CS492(J): Geometric Modeling and Processing
Minhyuk Sung, KAIST, Fall 2022
Time & Location
Time: Mon/Wed 10:30am - 11:45am (KST)
Location: Building N1, Room 201.
Description
3D content creation is a crucial part of many industries such as graphics, AR/VR, CAD/CAM, and digital fabrication, which tasks typically include designing and creating virtual objects/scenes or reconstructing a real environment. Processing scanned 3D data is also an important problem in many applications as 3D scanning technology is being widely applied, for example, in autonomous driving, robot navigation, and 3D object replication. In this course, we discuss fundamental mathematical methods for geometric 3D modeling and geometric data processing, which can be used (not only in graphics-related fields but) in many other areas in science and engineering. Topics to be covered include the followings:
- Homogeneous coordinates and geometric transformations
- Quaternions and their use in modeling 3-d rotations and rigid motions
- Parametric and implicit representations for curves
- Algebraic classification of the parametric polynomial curves of low degree
- Polar forms and the de Casteljau's subdivision algorithm
- The Bézier representation and the Bernstein basis
- Splines and continuity constraints
- B-Splines and the de Boor's algorithm
- Rational curves
- Parametric polynomial surfaces and NURBS
- Subdivision curves and surfaces
- Triangle meshes for surface representation and reconstruction
- The quad-edge data structure for manifold subdivision
- Volumetric representations and conversion algorithms
- Surface reconstruction from scattered points
- Scan alignment and shape matching
- Mesh simplification and fairing
- Mesh parametrization and other geometry processing algorithms
Prerequisites
The following courses are not required but recommended:
- CS380: Introduction to Computer Graphics
- MAS109: Introduction to Linear Algebra
Students are also expected to have good programming skills in C/C++.
Course Staff
Instructor: Minhyuk Sung
- Email: mhsung@kaist.ac.kr
- Office hours: By appointment (See #announcements channel in Discord.)
Course Assistant: Juil Koo
- Email: 63days@kaist.ac.kr
Links
- Course Website: https://mhsung.github.io/kaist-cs492j-fall-2022/
- Quizzes, Q&A, and communication: Discord (An invitation will be sent to the registered students by email.)
- Homework submission: Gradescope (An invitation will be sent to the registered students by email.)
Grading
- Homework (Including Programming Assignments): 50%
- Midterm Exam: 15%
- Final Exam: 20%
- Participation: 15%
Course Logistics
(Last Update: Aug 29, 2022)
Important Dates
ALL ASSIGNMENTS ARE DUE 23:59 KST. Each student is allowed five late days in total.
(Subject to Change)
- Homework 1: Due Sep 26 (Mon)
- Homework 2: Due Oct 12 (Wed)
- Midterm: Oct 19 (Wed) 9:30 a.m. - 12:00 p.m.
- Homework 3: Due Nov 2 (Wed)
- Homework 4: Due Nov 16 (Wed)
- Homework 5: Due Dec 5 (Mon)
- Final: Dec 14 (Wed) 9:30 a.m. - 12:00 p.m.
Schedule
(Subject to Change)
| Week | Mon | Topic | Wed | Topic |
|---|---|---|---|---|
| 1 | Aug 29 | Course Introduction Slides |
Aug 31 | Transformations / Homogeneous Coordinates Slides |
| 2 | Sep 5 | Projective Geometry / Oriented Projective Geometry Slides |
Sep 7 | Rotations / Quaternions Slides Homework 1 out |
| 3 | Sep 12 | No Class (Chuseok Holidays) | Sep 14 | Parametric and Implicit Representations Slides |
| 4 | Sep 19 | Bézier Curves / Polar Forms Slides |
Sep 21 | Continuity Constraints / Derivatives Slides |
| 5 | Sep 26 | De Boor Points Slides Homework 1 due, Homework 2 out |
Sep 28 | De Boor Points / B-Splines Slides |
| 6 | Oct 3 | No Class (National Foundation Day) | Oct 5 | Rational Curves Slides |
| 7 | Oct 10 | No Class (Hangul Day) | Oct 12 | Midterm Summary Slides Homework 2 due, Homework 3 out |
| 8 | Oct 17 | No Class (Midterm) | Oct 19 | No Class (Midterm) |
| 9 | Oct 24 | Tensor-Product and Total-Degree Parametric Surfaces Slides |
Oct 26 | Differential Geometry of Curves Slides |
| 10 | Oct 31 | Introduction to Geometry Processing Slides |
Nov 2 | Shape Registration Slides Homework 3 due, Homework 4 out |
| 11 | Nov 7 | Implicit Representations Slides |
Nov 9 | No Class |
| 12 | Nov 14 | Mesh Simplification / Global Matching Slides |
Nov 16 | Poisson Surface Reconstruction / Marching Cubes Slides Homework 4 due, Homework 5 out |
| 13 | Nov 21 | Shape Correspondence / Laplace-Beltrami Operator Slides |
Nov 23 | Heat Kernel Signature Slides |
| 14 | Nov 28 | Functional Maps Slides |
Nov 30 | Final Summary Slides |
| 15 | Dec 5 | KAIST Geometric and Visual Computing Workshop | Dec 7 | No Class Homework 5 due |
| 16 | Dec 12 | No Class (Final) | Dec 14 | No Class (Final) |
Acknowledgements
Most of the lectures will be based on the materials in the following courses:
Stanford CS348A: Geometric Modeling / Processing
Stanford CS233: Geometric and Topological Data Analysis
-
Teaser image credits (from left to right):
Ray et al., Periodic global parameterization, ACM ToG 2006.
Alliez et al., Recent Advances in Remeshing of Surfaces, Springer 2008.
https://help.autodesk.com/cloudhelp/2019/ENU/Alias-Tutorials/images/GUID-844B95EE-96B1-4C41-972D-835946754231.png ↩
