MATH6110P: Computer Aided Geometric Design (Autumn-Winter 2024-2025)

Graphics&Geometric Computing Laboratory

University of Science and Technology of China

Announcements    General     Course Goals     Texts     Grading      Syllabus

     Assignments     Requirements on Assignments      Professional Conduct     Miscellaneous

Announcements

• 2024.09.09: 开通课程QQ群679567939
• 2024.09.09: 学生ID号
• 2024.09.09: 课件下载（PPTs）
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General

Course Goals

Geometric modeling underlies applications from computer animation and special effects, to advanced modeling software for industrial design and architecture, to rapid prototyping machines that "print" 3-D objects in plastic, and many others. Geometric models represent the shapes and spatial relationships of the environment that is being studied, permitting a much deeper analysis than would be possible otherwise. How these models are encoded, and how the algorithms that utilize them are designed, comprise the field of computer-aided geometric design (CAGD), which is the subject of this course.

We will discuss a wide variety of techniques for representing and analyzing these models. Our emphasis will be on parametric curves and surfaces, subdivision methods, and meshes. 

Texts

参考书籍与资料:
            G.Farin. Curves and Surfaces for CAGD. Morgan Kaufmann Publishers, 2003.  Download
            Thomas W. Sederberg. Computer Aided Geometric Design. 2012. Download
            Josef Hoschek, Dieter Lasser. Fundamentals of Computer Aided Geometric Design, A K Peters/CRC Press, 1996.
            王国瑾, 汪国昭, 郑建民. 计算机辅助几何设计. 高等教育出版社. 2001. Download
            朱心雄. 自由曲线曲面造型技术. 科学出版社, 2000.
            施法中. 计算机辅助几何设计与非均匀有理B样条. 高等教育出版社. 2001.

Readings:
            Various journal, conference, 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.

Note: Final examination will be in-class, closed-book. More information will be provided prior to it.

Note: Here you can view or download the notes that we use in class. DO NOT depend solely on these notes as many details are missing. You should read the textbook and take notes in class. 

• Chapter 00_Intro
• Chapter 0a_Linear Algebra
• Chapter 01_Data Fitting
• Chapter 02_Bézier Curve
• Chapter 03_Bézier Curve (cont.)
• Chapter 04_Differential Geometry of Curves
• Chapter 05_Bézier Spline
• Chapter 06_B-spline
• Chapter 07_Blossoming and Polar Forms
• Chapter 08_Rational Splines
• Chapter 09_Spline Surfaces
• Chapter 10_Subdivision Curves & Surfaces

Homework

• Homework #1, deadline is Tuesday, Sep. 17, 2024
• assignment1_interp.m
• assignment1_interp.py
• Homework #2, deadline is Sunday, Oct. 6, 2024
• assignment2_bezier.m
• assignment2_bezier.py
• Homework #3, deadline is Sunday, Oct. 6, 2024
• Homework #4, deadline is Sunday, Oct. 20, 2024
• Homework #5, deadline is Sunday, Oct. 27, 2024
• Homework #6, deadline is Sunday, Nov. 3, 2024
• Homework #7, deadline is Sunday, Nov. 17, 2024
• Homework #8, deadline is Sunday, Nov. 24, 2024

Projects

• Project#1, deadline is ...

Note: Please zip your submission stuffs the assignment into one single file either using WinZip or WinRAR. Name the name as "ID_Name_Homework1.zip" or "ID_Name_Project1" where ID is your ID number in the class.

Requirements on Assignments

Requirements

• All students are expected to study the relevant portions of the textbook and handouts in conjunction with our class discussions (i.e., before coming to class). Explicit reading assignments will not always be given.
• All programming for this course will be done in Matlab according to the standard coding styles. We will test programs on Matlab 2019a under Windows 10. It is the responsibility of the student to submit a program that will successfully compile and execute on the specified platform.

Assignment Submission

• All students are expected to complete their homework assignments by their due dates.
• Submission stuffs
  Your ID number, your name, the number or name, source codes, related document
• Grading of programming assignments will be based on the following criteria:
  1. Correctness of program.
  2. Output from program that adequately demonstrates correctness.
  3. Documentation, internal and external, included as standards.
  4. Efficient use of algorithms and appropriate data structures.
  5. Stress - program must function correctly under all and/or extreme and unusual combinations of input.
  6. Creativity - credit for innovation in interface, implementation, style, etc.
• Submission approach
  Please submit your assignment stuffs via email.
• Late Work
  No late work will be accepted. If you know you will miss a test due to an excused absence, you must contact me ahead of time to schedule a make-up session.
• Late programming assignments follow the following rules:
  25% deduction for 1-day late
  50% deduction for 2-day late
  Not accepted after being 2-day late
  Regarding your marks, contact the grading TA within two weeks after the assignment is handed back. After this two-week period, your assignment stays as it is graded.

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 :

• User Interaction
      ̶  It would be nice to present the user with options to either test the program using internal tests or an interactive interface
      ̶  Work around limitations in the program. For example, if the program asks for lines of input and quits when it sees "X", invent a special syntax (called an escape sequence) to allow the user to type in "X" without the program exiting. Hypothetically, if the user enters $X the program interprets it as X, if the user enters $$ the program interprets it as $ and if the user enters X the program exits.
• Visualization
      ̶  A representation of how data is actually being stored in the data structure, by specific position and value (this would even help greatly with debugging) - this could be accomplished with specialized data access routines for output formatting
• Testing
      ̶  Simulating real-world conditions for input by making some assumptions about the distribution of operations performed and the rate of operations, then simulating using random number generators
      ̶  Intensively testing creation, usage and destruction of the data structure to prove there are no memory leaks
      ̶  Exhaustive automatic testing - go through many (or every) possible scenarios for the data structure (up to some time limit). For example, assign "add" and "remove" to a binary variable - then generate all possible strings of operations - test the structure for each case, and test the results automatically in your main program to make sure they are what was expected.
      ̶  Develop a syntax for file-based testing and use this as an option - eg. "enter X" and "retrieve"
• Efficiency
       ̶  Minimize the number of allocations of memory blocks by reusing deleted blocks
  Ask yourself these questions ...
      ̶  How can I make the interface more natural ?
      ̶  How can I make the program run faster ?
      ̶  How can I use less memory/disk space ?
      ̶  Have I thoroughly tested my program ? Will my program survive real-world tests ? Will my program survive worst-case scenario tests ?

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 or programming exercise 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:

• You may discuss ideas for homework and programming assignments with your classmates. However, you cannot collaborate on writing the solution or the program code. That is, you can talk about the problems and ideas for solving them, but you cannot write things down with anyone else. You are, of course, prohibited from copying or seeing another student's written solution, and you are not allowed to show your work to anyone else.
• You should accept help with care. If you work too closely with another student, you might mislead yourself into believing that you understand the concepts and techniques better than you actually do. Don't forget that the instructor has office hours and can probably give you hints or suggestions to get you started.
• You should give help with care. Do not help anyone too much. When you have solved a problem, it is tempting to just tell other students how you solved it. Instead, try to allow them to come to the solution on their own. Maybe give them a hint to help them get "over a hump." Remember that helping someone too much will hurt them in the long term if they can't work through problems on the exams by themselves. So avoid the temptation to do so. If you can't help other students without giving away the whole solution, direct them to see the instructor (who may or may not have a way to "edge" them toward the solution).
• You are not obligated to help anyone. If you feel uncomfortable helping another student for any reason, please direct them to see the instructor.

Miscellaneous

Send any comments or suggestions to Prof. Dr. Renjie Chen
Copyright © 2024, Renjie Chen