void center_tie_vertically (Tie_details const &);
Bezier get_transformed_bezier (Tie_details const &) const;
Bezier get_untransformed_bezier (Tie_details const &) const;
void center_tie_vertically (Tie_details const &);
Bezier get_transformed_bezier (Tie_details const &) const;
Bezier get_untransformed_bezier (Tie_details const &) const;
string tie_card (int i) const { return tie_score_cards_[i]; }
string complete_tie_card (vsize i) const;
string tie_card (int i) const { return tie_score_cards_[i]; }
string complete_tie_card (vsize i) const;