Reading: Geodesic Distance and the Heat Method

For the final reading, we will take a look at the paper “The Heat Method for Distance Computation”, by Crane, Weischedel, and Wardetzky. Note that all students should do this reading, even if you’ve already completed four written/coding assignments. The hand-in instructions are the same as for all previous reading assignments; the reading is due on Thursday, December 14th.

Optional Reading: Discrete Conformal Geometry

Those of you interested in taking a “deeper dive” into discrete conformal geometry might want to take a look at the course notes below, written for for an upcoming AMS short course on discrete differential geometry. Be warned that these notes are a (very) rough draft, and there will be errors and omissions! 🙂

[Note: these notes are not a required reading.]

Reading: Introduction to Curves & Surfaces (Due 10/24)

For your next reading assignment, you will read a few pages about curves and surfaces from the course notes: Chapter 2, pages 7–23. This material should be enough to get you started on the written/coding exercises NOW, rather than waiting until we are done with the full set of lectures. We will cover these topics in greater depth during lecture (especially the topic of curvature).

Assignment: Read the pages 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.

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 date of the next lecture (October 24, 2017).

Enjoy!

Reading: Overview of DDG (Due 9/7)

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 (September 7, 2017).

Enjoy!