061316601: Digital Geometry Processing

(Autumn-Winter 2007)

Department of Mathematics

Zhejiang University


Announcements     General     Description      Course Goals     Topics     Texts     Grading  

Syllabus     Assignments     Requirements on Assignments      Professional Conduct     Resources


Announcements


General
 

Times Friday (9:50-11:25)
Room Yuquan Campus, Ouyangchunmei Building Room 314
Instructor Dr. Ligang Liu ( ligangliu@zju.edu.cn )
Phone (+86) 571-8795-3668
Credit 2
Prerequisite Computer Graphics, CAGD, C/C++
   
Webpage http://www.math.zju.edu.cn/ligangliu/Courses/DGP_2007-2008/default.htm

 


Description

 

The arrival of 3D scanning has created a new wave of digital media after sound, images, and video, raising the need for digital processing algorithms. Traditionally fine detail geometry is represented through unstructured polygonal meshes. Such meshes are awkward for editing, filtering, and compression applications. This course will focus on Digital Geometry Processing (DGP), which addresses computerized modeling of discrete (digital) geometry, namely polygonal meshes.  We will show how to build semi-regular meshes from unstructured polygonal meshes and raw range data, and how to build applications such as filtering, editing, simulation, and compression using triangular meshes.

Prerequisite: Computer graphics, Computer aided geometric design, C++, MFC, OpenGL/DirectX

 


Course Goals

In this course, we will explore advanced techniques for representing and processing geometric object models. The goals of this course are to extend and deepen the student's knowledge and understanding of algorithms and data structures and the associated design and analysis techniques. It examines previously studied algorithms and data structures more rigorously and introduces the student to "new" algorithms and data structures. It focuses the student's attention on the design of program structures that are correct, efficient in both time and space utilization, and defined in terms of appropriate abstractions.


Topics
 

This course provides a comprehensive introduction to mesh processing, including their design, analysis, and implementation. Topics include:
   
·mesh data structure
   
·3D scanner techniques
   
·surface reconstruction
   
·mesh smoothing
   
·mesh simplification
   
·geometry compression
   
·mesh parameterization
   
·mesh segmentation
   
·deformation and morphing
   
·subdivision surfaces
   
·shape analysis
   
·discrete differential geometry


Texts
 

References:
            W. Sweldens and P. Schroder. Digital Geometry Processing, SIGGRAPH'2001, course notes.
            Many researchers' courseware (eg. Prof. Alla Sheffer)

Readings:
            Various journal papers, conference papers, or WWW materials as appropriate.
 


Grading

Credit toward the semester grade will be allocated to each of the components as indicated in the following table.

Programming exercises 20%
Projects (2 or 3) 40%
Literature survey and report 40%

Note: No final examination will be held in the end of this course. Programming projects and literature survey report are both required. More information will be provided in the class.


Syllabus

Note: The PPT courseware of all lectures are available upon request.

