The “cross pointed” is a translation of the French croix aiguisée [Woodward 162]; it’s found in the arms of Dokenfield or Dukenfeld, c.1510 [DBA3 152]. It’s sometimes misblazoned a “cross fitched at all points”, but this is a solecism; see the discussion under crosses fitchy.
Bryan Adyngton bears: Per chevron throughout sable and argent, three Latin crosses pointed counterchanged argent and vert.