在動作學習的領域中，一般需有專家在旁指導，學習者才有辦法知道自己的動作是否正確，而在電腦科技日新月異的今日，已可以透過感測器，擷取人體各肢段的資料出來分析。
本研究結合舞蹈學上的拉邦動作分析，將感測器抓取出來的數據進行分析學習者動作質地的特性，為了達到即時性分析，我們提出一個時間複雜度為O(n)的演算法，Triangle Area Smoothed (TAS) 演算法進行質地波形圖的平滑化，並藉由動作中的突然(sudden)、綿延(sustain)質地，分析學習者的動作行為模式，最後結合專家的指導術語，建立一個動作指導系統，提供學習者可以自我學習的環境。

In the motion learning domain, there is an expert to analyze the learner motion, to help learner to know whether his movement is correct or not. By the modern science and technology, we can analyze the motion of each body region by sensors. 
Our research is based on the Laban Movement Analysis (LMA) of dance, and we analyze the data from several different sensors. According to the data, we can examine learners’ motion characters and effort. For the real time analysis, we proposed a Triangle Area Smoothed (TAS) algorithm to smooth curve, which time complexity is O(n). We use the sudden and sustain effort to analyze learners’ motion and integrate expert’s guiding language to construct the guiding language system. In this way, we could provide an environment for learners who can learn by themselves.

目錄
第一章 緒論	1
1.1 研究動機及研究目的	2
1.2 論文架構	3
第二章 相關研究	4
2.1 Laban Movement Analysis	4
2.2 運動力學	12
2.3 Ramer-Douglas-Peucker Algorithm	14
第三章 研究方法	19
3.1 Collection Sensing Data	21
3.1.1	資料擷取	21
3.1.2	肢段的定義	22
3.2 Data Processing	28
3.2.1	計算運動學參數	28
3.2.2	紀錄速率波形圖的端點	29
3.2.3	Laban Motion Analysis 運動分析	31
3.2.4	Triangle Area Smoothed Algorithm	33
3.2.5	Time Effort Analysis	47
3.3 Guiding Language System	49
第四章 模擬實作與結果討論	59
4.1 模擬實作說明	59
4.1.1	模擬實作目標	59
4.1.2	模擬實作環境	59
4.1.3	Analyze Data of Motion Capture	60
4.1.4	Analyze Data of Angle Sensor	62
4.2 模擬結果與討論	67
第五章 結論與未來相關研究	71
5.1 結論	71
5.2 未來相關研究	72
參考文獻	73
附錄—英文論文	75

 
圖目錄
圖1.1指導語示意圖	3
圖2.1人體的二十面體	5
圖2.2 Effort 關係圖	7
圖2.3 Ramer-Douglas-Peuker algorithm curve smooth	14
圖2.4 RDP的worst case 範例圖	15
圖2.5 RDP worst case成本	16
圖2.6 RDP的average case 範例圖	17
圖2.7 RDP average case成本	18
圖3.1完整的動作包含各種質地的組合	19
圖3.2 動作質地研究方法	20
圖3.3 動作擷取系統環境示意圖	21
圖3.4舞者全身佈滿45個反光點	22
圖3.5 專家資料庫	24
圖3.6 人體肢段分類	26
圖3.7 運動學分析圖(a) 速率圖 (b)加速度圖	28
圖3.8 動作產生雜訊坡動	29
圖3.9 動作端點對應(a) 速率圖 (b)加速度圖	30
圖3.10 速率端點的標示	30
圖3.11 左上臂進行sustain動作	32
圖3.12 左上臂連續進行sustain動作	32
圖3.13 左上臂進行sudden動作	32
圖3.14 左上臂進行sudden動作	32
圖3.15 動作的時間差與速率差	33
圖3.16 有雜訊的動作	34
圖3.18 經過Curve Simplify 後得到較平順速率波形圖	38
圖3.19 Triangle Area Smoothed流程圖	39
圖3.20 RDP 不同Threshold所產生的結果	42
圖3.21 TAS 不同Threshold所產生的結果	44
圖3.22 RDP v.s.TAS 範例二	45
圖3.23 Frame數與計算成本的成長關係圖	46
圖3.24 Smooth後動作AB	47
圖3.25 Effort分析的結果	48
圖3.26 標準的律動Pattern	50
圖3.27 動作Pattern的切割	51
圖3.28 指導語決策樹	52
圖3.29 Pattern對應指導術語	53
圖3.30 重複Pattern動作	54
圖3.31循環動作分析Flow Chart	58
圖4.1 Time Effort 圖例對照	61
圖4.2 較規律的健康椅動作	62
圖4.3紊亂的健康椅動作	62
圖4.4 角度分析出Effort出現的節奏	63
圖4.5 λ值與Effort關係	64
圖4.6不規律的健康椅分析	65
圖4.7角速度經過Smooth	66
圖4.8 Sustain Pattern 對應的指導術語	68
圖4.9 紊亂的健康倚動作	69
圖4.10過快的健康椅分析	70

