В С++, как рассчитать длину пути инструмента?

Как насчет чего-то вроде этого - предположим, вам нужно расстояние между точками, а не от начала (строка 93 с комментарием):

#include "stdafx.h"
#include <iostream>
#include <fstream>
#include <vector>
#include<math.h>
#include <conio.h>

using std::cin;
using std::cout;
using std::endl;

using std::vector;

using std::ostream;
using std::istream;
using std::ifstream;

using std::operator>>;
using std::operator<<;

struct point

{
    float x ;
    float y ;
    float z ;
};

ostream& operator<< (ostream& out, const point &p)
{
    out << "(" << p.x << "," << p.y << " ," << p.z << "," << ")";
    return out;
}

istream& operator>> (istream& in, point& point)
{
    in >> point.x >> point.y >> point.z;
    return in;
}

struct line
{
    point start;
    point next;
    float sqDistance()
    {
        float dx = start.x - next.x;
        float dy = start.y - next.y;
        float dz = start.z - next.z;
        double distance = 0.0;
        distance = sqrt(dx * dx + dy * dy + dz * dz);
        return distance;
    }
};

ostream& operator<< (ostream& out, const line &ln)
{
    out << "From " << ln.start << " to " << ln.next;
    return out;
}

istream& operator>> (istream& in, line ln)
{
    cout << "Enter x y z start then x y z  next: ";
    in >> ln.start.x >> ln.start.y >> ln.start.z >>  ln.next.x >> ln.next.y >> ln.next.z;
    return in;
}

int main()
{
    point origin, input;
    line ray;
    vector<line> side;

    // READ POINTS FROM FILE
    ifstream pointfile("concave.txt");
    if (pointfile.is_open())
    {
        pointfile >> origin.x >> origin.y >> origin.z;
        cout << "origin: " << origin << endl;
        ray.start = origin;

        while (pointfile >> ray.next)
        {
            cout
                << " GOTO/ " << ray.next 
                << " The distance from point to the next is : "
                << ray.sqDistance() << endl;

            side.push_back(ray);
            ray.start = ray.next; // set start to last end (?)
        }
    }
    else
        cout << "Unable to open file";
    pointfile.close();

    vector<line>::iterator iter = side.begin();
    line temp, closest = *iter;
    float minimumDistance = closest.sqDistance(), distance, sumDistance = 0.0;
    cout << "Line coords" << endl << "distance, Sum of distances, minimum" << endl;
    while(iter != side.end()) {
        closest = *iter;
        distance = closest.sqDistance();
        sumDistance += distance;
        if (minimumDistance > distance) minimumDistance = distance;
        cout << closest << endl
              << distance << " | " << sumDistance << " | " << minimumDistance << endl;
        sumDistance += distance;
        iter++;
    }

    getch();

    return 0;
}

Извините за ошибку - строка суммы была там дважды - строка после cout была ошибкой, также заметил некоторое предупреждение о точности - смешанный double/float, поэтому везде переключился на double, теперь основной цикл выглядит так:

vector<line>::iterator iter = side.begin();
line closest = *iter;
double distance, sumOfDistances = 0.0;
cout << "Line coords" << endl << "distance | Sum of distances" << endl;
while (iter != side.end()) {
    closest = *iter;
    distance = closest.sqDistance();
    sumOfDistances += distance;
    cout << closest << endl << distance << " | " << sumOfDistances << endl; // step info output
    iter++;
}

Вот полная, немного более короткая версия, включая простой вывод файла results.txt. Вы можете удалить 2 строки с выводом информации о комментариях:

#include <iostream>
#include <fstream>
#include <vector>
#include <conio.h>

using namespace std;

struct point
{
    float x;
    float y;
    float z;
};

ostream& operator<< (ostream& out, const point &p)
{
    out << "(" << p.x << "," << p.y << " ," << p.z << "," << ")";
    return out;
}

istream& operator>> (istream& in, point& point)
{
    in >> point.x >> point.y >> point.z;
    return in;
}

struct line
{
    point start;
    point next;
    double sqDistance()
    {
        float dx = start.x - next.x;
        float dy = start.y - next.y;
        float dz = start.z - next.z;
        double distance = 0.0;
        distance = sqrt(dx * dx + dy * dy + dz * dz);
        return distance;
    }
};

ostream& operator<< (ostream& out, const line &ln)
{
    out << "From " << ln.start << " to " << ln.next;
    return out;
}

istream& operator>> (istream& in, line ln)
{
    cout << "Enter x y z start then x y z  next: ";
    in >> ln.start.x >> ln.start.y >> ln.start.z >> ln.next.x >> ln.next.y >> ln.next.z;
    return in;
}

int main()
{
    point origin, input;
    line ray;
    vector<line> side;

    // READ POINTS FROM FILE
    ifstream pointfile("concave.txt");
    if (pointfile.is_open())
    {
        pointfile >> origin.x >> origin.y >> origin.z;
        cout << "origin: " << origin << endl;
        ray.start = origin;

        while (pointfile >> ray.next)
        {
            cout
                << " GOTO/ " << ray.next
                << " The distance from point to the next is : "
                << ray.sqDistance() << endl;

            side.push_back(ray);
            ray.start = ray.next; // set start to last end (?)
        }
    }
    else
        cout << "Unable to open file";
    pointfile.close();

    ofstream results("results.txt");
    vector<line>::iterator iter = side.begin();
    line closest = *iter;
    double distance, sumOfDistances = 0.0;
    cout << "Line coords" << endl << "distance | Sum of distances" << endl;
    while (iter != side.end()) {
        closest = *iter;
        distance = closest.sqDistance();
        sumOfDistances += distance;
        results << distance << endl;
        cout << closest << endl << distance << " | " << sumOfDistances << endl; // info output
        iter++;
    }
    results << sumOfDistances << " << Sum" << endl;
    results.close();
    cout << "Complete path distance: " << sumOfDistances << endl; // info output

    getch();

    return 0;
}