Hi,
There were already triplane designs prior to the appearance of the Sopwith tripe but due to its ability to out fly the premiere German scout at the time..the Alb DIII, peaked further interest in the development of their own triplane. And as luck would have it they ended up with a captured Sopwith to study and expand on. But the DR.I was not a direct copy of the Sopwith tripe. It seems the German interest was also a case of keeping up with the jones's as Fokker already had planes in the works superior to the current Albatross machines.
Also it seems that Fokker had caught wind that the Idflieg was about to request submissions for a triplane design, so Fokker in the middle of producing his current V.4 switched the design to a 3 winged variant with his new cantilever wing. This is probably the biggest difference between the DR.I and the Sopwith tripe. Fokkers wing was superior in lift compared to the Sopwith but lost speed due to the drag caused by the thicker wing. As it would turn out, the lack of speed I think made the DR.I
less formidable as the fighting dragged on and new designs appeared from both sides.
I "believe" that's the gist of it....
HTH