Compare some swords of types used approximately 1000 years ago:
Europe: https://commons.wikimedia.org/wiki/File:ALB_-_Schwert_1.jpg
Western Asia: https://i.pinimg.com/564x/68/1a/21/681a21234f71b83ff5269eb871b5880a.jpg
India: https://i.pinimg.com/originals/76/12/8d/76128db20c017847ee874422b344152b.jpg (this example is probably much newer, but is in an old style known from about 1000 years ago)
China: https://commons.wikimedia.org/wiki/File:%E8%97%8F%E5%93%81%EF%BC%9A%E5%94%90%E5%88%80.JPG (modern replica)
All of these are straight.
Compare some 19th century swords:
Western Asia: https://commons.wikimedia.org/wiki/File:Saber_(Kilij)_with_Scabbard_MET_DP160077.jpg
India: https://commons.wikimedia.org/wiki/File:19th_century_Indian_tulwar_sword_1.jpg
China: https://commons.wikimedia.org/wiki/File:Sword_with_Scabbard_MET_21123_-_cropped.jpg
All are curved (the Chinese one only very slightly so).
The "Western = straight and pointy, Asian = curved" largely comes from comparing Medieval European swords with recent Asian swords, and from Medieval artwork where Saracens are drawn using European curved swords to differentiate them from Europeans. And ignoring straight and almost straight Chinese swords.
For a lot more on this, see https://www.reddit.com/r/AskHistorians/comments/86it3s/why_did_eastern_armies_prefer_curved_swords_over/ (apart from my comments there, note also u/MRPolo13 on Polish and Hungarian swords).
_with_Scabbard_MET_DP160077.jpg){kind=link}
