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 at AA 3357.

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

Course Work

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


Lectures are Tuesdays 9.30-11.30 (in AA 3195) and Thursdays 16.30-18.30 (in AA 1207).

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.

Thu5SeptBackground: OptimizationPDF
Tue10SeptShape RepresentationsPDF
Thu12SeptDifferential Geometry: CurvesPDF
Tue17SeptDifferential Geometry: SurfacesPDF
Thu19SeptApplications of curvature. Mesh simplification, visualization, saliencyPDF
Tue24SeptLaplacian Operator: ContinuousPDF
Thu26SeptLaplacian Operator: DiscretePDF
Thu3OctApplications of Laplacian OperatorPDF
Tue8OctVector FieldsPDF
Thu10OctVector Fields ApplicationsPDF
Tue15OctShape DeformationPDF
Tue22Oct(no class, reading week)
Thu24Oct(no class, reading week)
Tue29OctOverview of Computational GeometryPDF
Thu31OctMesh ParameterizationPDF
Tue12NovSurface ReconstructionPDF
Tue19NovStudents' paper presentations
Thu21NovStudents' paper presentations
Tue26NovClustering and SegmentationPDF
Thu28NovSketch-Based ModelingPDF
Tue3DecLearning (on) 3D GeometryPDF
Thu5DecFinal project presentations


#Date ReleasedDate dueLinks
1Sept, 19thOct, 3rdLink in Piazza
2Oct, 3rdOct, 22ndLink in Piazza
3Oct, 23thNov, 12thLink 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): Tue, Nov 19th & Thu, Nov 21st

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 15th, by midnight (1 page, Piazza private post)
Final presentation: Dec 5th, 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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