This function will get the approximate length of a mathematical function if it were stretched into a straight line. This works by splitting the curve of the function up into a bunch of right triangles and then adding their hypotenuses together. The precision argument simply dictates the amount of triangles used. The more there are, the more accu…

MathFunctionLength.cpp

#include <iostream>
#include <functional>
#include <algorithm>

using namespace std;

double GetFunctionLength(double start, double end, function<double(double)> mathFunc, int precision)
{
    if (precision < 1)
        return 0;

    double xChange = end - start;
    double sums = 0;
    for (int i = 1; i <= precision; i++)
    {
        double legA = xChange / precision;
        double legB = mathFunc(start + i * xChange / precision) - mathFunc(start + (i - 1) * xChange / precision);

        // if the function has a slope of 0, then we just add it on
        if (legB == 0)
            sums += legA;
        // otherwise, do pythagorean theorum to get the length of the side
        else
            sums += sqrt(legA * legA + legB * legB);
    }

    return sums;
}

int main()
{
    auto f = [](double d) { return sin(d); };
    cout << GetFunctionLength(0, 2 * 3.14159, f, 10000) << endl;
    return 0;
}