COMS E6998: Topics in Geometry Processing

Spring 2026 · Columbia University · Mondays 4:00–6:00pm · Uris Hall 306

Teaser image for COMS E6998: Topics in Geometry Processing

People

The instructor for this course is Silvia Sellán. Her office hours are by appointment at her office (CEPSR 624).

This course's teaching assistant is Swagat Shubham Bhuyan. Please contact him for any issues related to attendance, weekly role assignments and grading.

For any question about the course, papers or roles, please use EdStem.

Structure

This seminar course will take a deep look at some of the most important research areas and questions in the study of digital 3D geometry. Each week will be dedicated to a single paper: all students will read and summarize (in one or two paragraphs) the same paper each week, but each will have a additional unique, rotating role. Students will fulfill their role through a 5-minute presentation in each class session.

Roles

Computer Science impacts society thanks to the effort of many people, not just individual researchers: stakeholders in academia, industry and government work together to turn an idea into a reality that transform people's lives. The roles in this seminar course are designed to make students think about all these different stakeholders, and to prepare them for the many different career paths they may choose after graduating.

Each student will have a single assigned role each week, and must cycle through all roles. If two students choose the same role, they may collaborate (or not, their choice).

Role: Reviewer

Pretend you are a senior researcher in geometry processing living when the paper was first submitted for publication. Write a review using the SIGGRAPH reviewing form. The previous link also contains (not necessarily good!) examples.

Role: Historian

Put this paper into its historical context. What came before this paper? How does this paper differ from what came before it? Why was this an interesting topic to study? What subsequent scientific research work was made possible because of this? A possible structure for this role is to select two prior papers and a subsequent one and present them, with an emphasis on answering the questions above.

Role: Teacher

Choose one concept used in the paper, and prepare a 5-minute mini-lecture about it. Choose a target audience (high school, undergraduate, graduate). Don't rely only on verbal explanation: use visual and interactive elements, make handouts, etc.

Role: Journalist

Create a popular science blog post or article about the paper. It should be understandable to the general public, with an emphasis on making the research exciting and palpable, less on the technical details. Here are some examples:

Role: Programmer

Implement part of the paper: a part that can stand on its own, even if it is simpler than the entire paper (e.g., 2D instead of 3D, or one stage of multi-stage algorithm). You will do a live demo in class! Here's an example: loop_subdivision.

Role: Artist

Create a new piece of art using the method in the paper, or inspired by it. It can be any kind of art you want. It can be a drawing, digital art, illustration, music, poetry (??), or anything you can think of. You can use any software you want, including existing implementations of this paper or similar ones. Be creative! While you may use Generative AI for inspiration or to create small parts of your piece, the vast majority of it must be your original work.

Role: Illustrator

Make a new didactic figure for the paper, or improve an existing figure. Use Inkscape, Adobe Illustrator, Affinity Designer, or any other software. While you may use Generative AI for inspiration or to create small details in your figure, it must be your original work.

Role: Funding agency

Look at the paper's acknowledgements for the public agencies funding this work. Imagine you are a an officer or director at one of these agencies, and have to explain to the public or their representatives why it is worth to fund this research with taxpayers' money. As examples, you may look at the opening statements of NSF/NIH/NASA leaders in front of Congress , or the fact sheets that NSF publishes for every state .

What you emphasize should depend on the agency that funds the research (if none are listed, or if you want, you can also choose a different one). But the broad question you should be answering is the same: why should people's hard-earned money be dedicated to this?

Role: Graduate Student

You just saw this paper presented at a conference. Think of a follow-up project and propose it to your advisor. It can't just be the "future work" section of the paper. Propose a specific direction and/or research question that is specifically enabled by this paper, along with specific steps on how to start research in that direction.

Role: Ethicist

Is or will the world be a better or worse place because of this paper? Discuss both positive and negative impacts. Take this role seriously: the people that worked on this research probably dedicated hundreds of hours to producing this paper. Who is better off or worse off because of it?

Role: Overworked student

Sometimes, life gets in the way. Take a week off, no questions asked. You may pick this role up to twice in the entire semester.

Logistics

Each role will be fulfilled by adding a slide to a common slide deck that will be shared by the TA each week. No materials are to be submitted by the student: all content (e.g., full review, journalist blog post, etc.), must be either in the slide or linked to in the slide. Only the programmer, who is expected to do a live demo of their code, will be allowed to share content from their computer.

You can sign up for roles in this link: role signup sheet.

Calendar

Sessions will take place in Uris Hall 306. Click any session's name to open the paper, or download them all by clicking on this link.

Week Monday (4:10pm – 6:00pm) Notes
1February 2nd: Welcome
2February 9th: Marching cubes: A high resolution 3D surface construction algorithm
3February 16th: Dual Contouring of Hermite Data
4February 23rd: Neural Dual Contouring
5March 2nd: Reach for the Spheres: Tangency-Aware Surface Reconstruction of SDFs
6March 9th: Surface Extraction from Neural Unsigned Distance Fields
7March 16th: Spring break: No class-
8March 23rd: Surface Reconstruction from Unorganized Points
9March 30th: Robust inside-outside segmentation using generalized winding numbers
10April 6th: Poisson Surface Reconstruction
11April 13th: Screened Poisson Surface Reconstruction
12April 20th: Point2Mesh: a self-prior for deformable meshes
13April 27th: Students' voted choice I
14May 4th: Students' voted choice II

Evaluation

This class will be graded weekly based on attendance and quality of presentation, including whether the student fully understand every aspect of what they present in class (see "Generative AI policy"). There is no final project or exam. You will be graded on your performance on each of the ten roles, with your final grade being the average of them.

Academic honesty

Please review the Academic Honesty and Integrity policies from the Department of Computer Science and the School of Engineering . Students must abide by these policies, or suffer the penalties enumerated in them.

Generative AI policy

You are encouraged to use any generative AI to understand and read papers, prepare presentations and write code. However, students will be asked questions during their presentations, and will be graded based on their perceived understanding of the material they are presenting. If the student is judged to not understand the content of the work they are presenting, they may receive a failing grade regardless of the quality of said content.

In particular:

Content Warning

In this seminar course, we will discuss not only the technical aspects of geometry processing research, but also the ethical and societal implications of this work (e.g., military applications, surveillance, algorithmic bias). This may involve discussing sensitive topics, which may or may not be related to current events. Students are asked to read the following statement proposed by the Provost's Advisory Committee on Academic Freedom:

Knowledge flourishes when inquiry is free and respectful. Consistent with University and department policies, the instructor has the authority to set the class syllabus, which may include controversial material relevant to topics being studied. While all participants and their views will be treated respectfully, no one should expect to be shielded from challenging or even upsetting ideas, as thoughtfully engaging such ideas is crucial to free inquiry and intellectual growth.