Method vector_fit

deps/tesseract/ccstruct/linlsq.cpp:252–259

This is equivalent to returning the Principal Component in PCA, or the eigenvector corresponding to the largest eigenvalue in the covariance matrix. However, atan2 is much simpler! The one reference I found that uses this formula is http://web.mit.edu/18.06/www/Essays/tlsfit.pdf but that is still a much more complex derivation. It seems Pearson had already found this simple solution in 1901. http

// found this simple solution in 1901.
// http://books.google.com/books?id=WXwvAQAAIAAJ&pg=PA559
FCOORD LLSQ::vector_fit() const {
  double x_var = x_variance();
  double y_var = y_variance();
  double covar = covariance();
  double theta = 0.5 * atan2(2.0 * covar, x_var - y_var);
  FCOORD result(cos(theta), sin(theta));
  return result;
}