 
表目錄
表3.1 45個反光點的定義	22
表3.2 經過專家資料庫篩選後所取得的結果	25
表3.3反光點與15肢段的換算式	27
表3.4 Triangle Area Smoothed 資料結構	35
表3.5 TAS algorithm time complexity	40
表3.6 影片資訊	41
表3.7 Smooth Algorithm 比較	46
表3.8 Time Effort Analysis名稱定義	47
表3.9循環動作資料結構	55
表4.1 環境平臺軟硬體設備	60
表4.2 分析動作影片名稱定義	61

中文部份:
[楊云 08]	楊云、孫群、朱長青，曲線數據壓所的總體最小二乘算法，西安電子科學大學學報自然科學版，2008年10月第35卷第5期
英文部份:
[Badler 00]	Norman Badler, Monica Costa, Liwei Zhao, Diane Chi,“ To Gesture or Not to Gesture: What is the Question?,” Computer Graphics International, 2000. Proceedings, Center for Human Modeling and Simulation Univ ersity of Pennsylvania, pp. 3-9, Jun-19-24, 2000.
[Camurri 99]	Antonio Camurri, Shuji Hashimoto, Kenji Suzuki, Riccardo Trocca, “ KANSEI Analysis of Dance Performance,” proceedings of the Systems, Man, and Cybernetics. IEEE SMC ’99 Conference , vol.4, pp. 327-332, Oct-12-15, 1999.
[Chi 00]	Diane Chi, Monica Costa, Liwei Zhao, Norman Badler,“ The EMOTE Model for Effort and Shape,” proceedings of the 27th annual conference on Computer graphics and interactive techniques, Center for Human Modeling and Simulation University of Pennsylvania, pp. 173 - 182 , Jul. 2000.
[Douglas 73]	D. Douglas and T. Peucker,“ Algorithms for the Reduction of the Number of Points Required to Represent a Digitized Line or its Caricature,” The Canadian Cartographer, vol. 10, no. 2, pp. 112-122, Dec. 1973.
[Hachimura 05]	Kozaburo Hachimura, Katsumi Takashina, and Mitsu Yoshimura,  “Analysis and Evaluation of Dancing Movement Based on LMA,”  2005 IEEE International Workshop on Robots and Human Interactive Communication, Graduate School of Scinence and Engineering, Ritsumeikan University, Center for Promotion of the COE, Ritsumeikan University, pp. 294- 299, Aug. 2005.
[Harrower 06]	Mark Harrower, Matt Bloch,“ MapShaper.org: A Map Generalization Web Service,” Proceedings of AUTOCARTO 2006,  University of Wisconsin-Madison, vol. 26, no. 4, pp. 22-27, Jul. 2006.
[Hsu 07]	Shih-Hsu Hsu,“ Establishing of Laban Effort Analysis and Diagnosis Model,” Master thesis, National Taipei Univ, 2008.
[Huang 06]	Yen-Tzu Huang,” A quantitative study of Time, Space, and Weight Elements in Laban Movement Analysis: Using Action Drives as a tool,” Master thesis, National College of Physical Education and Sports Taiwan Republic of China., Taiwan, 2006.
[Lo 08]	Meng-Kang Lo,“ Applying Data Mining Technique to Effort of Body Movement Analysis – Based on LMA,” Master thesis, National Taipei Univ, 2008.
[Rett 07]	Jörg Rett, Jorge Dias,“ Human-robot Interface with anticipatory characteristics based on Laban Movement Analysis and Bayesian models,” Proceedings of the 2007 IEEE 10th International Conference on Rehabilitation Robotics, June 12-15, Institute of Systerns and Robotics, University of Coimbra, pp. 257-268, Jun. 2007.
[Yang 08]	Ti-Chiang Yang,“ Apply K-Means Algorithm to Human Body Movement Factors-Based on LMA,” Master thesis, National Taipei Univ, 2008.
[Wiki 07]	Wiki URL:Ramer-Douglas-Peucker algorithm 
http://en.wikipedia.org/wiki/Ramer-Douglas-Peucker_algorithm, 2007.