Assignment 6 [Written]: Vector Field Decomposition and Design (due 5/6)

Note: This last assignment serves as your “final”; we will not have any other kind of exam. Remember that you get a single “freebie” assignment, so if you already completed all the regular assignments: congratulations! You’re done, and can just relax during finals week (at least in this class). Or, if you’d like to get some extra credit—and have already completed the rest of the assignments—you can complete this assignment for up to one additional assignment’s worth of extra credit points.

In this assignment, you will investigate tools for working with tangent vector fields on surfaces. Tangent vector fields are central to classical differential geometry, and have many interesting applications. For this homework, we’ll look at one algorithm for designing vector fields, and along the way we’ll cover a lot of deep facts about surfaces.

There’s no PDF this week since the exercises are all from the notes. The notes will also give you all the background you’ll need to complete this assignment. It builds on a lot of the stuff we’ve already done in the class, especially discrete exterior calculus and the Laplacian.

Submit your written responses for Exercise 8.1 – Exercise 8.21 in the notes to Gradescope (per the usual submission instructions), except for Exercise 8.13.

Warning: You cannot use late days on this assignment!

The assignment is due on May 6, 2022 at 5:59:59pm Eastern (not at midnight!).

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