Author: Keenan

Assignment 0 (Written): Combinatorial Surfaces

For the written part of your first homework you will do some exercises that will help familiarize you with basic descriptions and representations of combinatorial surfaces (simplicial surfaces, adjacency matrices, halfedge meshes), which will help prepare you to work with such surfaces as we continue through the course. (If any of this stuff seems abstract right now, don’t worry: we’ll use it over and over again to implement “real” algorithms starting in just a couple weeks!)

You must complete all 15 exercises from the Written Exercises section of Chapter 2 of the course notes. If these exercises seem scary and unfamiliar, and you don’t know where to start, that’s ok! This is not typical computer science stuff, and you shouldn’t necessarily know how to do it right off the bat. If you find yourself stumbling, please reach out to the instructor/TAs and your classmates on Piazza, Discord, or during the office hours/Q&A sessions. We’ll have you up and running in no time. 🙂

The assignment is due on the date listed on the calendar, at 5:59:59pm Eastern (not at midnight!). Hand-in instructions can be found on this page.

Slides—Exterior Algebra

Today’s lecture will cover one of the basic tools we’ll use throughout the rest of the course: exterior algebra. The basic idea is to add a couple new operations to our usual list of vector operations (dot product, cross product, etc.) that make it easy to talk about volumes rather than just vectors. If you felt ok working with things like the cross product and the determinant in your linear algebra/vector calculus courses, this shouldn’t be too big of a leap. (If not, could be a good moment for a review!)

Reading 1: Overview of DDG (Due 1/24)

Your first reading assignment will be to read an overview article on Discrete Differential Geometry. Since we know we have a diverse mix of participants in the class, you have several options (pick one):

  1. (pages 1–3) Crane & Wardetzky, “A Glimpse into Discrete Differential Geometry”.
    This article discusses the “no free lunch” story about curvature we looked at in class, plus a broader overview of the field.
  2. (pages 1–5) Pottman et al, “Architectural Geometry”.
    This article discusses the beautiful tale of how discrete differential geometry is linked to modern approaches to computational design for architecture, as well as fabrication and “rationalization” of free-form designs.
  3. (pages 5–9) Bobenko & Suris, “Discrete Differential Geometry: Consistency As Integrability”.
    This article provides another overview of discrete differential geometry, with an emphasis on nets and their connection to the notion of integrability in geometry and physics.

Though written for a broad audience, be warned that all of these articles are somewhat advanced—the goal here is not to understand every little detail, but rather just get a high-level sense of what DDG is all about.

Assignment: Pick one of the readings above, and write 2–3 sentences summarizing what you read, plus at least one question about something you didn’t understand, or some thought/idea that occurred to you while reading the article.  For this first assignment, we are also very interested to know a little bit about YOU! E.g., why are you taking this course?  What’s your background?  What do you hope to get out of this course?  What are your biggest fears about the course?  Etc.

Handin instructions can be found in the “Readings” section of the Assignments page.  Note that you must send your summary in no later than 10am Eastern on the day of the next lecture (January 24, 2023).

Enjoy!

Assignment -1: Favorite Formula

Part of your course grade is determined by participation, which can include both in-class participation as well as discussion here on the course webpage.  Therefore, your first assignment is to:

  1. create an account, and
  2. leave a comment on this post containing your favorite mathematical formula (see below).
To make things interesting, your comment should include a description of your favorite mathematical formula typeset in $\LaTeX$.  If you don’t know how to use $\LaTeX$ this is a great opportunity to learn — a very basic introduction can be found here.  (And if you don’t have a favorite mathematical formula, this is a great time to pick one!)
 
(P.S. Anyone interested in hearing about some cool “favorite theorems” should check out this podcast.)

Welcome to Discrete Differential Geometry! (Spring 2023)

Welcome to the website for 15-458/858 (Discrete Differential Geometry).  Here you’ll find course notes, lecture slides, and homework (see links on the right).

If you are a student in the class, register now by clicking here!

To participate in the class, you must register using your Andrew (CMU) email address.

A few things to note:

  • You will be subscribed to receive email notification about new posts, comments, etc.
  • You can ask questions by leaving a comment on a post.  If you’re apprehensive about asking questions in public, feel free to register under a pseudonym.
  • Otherwise, please associate a picture to your profile by registering your email address at Gravatar.com—doing so will help us better recognize you in class!
  • You can include mathematical notation in your questions using standard $\LaTeX$ syntax.  For instance, when enclosed in a pair of dollar signs, an expression like dollar\int_M K dA = 2\pi\chidollar gets typeset as $\int_M K dA = 2\pi\chi$.
If you encounter any problems while trying to use the website, please contact the TA (listed under the course description).