Why exactly do we care about C2 continuity? I understand that C1 makes it look "smooth", but does C2 add anything? When would we need to differentiate it twice?

alexkassil

C2 continuity guarentees that our combined bezier surface is itself a bezier surface

FLinesse

I was confused by the above answer so I did some googling on why we want to ensure C2 continuity above C1. Turns out I found some really good answers on last year's slide comments! Thanks to @anup-h (now course staff) for starting this discussion!

@alexkassil and @glee- are essentially stating the same thing

borongzhang

Maybe we need to differentiate twice to compute things like curvature and torsion, and to find useful objects like geodesic curves, which are covered in math 140.

Why exactly do we care about C2 continuity? I understand that C1 makes it look "smooth", but does C2 add anything? When would we need to differentiate it twice?

C2 continuity guarentees that our combined bezier surface is itself a bezier surface

I was confused by the above answer so I did some googling on why we want to ensure C2 continuity above C1. Turns out I found some really good answers on last year's slide comments! Thanks to @anup-h (now course staff) for starting this discussion!

https://cs184.eecs.berkeley.edu/sp19/lecture/7-81/geometry-and-splines

@alexkassil and @glee- are essentially stating the same thing

Maybe we need to differentiate twice to compute things like curvature and torsion, and to find useful objects like geodesic curves, which are covered in math 140.