In recent years, development of computer graphics is incredibly fast from 2D graph to high quality of 3D environment. Applications of industrial design, animation and computer games are often seen to make progress; the analyzing of cost efficiency and quality standard are priorities of developing. To research for new methods of quickly displaying large numbers of data set, and massive scientific simulation is the trend of unceasing development.
In the procedure of industrial design, it is almost impossible for one person from initial idea conception to 3D realization. Designers sketch for conceiving concept and digital modelers have to operate CAD software to reconstruct 3D shapes of sketch. We could quickly sketch for idea conception without considering the precision. But it takes us lots of time to get familiar with massive commands and relevant knowledge of background. So we propose a real-time system of combining advantages of sketching and user interface for novice users which could intuitively do idea conception to reconstruct 3D objects as their wish at once.
First of all, users need use mouse or optical pen to input the plane information to provide the reference of 2D to 3D coordinate transformation. In the 3D coordination, sketch is processing in 2D virtual canvas and interactively calculating with system in real-time. Our system brings up a new idea of differential sketch sequence for displaying crabwise segment property. Because of providing the environment with less restriction, it could show variety of composition of segments. Surface boundary tracing algorithm is used for drafted segments to extract surface boundaries successfully, and then reconstructing for 3D object.
The experimental results are separated into two parts; stroke and surface performance. The stroke part could compose of complex segments for idea conception, and the surface part is also successfully reconstructing 3D objects designed by users to perform real 3D reception.

近十年來，計算機圖學(Computer Graphics)發展地異常迅速，從二維(2D)圖形進步到複雜的高品質的三維(3D)環境。而較常見則為工業設計以及動畫電玩類的應用發展，其發展之考量重點為成本效應分析與品質追求。研究新的方法，以快速地顯示大量數據集合和大規模科學仿真結果是不間斷的發展趨勢。工業設計流程中，從初期概念到三維實現幾乎不可為一人能力所涵蓋。設計師利用徒手草繪來傳達觀念，數位模型師必須將其手繪利用CAD軟體將其還原重建。而概念發想過程其實不需要考量精確度，利用手繪即可以快速實現。但是學習CAD軟體必須花費大量時間去熟悉複雜的指令以及相關的背景知識。
本論文提出一個結合了手繪以及CAD中互動介面的優點的即時系統，讓非專業的使用者可以直觀的做概念的發想，進而快速的重建出所欲表達之三維形體。 使用者首先利用滑鼠 / 光學筆輸入平面座標資訊，提供後續二維與三維座標轉換的參考資訊依據。在三維座標環境中，手繪動作於二維虛擬畫布中執行且與系統即時交互計算，進而取得所欲表達之筆觸線段資訊。本系統亦提出新的概念，利用繪畫順序差異表現出橫向線段的延伸特性。因為提供較不受限的使用環境，故可以表現出較為多樣性的線段組合。而繪畫線段經由曲面邊界追蹤演算法(Surface Boundary Tracing Algorithm)，可以成功的分類出面向邊界資訊，進而得以重建還原三維形體。
實驗結果分兩部分陳述;為線段與曲面呈現。線段部分得以複雜線段的組合表現出使用者的概念性思維。曲面部份亦成功重建出使用者所設計的三維形體，表現出真實的立體感受。

REFERENCES
[1] I.J.Grimstead and R.R.Martin. Creating solid models from single 2D sketches, in Proceedings of the third ACM symposium on Solid modeling and applications, pp. 323 – 337, 1995.
[2] Takeo Igarashi, Satoshi Matsuoka, Sachiko Kawachiya and Hidehiko Tanaka. Interactive beautification: a technique for rapid geometric design, in Proceedings of the 10th annual ACM symposium on User interface software and technology, pp. 105 – 114, 1997.
[3] Robert C. Zeleznik, Kenneth P. Herndon and John F. Hughes. SKETCH: an interface for sketching 3D scenes, in ACM SIGGRAPH 2007 courses, Article No. 19, 1998.
[4] Jennifer Mankoff, Scott E. Hudson and Gregory D. Abowd. Interaction techniques for ambiguity resolution in recognition-based interfaces, in Proceedings of the 13th annual ACM symposium on User interface software and technology, pp. 11 – 20, 2000.
[5] Henning Biermann, Adi Levin and Denis Zorin. Piecewise smooth subdivision surfaces with normal control, in Proceedings of the 27th annual conference on Computer graphics and interactive techniques, pp. 113 – 120, 2000.
[6] Hod Lipson and Moshe Shpitalni. Correlation-based reconstruction of a 3D object from a single freehand sketch, in ACM SIGGRAPH 2007 courses, Article No. 44, 2001.
