so my problem is that I've created a model that has a parametric form, so when I use subsurf to smoothen out the edges, these sort of faces are generated that interfere with even my freestyle outlining. How do I solve this problem?
This is most likely due to having n-gons or a mesh problem can we see a photo of your mesh or can we take a look at your blend file?
EDIT: It might be better to just smooth the model then add edge split. First u will need to remove doubles, select your mesh then press w and select remove doubles Then exit edit mode and select smooth