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 a 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:

#include <vector>
#include <math.h>
#include <algorithm>

// 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) );
}

Not upgraded version:

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

    std::vevtor<Eigen::Vector3d> vEv3dPtsOnLine; // contains points on line
    // In this way getting errors
    std::sort (vEv3dPtsOnLine.begin(), vEv3dPtsOnLine.end(), sortEuclideanToOriginalPoint( , , ev3dOriginalPoint) );

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

---

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

// Comparison function with third variable
// the distance compared is stored in the fouth value, index [3]
// it can be retrieved easily
bool sortEuclideanToOriginalPoint(const Eigen::Vector4d &ev4dPtsOnLine1, const Eigen::Vector4d &ev4dPtsOnLine2)
{
    return( ev4dPtsOnLine1[3] <  ev4dPtsOnLine2[3] );
}

    std::vevtor<Eigen::Vector3d> vEv3dPtsOnLine; // contains points on line
    // Load the square Euclidean distances of vEv3dPtsOnLine and ev3dOriginalPoint to the fouth value of Eigen::Vector4d, vEv3dPtsOnLine[3]
    // So std::sort can be used directly
    std::vector<Eigen::Vector4d> vEv3dPtsOnLine;
    double dDisToOriginalPoint; // calculate the square root of distance between vEv3dPtsOnLine and ev3dOriginalPoint
    for (int nIndex = 0; nIndex < vEPtsOnLine.size(); nIndex++)
    {
        dDisToOriginalPoint = std::sqrt( calculateEuclideanDistance( vEv3dPtsOnLine.at(nIndex), dPtToOriginalPoint ) );
        vE4dPtsOnLine.push_back( Eigen::Vector4d(vEv3dPtsOnLine.at(nIndex)(0), vEv3dPtsOnLine.at(nIndex)(1), vEv3dPtsOnLine.at(nIndex)(2), dDisToOriginalPoint) );
    }
    std::sort (vEv4dPtsOnLine.begin(), vEv4dPtsOnLine.end(), sortEuclideanToOriginalPoint );

A little trick is needed by the brain, not by the algorithm.

References

[1] std::sort - cppreference.com