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課程名稱 |
離散微分幾何
Discrete Differential Geometry |
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開課學期 |
109-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
陳宜良 |
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課號 |
MATH5100 |
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課程識別碼 |
221 U8450 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期五7,8,9(14:20~17:20) |
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上課地點 |
天數304 |
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備註 |
限學士班二年級以上
總人數上限：30人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1091MATH5100_DDG |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
Discrete differential geometry (DDG) is a new subject that originated from computer graphics. It has applications in geometric processing, computer-aided design, elastic/plastic material simulations, fluid flow simulations, electric-magnetic wave propagation, etc. In this course, I will partially follow my own Lecture Note and partially follow Professor Keenan Crane’s Lecture Note at CMU. As quoted in Crane’s website, DDG has been taught for semester-long courses at CMU (2016,2017,2019) Caltech (2011-2014,2016-2019), Columbia University (2013), and RWTH Aachen University (2014-2017), as well as special sessions at SIGGRAPH (2013) and SGP (2012, 2013, 2014,2017,2019). The contents of this course are
1. Combinatorial Surfaces
2. Curves
3. Exterior Algebra and Calculus
4. Discrete Exterior Calculus
5. Surfaces
6. Connection, Parallel Transport, Curvatures
7. Partial Differential Equations on Manifolds
8. Vector Field Decomposition and Design
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課程目標 |
1. Learn basic geometric representation on a computer.
2. To be able to do discrete exterior calculus
3. Understand the theory of discrete curves and surfaces
3. Understand discrete Laplacian and capable to solve Poisson equation on discrete manifolds.
4. Learn a topic of vector field design on discrete manifolds. |
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課程要求 |
Linear Algebra, Multi-variable Calculus, Matlab (or C, C++) programming Language.
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預期每週課後學習時數 |
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Office Hours |
每週五 10:00~11:00 備註： Friday morning, 10-11:30 |
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指定閱讀 |
• I-Liang Chern, A Supplementary Note on Discrete Differential Geometry (2019).
• Keenan Crane’s Lecture Note at CMU(2019): https://www.cs.cmu.edu/~kmcrane/Projects/DDG/paper.pdf |
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參考書目 |
Papers to be assigned. |
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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第1週 |
9/18 |
Combinatorial Surfaces |
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第2週 |
9/25 |
Curves, framed curves |
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第3週 |
10/02 |
放假日，本周上課內容延後。
Framed Curve, Quaternions, discrete spatial curves |
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第4週 |
10/09 |
放假日，本周上課內容延後。 A note by Albert was uploaded.
Exterior Algebra |
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第5週 |
10/16 |
Exterior Calculus: DDG dated 10/23 is uploaded. |
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第6週 |
10/23 |
Discrete Exterior Calculus
Note by Albert Chern |
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第7週 |
10/30 |
Hodge star operator |
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第8週 |
11/06 |
本周仍要上課，沒有期中考。 |
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第9週 |
11/13 |
Exterior Calculus
New version after class |
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第10週 |
11/20 |
Surfaces, Connection, Parallel transport and curvatures |
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第11週 |
11/27 |
Surfaces, Connection, Parallel transport and curvatures |
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第12週 |
12/04 |
Discrete Laplacian, PDE on manifold |
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第13週 |
12/11 |
PDEs on discrete manifolds |
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第14週 |
12/18 |
Hodge decomposition |
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第15週 |
12/25 |
Vector Fields design |
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第16週 |
1/08 |
Students' presentation |
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