[2013 Fall]
CIS-6930-U03: Special Topics - Digital Geometry Processing


Conference: ECS 134, Friday 3:00-5:50PM

Instructor: Dr. Wei Zeng

Office: ECS 357

Office Hours: Wed 2:00-5:00PM, or by appointment

Homepage: http://www.cis.fiu.edu/~wzeng/


Email: N/A


12/18: Grades are ready for review!

12/01: All the project materials should be submitted to Moodle by Dec 13!

11/19: Visted Discovery Lab @ FIU-SCIS (see snapshots in the bottom)! Great Thanks to Dr. Jong-Hoon Kim!

10/18: Midterm presentation on Nov 01!

09/02: Conference time has been changed from 1:00-3:50pm to 3:00-5:50pm on Friday!

08/11: Syllabus was released!

Lecture Schedule

Notes: More course materials can be found in Moodle.

08/30: Lecture#01: Introduction to Geometry & Topology; Project Assignment.

09/06: Lecture#02: Discrete Surface; Project Presentation and Discussion (P&D).

09/13: Lecture#03: Half Edge; Project P&D.

09/20: Lecture#04: Homology; Project P&D.

09/27: Lecture#05: Fundamental Domain; Project P&D.

10/04: Lecture#06: Homotopy; Project P&D.

10/11: Lecture#07: Universal Cover; Project P&D.

10/18: Lecture#08: Topological Algorithm; Project P&D.

10/25: Lecture#09: Project Review & Discussion

11/01: Lecture#10: Midterm Project Presentation

11/08: Lecture#11: Hodge Decomposition; Project P&D.

11/15: Lecture#12: Harmonic Map; Project P&D.

11/22: Lecture#13: Ricci Flow; Project P&D.

11/29: Lecture#14: Thanksgiving Holiday

12/06: Lecture#15: Sureface Registration and Shape Analysis; Applications; Project P&D.

12/13: Lecture#16: Final Project Presentation


1. 2D/3D Computer Graphics: Raytracer, Rendering, Texture Mapping, Parameterization, Animation.

2. Introduction to Geometry & Topology: 2D/3D mapping, Surface uniformization, Conformal structure

3. Discrete surface: Gauss-Bonnet theorem, HalfEdge data structure

4. Topology: Simplicial homology, Fundamental group, CW-cell decomposition

5. Holomorphic 1-form, Combinatorial Hodge decomposition

6. Harmonic mapping, Heat diffusion

7. Ricci flow: Euclidean Ricci flow, Inversive distance Ricci flow, Yamabe flow, Hyperbolic Ricci flow

8. Surface registration & Shape analysis

9. Applications: Computer Vision, Medical Imaging, Wireless Sensor Network

10. Paper reading, Project discussion


None Required


SCIS Graduate Standing (or equivalents, or permission of instructor)


Elective for MSCS, MSIT, MSTN, and Ph.D. students 

Course Objectives

Students will learn fundamental theories and computational algorithms for conformal geometry, and broad applications in engineering and biomedical fields. The seminar course aims at using computational approach and visualization techniques to teach abstract geometric theories and prepare for Graphics related research.


1. Computational Conformal Geometry. Xianfeng David Gu and Shing-Tung Yau. International Press, 2008.

2. Ricci Flow for Shape Analysis and Surface Registration: Theories, Algorithms, and Applications. Wei Zeng and Xianfeng David Gu. Springer, 2013.

Other Reading Material: Lecture notes; Related journal articles and conference papers.

Grading Policy

Midterm report (project preparation: paper reading / outline / presentation): 40%

Final report (project implementation: programming / report / presentation / demo): 60% 

Notes: All the midterm/final assignment, submission, and grading will be done through Moodle.

1. The due date will be announced with assignment. Late submission will generally not be accepted. If there are extenuating circumstances, you should make prior arrangements with Instructor .

2. The midterm/final projects can be done independently or in a form of study group.

3. Each report includes: 1) your name, and 2) the names of any people you worked with, or ¡°Collaborators: none¡± if you did that completely alone.

4. Plagiarism and other dishonest behavior cannot be tolerated in any academic environment that prides itself on individual accomplishment.

University Policies and Regulations

1. Regulations concerning Incomplete Grades: http://academic.fiu.edu/polman/sec16web.htm 

2. For academic misconduct, sexual harassment, religious holydays, and information on services for students with disabilities, please see:





©2013 Wei Zeng        http://www.cs.fiu.edu/~wzeng           Last Updated: 12/18/2013