope * x0;

    // 点在同一直线上的特殊情况处理
    if (std::abs(slope) == std::numeric_limits<double>::infinity()) {
        return (x1 == x0 && y1 <= y0) || (x2 == x0 && y2 >= y0);
    }

    double m1 = slope * (x1 - x0) + intercept;
    double m2 = slope * (x2 - x0p) + intercept > y1 - y0p && m2 * (x2 - x0p) + intercept > y2 - y0p);
}

// 使用示例
int main() {
    double x1 = 0, y1 = 0, x2 = 5, y2 = 4, x0 = 1, y0 = 2, x0p = 3, y0p = 2;
    bool sameSide = arePointsOnSameSide(x1, y1, x2, y2, x0, y0, x0p, y0p);
    if (sameSide) {
        std::cout << "Points A and B are on the same side of the line." << std::endl;
    } else {
        std::cout << "Points A and B are on different sides of the line." << std::endl;
    }
    return 0;
}