You might be interested in a previous thread comparing square and lateen sails:

Comparing Square and Lateen Sails

• Why were Europeans so slow to adopt fore-and-aft rigging? - 4 comments, over 2 months old.
• A flaired user gives a detailed rundown of the advantages and disadvantages of square and lateen sails, paying particular attention to how the scale and materials of the ships changed the efficiency of the designs.

Alternate Ship Designs

• Are there any reasons why historic Asian sailing ships looked so differently from the sailing ships of the rest of the world? - 31 comments, over 10 months old.

• General details about Chinese ship construction are given in this thread along with a variety of book sources on the subject for further reading.

• Why did no mayor seafaring nation use catamarans/trimarans between 1400 and 1800? - 9 comments, over 2 years old.

• The commenters discuss several European examples (and their failures whether practical or commercial) although the topic could use a great deal of fleshing out.