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, 1pm-2pm (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

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 (zoom link in your email or Piazza).

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.

Thu3SeptBackground: Linear Algebra and OptimizationPDF
Thu10SeptShape RepresentationsPDF
Tue15SeptDifferential Geometry: CurvesPDF
Thu17SeptDifferential Geometry: SurfacesPDF
Thu24SeptApplications of CurvaturePDF
Tue29SeptContinuous LaplacianPDF
Thu1OctDiscrete LaplacianPDF
Tue6OctLaplacian ApplicationsPDF
Tue13OctVector FieldsPDF
Thu15OctApplications of Vector FieldsPDF
Tue20Oct(no class, reading week)
Thu22Oct(no class, reading week)
Tue27OctShape DeformationPDF
Thu29OctOverview of Computational GeometryPDF
Tue3NovMesh ParameterizationPDF
Thu12NovSurface ReconstructionPDF
Thu19NovStudents' paper presentations
Tue24NovClustering and SegmentationPDF
Thu26NovSketch-Based ModelingPDF
Tue1DecLearning (on) 3D Geometry
Thu3Dec(Discrete Exterior Calculus?)
Tue8DecFinal project presentations


#Date ReleasedDate dueLinks
1Sept, 10thOct, 1stLink in Piazza
2Oct, 2ndOct, 16thLink in Piazza
3Oct, 27thNov, 13thLink 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 19th

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 16th, by midnight (1 page, Piazza private post)
Final presentation: Dec 8th, in class (20 min + questions)

Coding: Unless you chose a paper that can be done in Matlab, 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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