What is the relation between Computer Graphics, Discrete Geometry, and Complexity Theory?

I am a master computer science student, and I am interested in both geometry and complexity theory. So I would like to know what is the relations between discrete geometry, computer graphics, and complexity theory ?

I know the answer partially but I would like to have a clear answer since I do like to work on these fields in the future.

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.