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 [email protected]

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