A magic method allowing a third variable used in comparison function of std::sort

Problem background

Let's say I have a bunch of points on the 3D line. Each of them is an Eigen::Vector3d variable with three values of x, y, and z of its coordinate. The algorithm is to sort them by the distance to the original point in order from the closest to farthest.

Coding

At first, the code snippet is:

// Eigen
#include <Eigen/Core>

// 'Cause we just want to sort them, it doesn't matter about whether should take the square root of them
double calculateEuclideanDistance(const Eigen::Vector3d &ev3dPt1, const Eigen::Vector3d &ev3dPt2)
{
    return ( (ev3dPt1 - ev3dPt2).dot(ev3dPt1 - ev3dPt2) );
}

Unupgraded version:

bool sortEuclideanToOriginalPoint(const Eigen::Vector3d &ev3dPtsOnLine1, const Eigen::Vector3d &ev3dPtsOnLine2, const Eigen::Vector3d &ev3dOriginalPoint)
{
    return( calculateEuclideanDistance( ev3dPtsOnLine1, ev3dOriginalPoint) <  calculateEuclideanDistance( ev3dPtsOnLine2, ev3dOriginalPoint) );
}

    std::vector<Eigen::Vector3d> vEv3dPtsOnLine;
    double dPtToOriginalPoint; // calculate the square root of distance between ePtsOnLine and ev3dOriginalPoint
    for (int nIndex = 0; nIndex < vEv3dPtsOnLine.size(); nIndex++)
    {
        dPtToEnd = std::sqrt( calculateEuclideanDistance( vEv3dPtsOnLine.at(nIndex), ev3dOriginalPoint ) );
        vE4dPtsOnLine.push_back( Eigen::Vector4d(vEPtsOnLine.at(nIndex)(0), vEPtsOnLine.at(nIndex)(1), vEPtsOnLine.at(nIndex)(2), ev3dOriginalPoint) );
    }
    // In this way to get errors
    std::sort (vEv4dPtsOnLine.begin(), vEv4dPtsOnLine.end(), sortEuclideanToOriginalPoint( , , ) );

I look for the usage of std::sort ^[1], and the comparison function seems forbidden to take the third variable.

So I update my code, using Eigen::Vector4d instead of Eigen::Vector3d, So the euclidean distance can be taken in the variable itself and no need for a third one.

    // Load the square Euclidean distances of ePtsOnLine and eLineEnd to Eigen::Vector4d
    // So std::sort can be used directly
    std::vector<Eigen::Vector4d> vEv4dPtsOnLine;
    double dPtToOriginalPoint; // calculate the square root of distance between ePtsOnLine and ev3dOriginalPoint
    for (int nIndex = 0; nIndex < vEPtsOnLine.size(); nIndex++)
    {
        // calculate the distance with closet poleEnd. Here is poleEnd1
        dPtToEnd = std::sqrt( calculateEuclideanDistance( vEv4dPtsOnLine.at(nIndex), ev3dOriginalPoint ) );
        vE4dPtsOnLine.push_back( Eigen::Vector4d(vEPtsOnLine.at(nIndex)(0), vEPtsOnLine.at(nIndex)(1), vEPtsOnLine.at(nIndex)(2), ev3dOriginalPoint) );
    }
    std::sort (vEv4dPtsOnLine.begin(), vEv4dPtsOnLine.end(), sortEuclideanToOriginalPoint );

References

[1] std::sort - cppreference.com