This course aims to develop the students’ intuition to develop systems that process polygon mesh surfaces. It presents the mathematical tools used for mesh processing, as well as algorithmic approaches to represent and process meshes.

Upon completion of this course, students will be able to: select and assemble appropriate operators to modify meshes; select and execute geometry processing operators on meshes; design software solutions involving polygon mesh processing.

Covered topics: polygonal modeling, surface filtering, Laplacian, surface editing, mesh quality and its improvement, parameterization, surface distortion, curvature, geodesic distance and path, mesh matching, surface reconstruction.

The course will be thought in English. Students can ask questions in either English or French.

The lectures and examinations will be conducted online using Zoom and Moodle.

The learning objectives will be met through weekly three-hour lectures, a series of quizzes, practical implementation tasks, and a presentation. 

Students can write their examinations in either English or French. Presentations must be done in English

• Surface modeling: polygons, meshes, data structures, adjacency matrix (3 hours)
• Properties of triangles, meshes, and surfaces: normal, curvature, homeomorphism, topology, barycentric coordinates, valence, degree (3 hours)
• Visualization of surface properties, mesh processing tools, mathematical tools: HSV color space, least-squares minimization, staggered grids, Jacobian (3 hours)
• Convex hull, bounding volume (3 hours)
• Quality of polygons and meshes: vertex position, vertex split, edge collapse (3 hours)
• Surface processing: smoothing, filtering, subdivision (3 hours)
• Surface deformation: free-form deformation, Laplacian surface editing, gradient-based editing (3 hours)
• Animation by surface deformation: blend shapes, skeletal animation, linear blend skinning, dual quaternions (3 hours)
• Textures and surface parameterization (3 hours)
• Distortion measurements (3 hours)
• Surface reconstruction and triangulation: point cloud, Delaunay, Poisson surface reconstruction, marching cubes (3 hours)
• Distances: L₀, L₁, L₂, L_inf, Dijkstra, geodesic, Hausdorff (3 hours)
• Curves and surfaces: Bézier, BSpline, subdivision surfaces, implicit surfaces (3 hours)

The list of topics and sequence of topics may vary. The hours listed are approximate and for informational purposes only.

60% Quizzes (4 x 15%) – Online/Moodle
40% Practical Work on Mesh/Surface Processing

• Personal project - proposal (5%), interim report (10%), final report (15%), presentation (10%)
• Presentations will be done online over Zoom

Note: Bilingual students can decide to write the text of their quizzes and reports in English or French.

Late submissions will incur a 20% penalty, plus an additional 20% deduction for each full day of delay. If multiple components are required for a single assignment, the work is considered submitted only when all components have been handed in.

Afin de faire valider une absence à une évaluation en vue d’obtenir un examen de compensation, l’étudiante ou l’étudiant doit utiliser le formulaire prévu à cet effet dans son portail MonÉTS pour un examen final qui se déroule durant la période des examens finaux ou pour tout autre élément d’évaluation surveillé de 15% et plus durant la session. Si l’absence concerne un élément d’évaluation de moins de 15% durant la session, l’étudiant ou l’étudiante doit soumettre une demande par écrit à son enseignante ou enseignant.

Toute demande de validation d’absence doit se faire dans les cinq (5) jours ouvrables suivant la tenue de l’évaluation, sauf dans les cas d’une absence pour participation à une activité prévue aux règlements des études où la demande doit être soumise dans les cinq (5) jours ouvrables avant le jour de départ de l’ÉTS pour se rendre à l’activité.

Toute absence non justifiée par un motif majeur (voir articles 7.2.6.1 du RÉPC et 6.5.2 du RÉCS) entraînera l’attribution de la note zéro (0).

None

BOTSCH, KOBBELT, PAULY, ALLIEZ, LÉVY, Polygon Mesh Processing, A K Peters, 2010.

https://ena.etsmtl.ca/   
libigl Tutorial: https://libigl.github.io/tutorial/