求平面两直线的交点，两直线段的交点

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//aa, bb为一条线段两端点 cc, dd为另一条线段的两端点 相交返回true, 不相交返回false
bool LinesProject::getCrossPoint(const PointType& aa, const PointType& bb, const PointType& cc, const PointType& dd, PointType& crossPoint) {
    if (max(aa.x, bb.x)<min(cc.x, dd.x))
    {
        return false;
    }
    if (max(aa.y, bb.y)<min(cc.y, dd.y))
    {
        return false;
    }
    if (max(cc.x, dd.x)<min(aa.x, bb.x))
    {
        return false;
    }
    if (max(cc.y, dd.y)<min(aa.y, bb.y))
    {
        return false;
    }
    if (mult(cc, bb, aa)*mult(bb, dd, aa)<0)
    {
        return false;
    }
    if (mult(aa, dd, cc)*mult(dd, bb, cc)<0)
    {
        return false;
    }

    float a1 = bb.y - aa.y;
    float b1 = aa.x - bb.x;
    float c1 = aa.x*bb.y - bb.x*aa.y;
    float a2 = dd.y - cc.y;
    float b2 = cc.x - dd.x;
    float c2 = cc.x*dd.y - dd.x*cc.y;
    float det = a1*b2 - a2*b1;

    if (det == 0)
        return false;    //说明两线段平行

    crossPoint.x = (c1*b2 - c2*b1) / det;
    crossPoint.y = (a1*c2 - a2*c1) / det;

    return true;
}

 

        //getCrossPoint 计算两直线交点
        int getCrossPoint(cv::Point& A, cv::Point& B, cv::Point& C, cv::Point& D, cv::Point& crosspoint)
        {
                double m = (B.y - A.y)*(C.x - D.x) - (D.y - C.y)*(A.x- B.x);
            if (m == 0) {   //平行不相交

                crosspoint.x = 0;
                crosspoint.y = 0;
                return -1;    
            }
            else
            {
                crosspoint.x = ((D.x * C.y - C.x * D.y)*(A.x - B.x) - (B.x * A.y - A.x * B.y)*(C.x - D.x)) / m;
                crosspoint.y = ((B.x * A.y - A.x * B.y)*(D.y - C.y) - (D.x * C.y - C.x * D.y)*(B.y - A.y)) / m;
            }
            return 0;
        }

 

int crossPointsOfTwoLines(const Eigen::Vector2f &p0,
                          const Eigen::Vector2f &p1,
                          const Eigen::Vector2f &p2,
                          const Eigen::Vector2f &p3, Eigen::Vector2f &cross_pt)
{
    auto A1 = p1.y() - p0.y();
    auto B1 = p0.x() - p1.x();
    auto C1 = A1 * p0.x() + B1 * p0.y();
    auto A2 = p3.y() - p2.y();
    auto B2 = p2.x() - p3.x();
    auto C2 = A2 * p2.x() + B2 * p2.y();
    auto denominator = A1 * B2 - A2 * B1;

    // 如果分母为0 则平行或共线, 不相交
    if (denominator == 0)
    {
        return -1;
    }
    cross_pt.x() = (B2 * C1 - B1 * C2) / denominator;
    cross_pt.y() = (A1 * C2 - A2 * C1) / denominator;

    // // 2 判断交点是否在两条线段上
    // auto rx0 = (cross_pt.x() - p0.x()) / (p1.x() - p0.x());
    // auto ry0 = (cross_pt.y() - p0.y()) / (p1.y() - p0.y());
    // auto rx1 = (cross_pt.x() - p2.x()) / (p3.x() - p2.x());
    // auto ry1 = (cross_pt.y() - p2.y()) / (p3.y() - p2.y());
    // if (
    //     // 交点在线段1上
    //     ((rx0 >= 0 && rx0 <= 1) || (ry0 >= 0 && ry0 <= 1)) &&
    //     // 且交点也在线段2上
    //     ((rx1 >= 0 && rx1 <= 1) || (ry1 >= 0 && ry1 <= 1)))
    // {
    //     return 1;
    // }
    // else
    // {
    //     return 0;
    // }

    return 0;
}