#include <iostream>
#include <glm/glm.hpp>

glm::vec3 sum_over_e(glm::vec3* e, glm::vec3* e_prime, int& i)
{
    int k = 0;
    glm::vec3 result;

    while (k < i-1)
    {
        float e_prime_k_squared = glm::dot(e_prime[k], e_prime[k]);
        result += ((glm::dot(e[i], e_prime[k]) / e_prime_k_squared) * e_prime[k]);
        k++;
    }

    return result;
}

int main(int argc, char** argv)
{
    int n = 3;  // number of vectors we're working with
    glm::vec3 e[] = {
        glm::vec3(sqrt(2)/2, sqrt(2)/2, 0),
        glm::vec3(-1, 1, -1),
        glm::vec3(0, -2, -2)
    };

    glm::vec3 e_prime[n];
    e_prime[0] = e[0];  // step A

    int i = 0;  // step B

    do  // step C
    {
        e_prime[i] = e[i] - sum_over_e(e, e_prime, i);

        i++;    // step D
    } while (i < n);

    for (int loop_count = 0; loop_count < n; loop_count++)
    {
        std::cout << "Vector e_prime_" << loop_count+1 << ": < " 
                  << e_prime[loop_count].x << ", " 
                  << e_prime[loop_count].y << ", " 
                  << e_prime[loop_count].z << " >" << std::endl;
    }

    return 0;