Assignment 2 (Written): Investigating Curvature (Due 3/19)

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.

4 thoughts on “Assignment 2 (Written): Investigating Curvature (Due 3/19)”

  1. Hi,

    I noticed in the slides on smooth curves ( 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?

  2. 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?

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