点到线段(或直线)的最近点

2D直角坐标系

// 点到线段(或直线)的最近点
Point2D calNearestPoint(
    const Point2D& P,  //[in] 当前点
    const Point2D& A, const Point2D& B, //[in] 线段的两个端点，A->B
    bool isSegment     //[in] true线段；false直线 
)
{
    auto AB_vector = B - A; //向量AB=B-A

    double AB_length2 = AB_vector.dot(AB_vector); //|AB|的平方
    if(AB_length2 < 1.0e-16)
    {
        //线段退化成点
        return A; 
    }

    //记P到直线AB的垂足为Q
    auto AP_vector = P - A;                             //向量AP=P-A
    double k = AB_vector.dot(AP_vector) / AB_length2;   //向量AQ = k * 向量AB

    if(isSegment)
    {
        if(k > 1) 
        {
            //Q在线段AB的延长线上
            return B; 
        }
        else if(k < 0) 
        {
            //Q在线段BA的延长线上
            return A; 
        }
    }

    return A + AB_vector * k; //垂点
}

3D空间直角坐标系

todo:

完整代码

2D直角坐标系

#include <iostream>
using namespace std;

#include <cmath>    //sqrt
class Point2D
{
public:
    Point2D() = default;
    Point2D(double x, double y) :m_Value{x,y} {}
    double x() const { return m_Value[0]; }
    double y() const { return m_Value[1]; }

    double length() const  { return sqrt(x() * x() + y() * y()); }

    Point2D operator+(const Point2D& rhs) const { return Point2D(x() + rhs.x(), y() + rhs.y()); }
    Point2D operator-(const Point2D& rhs) const { return Point2D(x() - rhs.x(), y() - rhs.y()); }
    Point2D operator*(double value) const { return Point2D(x() * value, y() * value); }

    double dot(const Point2D& rhs) { return x() * rhs.x() + y()* rhs.y(); }

    friend std::ostream& operator<<(std::ostream& out, const Point2D& p) { out << p.x() << " " << p.y(); return out; }

protected:
    double m_Value[2];
};

// 点到线段(或直线)的最近点
Point2D calNearestPoint(
    const Point2D& P,  //[in] 当前点
    const Point2D& A, const Point2D& B, //[in] 线段的两个端点，A->B
    bool isSegment     //[in] true线段；false直线 
)
{
    auto AB_vector = B - A; //向量AB=B-A

    double AB_length2 = AB_vector.dot(AB_vector); //|AB|的平方
    if(AB_length2 < 1.0e-16)
    {
        //线段退化成点
        return A; 
    }

    //记P到直线AB的垂足为Q
    auto AP_vector = P - A;                             //向量AP=P-A
    double k = AB_vector.dot(AP_vector) / AB_length2;   //向量AQ = k * 向量AB

    if(isSegment)
    {
        if(k > 1) 
        {
            //Q在线段AB的延长线上
            return B; 
        }
        else if(k < 0) 
        {
            //Q在线段BA的延长线上
            return A; 
        }
    }

    return A + AB_vector * k; //垂点
}

int main()
{
    Point2D A(0,0), B(3,0);
    {
        Point2D p(-1, 1);
        std::cout << calNearestPoint(p, A, B, true) << std::endl;   //0 0
        std::cout << calNearestPoint(p, A, B, false) << std::endl;  //-1 0
    }
    {
        Point2D p(1, 1);
        std::cout << calNearestPoint(p, A, B, true) << std::endl;   //1 0
        std::cout << calNearestPoint(p, A, B, false) << std::endl;  //1 0
    }

    return 0;
}