Thank you Gonzalo, you are right that is the accepted theory. I meant to suggest that there was distinct similarity in the weapons of Islamic Spain and Europe just as there were apparant cross influences between North Africa and Europe, particularly Italy which predominated trade in many Meditteranean routes as well as others. As I noted, I have worked on focused research regarding these developments for some time.
I hope that my comments regarding the drooping quillons on medieval Islamic broadswords being intended to deviate from the cross representation on the European broadsword will not be perceived as 'theory'
While there are many similarities and suggestions of influence reflected in a number of sword forms between varying cultural spheres, it is difficult to determine exactly which direction the influence moved in many cases. What I meant to say it that it seemed unlikely that Islamic design preferences would influence European hilt forms such as in this case of drooping quillons.
It does seem however that European designs did influence many sword hilt forms in the Islamic sphere such as the Moroccan 'nimcha' from the Italian stortas and others; the 'Zanzibar' type s'boula from baselards of undetermined origin but certainly European; and the koummya, whose pommel closely resembles and has been suggested to have developed from the Italian cinqueda.
Ariel, you asked a question, do you have thoughts?