What is the relation between Computer Graphics, Discrete Geometry, and Complexity Theory?
Have a look at this slide of David Eppstein in which he tries to draw connections between these subfields. In my opinion, a computational-geometric complexity result is likely to be confined to computational geometry itself without broadly affecting complexity theory in general.

Excerpt from the above slide: Some computational geometry problems have practical applications. Their theoretical hardness are all conjectured to be $NP$-hard but still have not been proven. Some have approximation schemes.