The written portion of Assignment 2 can be found below. It takes a look at the curvature of smooth and discrete surfaces, which we have been talking about in lecture. **Note that you are required to complete only two problems from each section!**

Warning: We renumbered the Exercises in the course notes to make more sense, so you make sure you refer to the updated notes when doing these exercises.

Hi,

I noticed in the slides on smooth curves (http://brickisland.net/DDGSpring2019/wp-content/uploads/2019/02/DDG_458_SP19_Lecture10_SmoothCurves.pdf) the slide on Frenet-Serret and the following example (slides 40 + 41) that on slide 40 that $\frac{d}{ds} T(s) = -\kappa N $, but on slide 41 it seems like $\frac{d}{ds} T(s) =\kappa N $, since $\frac{d}{ds} T(s) = -a (\cos(s), \sin(s), 0) \Rightarrow \kappa(s) = -a $ and $N(s) = (\cos(s), \sin(s), 0)$—am I missing something?

No, it looks like the slides just have a sign error. Thanks for catching it! We’ll try to update the slides with a fixed version soon.

When deriving the gradient of the total surface area and the gradient of the total discrete scalar mean curvature, wouldn’t moving vertex $$f_i$$ in the direction of $$-e_{ij}=f_i-f_j$$ provide the fastest increase for those quantities, rather than the $$f_j-f_i$$ stated?

Yes, that’s exactly right. Sorry for the typo