IFT 6113:
Geometric Modeling
and Shape Analysis

This course provides an advanced introduction to the digital geometry processing, modeling, and shape analysis.

We will learn the math and the algorithms behind modern mesh processing and modeling. For our assignments we'll use MATLAB and C++.

Please see the official UdeM course description for prerequisites and schedules.

Instructor: Mikhail Bessmeltsev. Office hour: Fri, 5pm-6pm (Zoom link announced in Piazza).

TA: Ivan Puhachov

Contact: We will use Piazza for all the announcements and questions. Please sign up!

Previous years: 2019, 2020

Course Work

Mark distribution: Assignments (33%), Paper Presentation (25%), Participation (2%), Final Project (40%)


Lectures are Tuesdays 9.30-11.30 and Thursdays 16.30-18.30, both in AA 1411.

Here lecture materials will appear as we proceed, with no guarantee we'll post everything. So do come to the lectures!

Topics for the future dates are subject to change with no warning, so do not rely on them.

Tue7SeptBackground: Linear Algebra and OptimizationPDF | Notes
Tue14SeptShape RepresentationsPDF
Thu16SeptDifferential Geometry: CurvesPDF | Notes
Tue21SeptDifferential Geometry: SurfacesPDF | Notes
Tue28SeptApplications of CurvaturePDF
Thu30SeptContinuous LaplacianPDF | Notes 1 | 2
Tue5OctDiscrete LaplacianPDF
Thu7OctLaplacian ApplicationsPDF | Notes
Tue12OctVector FieldsPDF
Thu14OctApplications of Vector FieldsPDF
Tue19Oct(no class, reading week)
Thu21Oct(no class, reading week)
Thu28OctShape DeformationPDF
Tue2NovOverview of Computational GeometryPDF
Thu4NovMesh ParameterizationPDF
Thu11NovRemeshingPDF | Notes
Tue16NovSurface ReconstructionPDF | Notes
Thu18NovStudents' paper presentations
Thu25NovLearning (on) 3D Geometry (Guest lecture)
Tue30NovClustering and Segmentation
Thu2DecSketch-Based Modeling
Tue7DecFinal project presentations


#Date ReleasedDate dueLinks
1Sept, 14thOct, 1stLink in Piazza
2Oct, 4thOct, 18thLink in Piazza
3Nov, 1stNov, 15thLink in Piazza

Each programming assignment is due 23:59:59 pm on the day specified, measured by Piazza. No late assignments accepted, except for the grace days:

Grace days: Each student may use up to 3 grace days per term. We will keep track of your grace days. Use these as you wish to help manage your time, but use them wisely. You can use all three on one assigment, or one day for each of three assignments. Grace days are counted as integers, i.e., if you are one hour late, that counts as one grace day. Once your grace days are all used, late assignments will receive a grade of zero.

Grading: We will use "face-to-face grading," i.e., you will be required to demonstrate that you understand why your program works. You must be able to explain every single line you wrote! You must get a passing grade in assignments to pass the course.

Paper Presentation

Each student should present a paper published at SIGGRAPH in the recent years. Every other (non-presenting) student should prepare, read the paper, and ask at least one question. Here's a list of papers to choose from, but feel free to suggest a different interesting paper, prior to my approval.

Please let me know which paper you choose to present by Oct 29th.
In-class paper presentation (10min + 4 min questions): Thu, Nov 18th

Final Project

Choose any paper published in the recent 5 years in SIGGRAPH (see Ke-Sen Huang's website), propose a modification/improvement, implement, present. Your grade for the project will be 80% for implementation (marked at face-to-face grading), and 20% for the final presentation.

Important dates:
Project proposal: Oct 25th, by midnight (1 page, Piazza private post)
Final presentation: Dec 7th, in class (20 min + questions)

Coding: Unless you chose a paper that can be easily done in Matlab or Python, I strongly recommend coding in C++ using libigl: it's easy to use and has a very nice set of tutorials. Clearly, if you're using libigl, you can't implement something that is already implemented in the library.


There is no official textbook for the course, but a lot of material is covered in Polygon Mesh Processing by Botsch et al. More reading materials will appear here as we go.

The course is based on similar courses by Justin Solomon (MIT) and Alla Sheffer (UBC). Many slides are derived from their slides.

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