The Katana was long predated by the Tachi in Feudal Japan. The Ōdachi and Nodachi were period, but were not the main sidearm, nor were they routine carry except on warmarch.
The standard samurai sidearm was the Tachi - which, essentially, is the parent of the Gatana family (including the Wakizashi and Katana) The Gatana family starts becoming present in the 1400's. The largest difference is in how it was rigged to the obi - two separate ties, holding it largely parallel to the ground. The blades tended to be little different in overall shape, but the handle:blade ratio a bit different. Still single edged, still curved, still 2 handed at 2.5 to 3.5 shaku long, and with lengths up to over a meter... the first ōdachi are tachi, and the tachi is documented all the way back to the Kofun period.
Jokoto tachi (pre heian) have sifgnificant differences in hilts and pommels, and not all swords were the gatana-like blades; many were still chokuto (straight swords, often double edged).
THe heian period begins the migration to the beatifully curved, "Traditional" Japanese swords, typically in the 2 to 3 shaku long for the sidearm. (Odachi/nodachi, the larger blades, were specialist weapons - intended for killing horses more than for killing men. Usually by shattering the fetlock and metacarpals when it was charging.)
An interesting (if only partially available online) book:
https://books.google.com/books?id=zP...page&q&f=false
It's worth pointing out that the largest tachi in the 14th C (the early nodachi) tended to be in the 4 to 5 shaku (1 shaku = 30.3 cm) range. The same period tanto was typically 1 shaku long, but up to 1.5 shaku... The fad ended, and most were cut down to katana following.
THe 14th C is also the period of the Nagamaki - a 2.5 to 4 shaku long blade, with a 3-4 shaku handle, and sometimes a full-length tang. Often called a pole sword, it's a hybrid of sword and polearm... and particularly effective against horses' legs.