MA06424 : Selected Topics in Geometric Modeling (Seminar)

(09/2011-01/2012)

School of Mathematical Sciences, University of Science and Technology of China

Announcements     General     Description     Textbooks     Coursework and Grading    Syllabus    Links

Announcements

• 31 Dec.: The third programming assignment is released.
• 30 Dec.: The last class of this seminar.
• 23 Dec.: Class canceled due to the absence of Changsen.
• 11 Nov.: The second programming assignment is released.
• 30 Sep.: The first programming assignment is released.
• 18 Sep.: Xiaoming will give an introuction to subdivision curves/surfaces.
• 09 Sep.: The website is open, and the course is started.

General

Description

This course will explore a number of topics that relate to the construction, representation and manipulation of geometric models on a computer, with the emphasis on three-dimensional surfaces. The purpose of the course is to allow students to explore several aspects in depth through programming and reading recently published articles.

A possible list of basic topics to be covered includes:

• Geometric Modeling Based on Polygonal Meshes
• Subdivision Curves and Surfaces
• Implicit Surfaces
• Point-Based Graphics

What we'll actually get to during the quarter will be determined by the interests of the participants.

Textbooks

There is no formal textbook for this course. However, you will probably find the following books very useful.

• M. Botsch, L. Kobbelt, M. Pauly, P. Alliez, B. Levy. Polygon Mesh Processing. A K Peters. 2010.
• J. Warren, H. Weimer. Subdivision Methods for Geometric Design A Constructive Approach. Morgan Kaufmann Publishers. 2002.
• J. Peters, U. Reif. Subdivision Surfaces. Springer. 2008.
• A. J. P. Gomes, I. Voiculescu, J. Jorge, B. Wyvill, C. Galbraith. Implicut Curves, and Surfaces: Mathematics, Data Structures and Algorithms. Springer. 2009.
• J. Bloomenthal, C. Bajaj, J. Blinn, M. P. Cani-Gascuel, A. Rockwood, B. Wyvill, G. Wyvill. Introduction to Implicit Surfaces. Morgan Kaufmann Publishers. 1997.
• M. Gross, H. Pfister. Point-Based Graphics. Morgan kaufmann Publishers. 2007.

Coursework and Grading

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

Note: No final examination will be held in the end of this course. But programming and presentations are both required. More information will be provided in the class.

Coursework will be split into two categories: programming assignments and oral presentations, and course projects.

• Programming Assignments:

  There will be a 3-5 programming assignments for which students will implement an algorithm in 3D geometric modeling. Approximately three weeks will be allowed for each programming assignment.
  

  1. For this assignment, you will write a program that provides a framework for rendering 3D graphics scenes based on MFC plus OpenGL, which should fulfill the following requirements:
     • The program must be able to read a mesh from an arbitrary *.off file, and convert the representation to a half-edge data structure.
     • The program should render the mesh to the viewport. The minimum requrirtments are that you render the mesh flat shaded and as a wireframe composite. It is better to implement Gouraud shading model as well.
     • The user interface(UI) should be able to (a) translate, rorate and zoom the model by holding the left mouse button over the viewport and dragging the mouse(possibly holding down a key modifier), and (b) manually select the rendering mode (flat, wireframe, composite, etc.).
     • Bonus: the program is able to load an arbitrary *.ply file.
     • Handout: Friday, 09/30/2011-Due date: Friday, 10/21/2010.
     
     
  2. In this assignment you will extend your mesh program with smothing tools. Implemen the following algorithms:
     • The explicit mesh faring algorithms (Section 2) described in the paper titled with "A Signal Processing Approach To Fair Surface Design" by G. Taubin in the proceeding of ACM SIGGRAPH 1995.
     • The implicit mesh faring algorithms (Section 2 and 5) described in the paper titled with "Implicit Fairing of Arbitrary Meshes using Diffusion and Curvature Flow" by M. Desbrun et al. in the proceeding of ACM SIGGRAPH 1999.
     • The user interface(UI) should be able to set parameters in the previous algorithms.
     • Bonus: the program is able to show reflect lines (hints: use texture mapping).
     • Handout: Friday, 11/11/2011-Due date: Friday, 12/02/2011.
     
     
  3. (optional) In this assignment you will implement two subdivsion algorithms:
  • The Catmull-Clark subdivision described in the paper titled with "Recursively generated B-spline surfaces on arbitrary topological meshes" by E. Catmull and J. Clark in Computer-Aided Design 10(6): 350-355, 1978.
  • The Doo-Sabin subdivision described in the papre titled with "Behaviour of recusive division surfaces near extraordinary points" by D. Doo and M. Sabin in Computer-Aided Design 10(6): 356-360, 1978.
  • Bonus: the program is able to show reflect lines and curvature map (hints: use texture mapping and color mapping).
  • Handout: Saturday, 12/31/2011-Due date: Sunday, 01/08/2012.


• Oral Presentations:

  Each student will be asked to prepare a lecture on a specific topic for this course. A list of papers on the topic will be provided by the instructor. The student will read the papers, find other relevant papers, and present a synthesized view of the problems, previous approaches, and outstanding research issues. One week before the lecture, the student will submit a draft version of ``overhead slides'' to the instructor for discussion.
  

Syllabus and Schedule

Links

• Windows OpenGL: Programming Guide from MSDN
• MFC + OpenGL: An Example
• Test Modles: two OFF, and two PLY files
• TAUCS Library Source Code