IFT 6112:
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: 1pm-2pm at AA 6191.

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 14.30-16.30 (in AA 1409).

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.

Thu, Sept 601 - Intro[PDF]
Tue, Sept 1102 - Background: Optimization[PDF]
Thu, Sept 1303 - Shape Representations[PDF]
Tue, Sept 1804 - Differential Geometry: Curves[PDF]
Thu, Sept 2005 - Differential Geometry: Surfaces[PDF]
Tue, Sept 2506 - Applications of curvature. Mesh simplification, visualization, saliency[PDF]
Thu, Sept 2707 - Laplacian Operator: Continuous[PDF]
Tue, Oct 208 - Laplacian Operator: Discrete[PDF]
Thu, Oct 4(Still finishing Laplacian)
Tue, Oct 909 - Applications of Laplacian Operator[PDF]
Thu, Oct 1110 - Vector Fields[PDF]
Tue, Oct 1611 - Vector Fields Applications[PDF]
Thu, Oct 1812 - Shape Deformation[PDF]
Tue, Oct 23(no class, reading week)
Thu, Oct 25(no class, reading week)
Tue, Oct 30(finishing deformation)
Thu, Nov 113 - Overview of Computational Geometry[PDF]
Tue, Nov 614 - Mesh Parameterization[PDF]
Thu, Nov 8(finishing parameterization)
Tue, Nov 1315 - Surface Reconstruction[PDF]
Thu, Nov 1516 - Remeshing[PDF]
Tue, Nov 2017 - Geodesics[PDF]
Thu, Nov 22(Students' paper presentations)
Tue, Nov 2718 - Clustering and Segmentation[PDF]
Thu, Nov 2919 - Sketch-Based Modeling[PDF]
Tue, Dec 4(Final project presentations)
Thu, Dec 6Course recap


#Date ReleasedDate dueLinks
1Sept, 20thOct, 4thInstructions
2Oct, 4thOct, 18thInstructions
3Oct, 23rdNov, 12thInstructions

To submit your programming assignment, please use handin.

Each programming assignment is due 23:59:59 pm on the day specified, measured by the handin. 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. Presentation should be around 40 minutes, not including questions. 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 21st (before the reading week).

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, email me)
Final presentation: Dec 6th, 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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