// Polynomial regression function
cv::vector fitPoly(cv::vector points, int n) {

//Number of points
int nPoints = points.size();

// Vectors for all the points' xs and ys
cv::vector xValues = cv::vector();
cv::vector yValues = cv::vector();

// Split the points into two vectors for x and y values
for(int i = 0; i < nPoints; i++) {
xValues.push_back(points[i].x);
yValues.push_back(points[i].y);
}

//Augmented matrix
double matrixSystem[n+1][n+2];
for (int row = 0; row < n+1; row++) {
for (int col = 0; col < n+1; col++) {
matrixSystem[row][col] = 0;
for (int i = 0; i < nPoints; i++) matrixSystem[row][col] += pow(xValues[i], row + col);
}

matrixSystem[row][n+1] = 0;
for (int i = 0; i < nPoints; i++) matrixSystem[row][n+1] += pow(xValues[i], row) ∗ yValues[i];
}

//Array that holds all the coefficients
double coeffVec[n+2];

//Gauss reduction
for (int i = 0; i <= n − 1; i++)
for (int k = i + 1; k <= n ; k++) {
double t = matrixSystem[k][i] / matrixSystem[i][i];
for (int j = 0; j <= n+1; j++) matrixSystem[k][j] = matrixSystem[k][j] − t ∗ matrixSystem[i][j];
}

// Back−substitution
for (int i = n; i >= 0; i−−) {
coeffVec[i] = matrixSystem[i][n+1];
for (int j = 0; j <= n+1; j++) if (j != i) coeffVec[i] = coeffVec[i] − matrixSystem[i][j] ∗ coeffVec[j];

coeffVec[i] = coeffVec[i] / matrixSystem[i][i];
}

// Construct the cv vector and return it
cv::vector result = cv::vector();

for (int i = 0; i < n+1; i++) result.push_back(coeffVec[i]);
return result;
}

// Returns the point f o r the equation determined
//by a vector of coefficents, at a certain x location
cv::Point pointAtX (cv::vector coeff, double x) {
double y = 0;
for (int i = 0; i < coeff.size(); i++) y += pow(x, i) ∗ coeff[i];
return cv::Point(x, y);
}