[7] Takeo Igarashi and John F. Hughes. A suggestive interface for 3D drawing, in Proceedings of the 14th annual ACM symposium on User interface software and technology, pp. 173 – 181, 2001.
[8] Tevfik Metin Sezgin, Thomas Stahovich and Randall Davis. Sketch based interfaces: early processing for sketch understanding, in Proceedings of the 2001 workshop on Perceptive user interfaces, pp. 1 – 8, 2001.
[9] Tovi Grossman, Ravin Balakrishnan, Gordon Kurtenbach, George Fitzmaurice, Azam Khan and Bill Buxton. Creating principal 3D curves with digital tape drawing, in Proceedings of the SIGCHI conference on Human factors in computing systems: Changing our world, changing ourselves, pp. 121 – 128, 2002.
[10] Jeffrey Bolz and Peter Schroder. Rapid evaluation of Catmull-Clark subdivision surfaces, in Proceeding of the seventh international conference on 3D Web technology, pp. 11 – 17, 2002.
[11] Paul Michalik, Dae Hyun Kim and Beat D. Bruderlin. Sketch- and constraint-based design of B-spline surfaces, in Proceedings of the seventh ACM symposium on Solid modeling and applications, pp. 297 – 304, 2002.
[12] P.A.C.Varley and R.R.Martin. Estimating depth from line drawing, in Proceedings of the seventh ACM symposium on Solid modeling and applications, pp. 180 – 191, 2002.
[13] Bo Yu. Recognition of freehand sketches using mean shift, in Proceedings of the 8th international conference on intelligent user interfaces, pp. 204 – 210, 2003.
[14] Bo Yu and Shijie Cai. A domain-independent system for sketch recognition, in Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia, pp. 141 – 146, 2003.
[15] Steve Tsang, Ravin Balakrishnan, Karan Singh and Abhishek Ranjan. A suggestive interface for image guided 3D sketching, in Proceedings of the SIGCHI conference on Human factors in computing systems, pp. 591 – 598, 2004.
[16] P.A.C.Varley, R.R.Martin and H.Suzuki. Making the most of using depth reasoning to label line drawings of engineering objects, in Proceedings of the ninth ACM symposium on Solid modeling and applications, pp. 191 – 202, 2004.
[17] Yuan Sun and Yong Tsui Lee. Topological analysis of a single line drawing for 3D shape recovery, in Proceedings of the 2nd international conference on Computer graphics and interactive techniques in Australasia and South East Asia, pp. 167 – 172, 2004.
[18] Joseph Jacob Cherlin, Faramarz Samavati, Mario Costa Sousa and Joaquim A.Jorge. Sketch-based modeling with few strokes, in Proceedings of the 21st spring conference on Computer graphics, pp. 137 – 145, 2005.
[19] M.Masry, D.Kang and H.Lipson. A freehand sketching interface for progressive construction of 3D objects, in ACM SIGGRAPH 2007 courses, Article No. 30, 2005.
[20] Andrew Nealen, Olga Sorkine, Marc Alexa and Daniel Cohen-Or. A sketch-based interface for detail-preserving mesh editing, in ACM SIGGRAPH 2005 Papers, pp. 1142 – 1147, 2005.
[21] Levent Burak Kara, Chris M.D'Eramo and Kenji Shimada. Pen-based styling design of 3D geometry using concept sketches and template models, in Proceedings of the 2006 ACM symposium on Solid and physical modeling, pp. 149 – 160, 2006.
[22] Olga A.Karpenko and John F.Hughes. SmoothSketch: 3D free-form shapes from complex sketches, in ACM SIGGRAPH 2006 Papers, pp. 589 – 598, 2006.
[23] Li Han, Raffaele De Amicis and Giuseppe Conti. Interactive spline-driven deformation for free-form surface styling, in Proceedings of the 2006 ACM symposium on Solid and physical modeling, pp. 139 – 147, 2006.
[24] Yuki Mori and Takeo Igarashi. Plushie: an interactive design system for plush toys, in ACM SIGGRAPH 2007 papers, Article No. 45, 2007.
[25] Andrew Nealen, Takeo Igarashi, Olga Sorkine and Marc Alexa. FiberMesh: designing freeform surfaces with 3D curves, in ACM SIGGRAPH 2007 papers, Article No. 41, 2007.
[26] Samuel R. Buss. 3D COMPUTER GRAPHICS_A Mathematical Introduction with OpenGL, 2006.
[27] Edward Angel. Interactive Computer Graphics_ A Top-Down Approach Using OpenGL 4th Edition, 2007.