CS492(J): Geometric Modeling and Processing
Minhyuk Sung, KAIST, Fall 2022
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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 graphicsrelated 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 3d 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
 BSplines 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 quadedge 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/kaistcs492jfall2022/
 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 / BSplines 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  TensorProduct and TotalDegree 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 / LaplaceBeltrami 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.
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