Seminar

Week

Date

Topic

Papers

Speaker

PPT
1 2007.11.02. Shape deformation * Olga Sorkine and Marc Alexa. As-Rigid-As-Possible Surface Modeling. SGP 2007.
* Takeo Igarashi, Tomer Moscovich, John F. Hughes. As-Rigid-As-Possible Shape Manipulation. Siggraph 2005.
* M. Alexa et al. As-rigid-as-possible shape transformation. Siggraph 2000.
张正 PPT
2 2007.11.09. Barycentric coordinates * Yaron Lipman, Johannes Kopf, David Levin and Daniel Cohen-Or. GPU-assisted Positive Mean Value Coordinates for Mesh Deformation. SGP 2007.
* K. Hormann and S. Floater. Mean value coordinates for arbitrary planar polygons. ACM Transactions on Graphics 25, 4 (2006), 1424–1441.
* T. Ju, S. Schaefer, J. Warren. Mean value coordinates for closed triangular meshes. Siggraph 2005.
周世哲 PPT
3 2007.11.15. Mean shift * Mean Shift Theory and Applications 计忠平 PPT
4 2007.11.23. Skeletal deformation * Shin Yoshizawa, Alexander Belyaev, Hans-Peter Seidel. Skeleton-based Variational Mesh Deformations. Eurographics 2007.
* Ofir Weber, Olga Sorkine, Yaron Lipman, Craig Gotsman. Context-Aware Skeletal Shape Deformation. Eurographics 2007.
金亮 PPT
5 2007.11.30. Surface Parametrization * A. Sheffer and E. de Sturler. Parametrization of faceted surfaces for meshing using angle-based flattening. EWC 2001.
* A. Sheffer et al. ABF++: Fast and robust angle based flattening. ACM TOG, 2005.
* Rhaleb Zayer, Bruno Levy, and Hans-Peter Seidel. Linear Angle Based Parameterization. SGP 2007.
徐寅 PPT
6 2007.12.07. Discrete differential geometry * Max Wardetzky, Felix Kaelberer, Saurabh Mathur and Eitan Grinspun. Discrete Laplace Operators: No Free Lunch. SGP 2007.
* Evangelos Kalogerakis, Patricio Simari, Derek Nowrouzezahrai and Karan Singh. Robust Statistical Estimation of Curvature on Discretized Surfaces. SGP 2007.
朱薇 PPT
7 2007.12.14. Surface reconstruction * Yaron Lipman, Daniel Cohen-Or and David Levin. Data-Dependent MLS for Faithful Surface Approximation. SGP 2007.
* Jean-Daniel Boissonnat and Pooran Memari. Shape Reconstruction from Unorganized Cross-Sections. SGP 2007.
* Shachar Fleishman, Claudio Silva, and Daniel Cohen-Or. Robust Moving Least-squares Fitting with Sharp Features. Siggraph 2005.
于洋 PPT
8 2007.12.21. Data registration and alignment * B. J. Brown, S. Rusinkiewicz. Global Non-Rigid Alignment of 3-D Scans. Siggraph 2007.
* Niloy J. Mitra et al. Dynamic Geometry Registration. SGP 2007.
* H. Pottmann, Q.-X. Huang, Y.-L. Yang and S.-M. Hu. Geometry and convergence analysis of algorithms for registration of 3D shapes. International Journal of Computer Vision, 2006.
刘羽 PPT
9 2007.12.28. Surface Fairing and Optimization * Ilya Eckstein, Jean-Philippe Pons, Yiying Tong, C.-C. Jay Kuo and Mathieu Desbrun. Generalized Surface Flows for Mesh Processing. SGP 2007.
* Elif Tosun, Yotam I. Gingold, Jason Reisman and Denis Zorin. Shape Optimization Using Reflection Lines. SGP 2007.
* Klaus Hildebrandt and Konrad Polthier. Constraint-Based Fairing of Surface Meshes. SGP 2007.
陈佳舟 PPT
10 2008.01.04. Skeleton extraction * Andrei Sharf, Thomas Lewiner, Ariel Shamir, Leif Kobbelt. On-the-fly Curve Skeleton Computation for 3D Shapes. Eurographics 2007.
* Valerio Pascucci et al. Robust On-line Computation of Reeb Graphs: Simplicity and Speed. Siggraph 2007.
吴晓群 PPT
11 2008.01.11. Shape space * Martin Kilian, Niloy Mitra and Helmut Pottmann. Geometric Modeling in Shape Space. Siggraph 2007. 刘刚 PPT
           

Assignments

Note: Please zip your submission stuffs of the assignment into one single file either using WinZip or WinRAR. Name the file name as "ID_Name_Assignment_#1.zip" or "ID_Name_Project _#1.zip" where ID is your unique ID number in the class. For Example, my submission file name might be "66_刘利刚_Assignment_01.zip".


Requirements on Assignments
 

Requirements

Assignment Submission

What constitutes Creativity ?

Creativity is any substantial improvement beyond the basic solution - it can be applied to any part of the project. For example, the following are relevant in most cases :


Professional Conduct

As a student in our class, you are expected to conduct yourself in a professional manner.

Limited Collaboration Policy. Unless otherwise indicated, any homework assignment given in this class will be an individual assignment. The work you submit is to reflect the knowledge, understanding, and skill that you have attained as an individual. However, the instructor does want to encourage the development of a community of scholars who are actively engaged in discussion of the ideas related to this course. With this in mind, you are allowed to discuss solutions of the homework and programming problems with other students if done so according to the following guidelines:


Resources

C++ coding styles

Computer Program Documentation Standards

Advices on Researches:

Mesh Models:

Mesh library on the internet:

Model formats:

  • nThe Graphics File Formats Page
  • dxflib — for reading DXF models
  • lib3ds — for reading 3D studio files
  • ply 1.1 — an older version of the PLY library from Stanford
  • PLYtools — Greg Turk’s code for working with PLY files
  • trimesh — a C++ library for working with PLY files from Szymon Rusinkiewicz [not quite as general as the libraries above]
  • Wotsit’s List — as with the image formats, a rather comprehensive list

OpenGL programming:

GUI toolkits:

  • nFLTK — cross-platform toolkit with good OpenGL support
  • GLUT — standard but minimal OpenGL cross-platform toolkit
  • freeglut — Open Source reimplementation of GLUT
  • GLUI — implements typical GUI widgets with OpenGL in GLUT windows
  • GLOW — another OpenGL-based widget set
  • PUI — similar in spirit to GLUI
  • GLGooey — another widgets-in-OpenGL library
  • Cpw — application framework for OpenGL programs (Windows only)

Renders:

Useful coding related sites on the internet:


Send any comments or suggestions to Dr. Ligang Liu, ligangliu@zju.edu.cn
Copyright © 2007, Ligang Liu
Last modified: 01. 11, 2008