Fundamentals of Computer Graphics
Course material
News
- 23/06/2019: The final exam dates are from 15 Jul to 19 Jul 2019. Please contact me directly to fix the exact date and time, and remember to register on Infostud.
Logistics
Who: Prof. Emanuele Rodolà
When: Mondays 14:00-16:30 and Thursdays 08:00-10:30 (see the official schedule)
Where: Aula Alfa - Sociologia, via Salaria 113
Office Hours: Drop me an email at my-last-name-without-accent@di.uniroma1.it
Pre-requisites
Fundamentals of programming is a must-have, since there are coding assignments; there is no mandatory language, although lecture material will prefer Matlab. Linear algebra, calculus and numerical methods are nice-to-have, but not essential; the key concepts will be reviewed throughout the course.
Syllabus
The course will cover topics of 3D shape representation, analysis, processing, matching, and modeling. An emphasis will be put on discrete geometry processing algorithms with applications in computer vision and graphics. Shape rendering and visualization will also be touched upon. The course will start from scratch by reviewing the key mathematical concepts and will proceed step by step up to the most recent advances in the area. Invited lectures from prominent scientists in the field are also expected.
Text book and reading material
The lectures are not based on any text book in particular. Reading material suggested throughout the lectures is listed here:
- [A15] Axler, “Linear algebra done right - 3rd edition”. Springer, 2015.
- [BBI01] Burago, Burago, Ivanov, “A course in metric geometry”. AMS, 2001.
- [POV] POV-Ray reference
- [dC76] Do Carmo, “Differential geometry of curves and surfaces”. Prentice-Hall, 1976.
Grading
Grades for the midterm evaluation are available here.
The final project will be discussed in an oral examination, and may fall into one of these categories:
- In-depth survey of a topic related to the syllabus
- Coding assignment plus report
A non-definitive list of topics / coding projects is the following:
- “Biharmonic distance”
- “Earth mover’s distances on discrete surfaces”
- “Geodesics in heat”
- “Blended intrinsic maps”
- “Partial functional correspondence”
- “Fast approximation of Laplace-Beltrami eigenproblems”
- “An operator approach to tangent vector field processing”
- “Linear rotation-invariant coordinates for meshes”
- “Deblurring and denoising of maps between shapes”
- “As-rigid-as-possible surface modeling”
- “Bounded biharmonic weights for real-time deformation”
- “Convolutional Wasserstein distances”
- “Laplace-Beltrami spectra as ‘Shape-DNA’ of surfaces and solids”
- “Can mean-curvature flow be made non-singular?”
Lectures
| Date | Topic | Reading | Code & Data |
|---|---|---|---|
| Mon 24 Sep | Introduction; Shape representation | slides | cat0.off ; load_off.m ; save_as_off.m ; calc_tri_areas.m ; calc_boundary_edges.m |
| Thu 27 Sep | Metric geometry | slides | fps_euclidean.m ; voronoi_euclidean.m |
| Mon 01 Oct | Euclidean embeddings | slides | sphere.off ; tr_reg_000.off ; geodesic distances for tr_reg_000.off |
| Thu 04 Oct | Shape visualization I; Piecewise-linear approximation | slides | cat_partial.off |
| Mon 08 Oct | Recap of linear algebra I | slides ; [A15] | bunny.off |
| Thu 11 Oct | Assignment problems | slides ; RL11 ; [BBI01] | tr_reg_001.off ; tr_reg_002.off ; tr_reg_003.off ; bun000.off ; bun045.off |
| Mon 15 Oct | Shape visualization II | slides ; [POV] | cat2.off ; load_mesh.inc ; save_mesh_povray.m ; demo.m ; render.pov |
| Thu 18 Oct | Recap of linear algebra II | slides ; [A15] | tr_reg_010.off ; tr_reg_031.off |
| Thu 25 Oct | Wrap-up | slides | dog0.off ; dog.sym.labels |
| Mon 05 Nov | Midterm evaluation | ||
| Thu 08 Nov | Mesh processing I | slides ; SC04 | |
| Mon 12 Nov | Regular surfaces | slides ; [dC76] | |
| Thu 15 Nov | Projects | ||
| Mon 19 Nov | Lengths and areas | slides (pdf) ; slides (pptx) ; [dC76] | |
| Thu 22 Nov | The gradient | slides (pdf) ; slides (pptx) | |
| Mon 26 Nov | The Laplace-Beltrami operator | slides | |
| Thu 29 Nov | Spectral geometry | slides | deadpool.off |
| Mon 03 Dec | Paper reading: Functional maps | paper | |
| Thu 06 Dec | Heat diffusion | slides ; SOG09 ; C05 | |
| Mon 10 Dec | Exercises | slides ; MRCB18 | calc_LB_FEM.m |
| Thu 13 Dec | Talk: Isospectralization | slides ; CPROBR18 | |
| Thu 20 Dec | Current and future perspectives | RPWO18 ; WHOG14 ; RO13 ; RLBBS18 ; MBBV15 | |
| End |