3D模型被普遍運用於設計、工程製造等多種領域，現今的電腦輔助設計系統大多可幫助設計者從3D模型自動產生2D的工程繪圖，但若要要建立複雜的3D模型仍需花費許多技術與時間。除了一般的3D工程模型之外，爲了符合顧客的需求，具有自由幾何特性(freeform)之曲面也愈來愈常被使用於產品客製化上。然而，自由幾何產品之建模通常會比一般工程產品複雜，所需要耗費的時間成本也就更多。本研究以此問題為出發點，期望將以往僅被運用於工程產品上之參數設計(Parametric design)方法，應用於自由幾何之產品建模，幫助設計者建立或修改模型，增進在設計研發階段之效率，達到降低時間及金錢成本之目的。
　　參數設計是一種利用物件幾何限制來修改或產生模型幾何的方式，但對於自由幾何物件，我們卻難以明確定義其幾何作為參數限制，因此，參數設計以往並不常被使用於自由幾何物件之建模，學界亦缺乏關於此方面之探討。本研究之首要目的，即是針對自由幾何物件發展一套語意參數設計(Semantic Parametric Design)演算法，使設計者可直接透過語意參數的修改，產生符合顧客需求之自由幾何模型，以達到客製化之目的。此演算法以統計方法中的線性迴歸作為基礎，必須先建立數量足夠的模型作為參考模型組，每個參考模型皆有對應的語意設計參數，在符合系統限制之下，本研究使用線性迴歸以求得模型三角網格(Triangular mesh)與語意設計參數之對應關係。基於此演算法得到之網格與參數對應關係，設計者可透過直接修改參數來得到客製化之模型。本研究發展之方法具有高度實用性，在服飾設計方面，可用於衣服、珠寶等自由幾何產品；在生物應用方面，可修改人體模型，建立人體資料庫。此外，以MATLAB為環境之演算法亦具有高度的系統合適性。

A 3D solid model is used in various processes such as design, engineering evaluation, drafting, manufacturing, and so on. Most commercial CAD tools support functions to generate engineering drawings from solid models automatically. However, It is a time-consuming and skill-required job to create a complicated 3D solid model. Parametric modeling is an approach to construct and to modify model geometry with geometric constraints. Nowadays, freeform surfaces are frequently used in a product design in order to meet customers’ aesthetic needs. Freeform modeling requires considerably more time and effort than ordinary mechanical modeling. It is difficult to impose parametric constraints on freeform models since the shape of freeform models is fully arbitrary as its name implies. As a result, parametric modeling has not been popular in freeform modeling.
The primary objective of this research is to simplify the geometric processing required by freeform product customization. We develop a statistical model and a reliable Semantic Parametric Design algorithm applicable to various areas including human body shape, and garment design. The algorithm helps user construct a new model which is conformed to its semantic parameter and the user’s request. We build a reliable object database and compute models and semantic parameters as a statistical linear system. After linking each parameters and triangular mesh of corresponding models, we can generate a new model fitted with the user’s needs by this association. Besides, we provide a method to inspect if the new modified value is reasonable. This makes great helpful for design efficiency.

[1] Eliashberg, J., Lilien, G.L., Rao, V.R. (1997) “Minimizing Technological Oversights: a Marketing Research Perspective”, In R. Garud, P.R. Nayyar, Z.B. Shapira (Eds.), Technological Innovation: Oversights and Foresights: 214-230.
[2] Brown, S.L., Eisenhardt, K.M. (1995) “Product Development: Past Research, Present Findings, and Future Directions”, Academy of Management Review, 20(2): 343-378.
[3] Cooper, R.G., Kleinschmidt, E.J. (1987) “New Products: What Separates Winners from Losers ?”, Journal of Product Innovation Management, 4: 169-184.
[4] Jonathan, C., Craig, M.V. (2002) Creating Breakthrough Products - Innovation from Product Planning to Program Approval, Prentice Hall.
[5] Petiot, J.F., Yannou, B. (2004) “Measuring Consumer perceptions for a Better Comprehension, Specification and Assessment of Product Semantics”, International Journal of Industrial Ergonomics, 33(6): 507-525.
[6] Anderl R., Mendgen R. (1995) “Parametric Design and Its Impact on Solid Modeling Applications”, In: Proceedings of the Third ACM Symposium on Solid Modeling and Applications: 1–12.
[7] Lee K.H. (2002) “Engineering Design Representation by Feature-based Design in Design Automation – Multiple Viewpoint Dependent Models in Product Development”, PhD dissertation, University of Bristol
[8] Ke, Y.L., Fan, S.Q., Zhu, W.D., Li, A., Lie, F.S., Shi, X.Q. (2006) “Feature-based Reverse Modeling Strategies”, Computer-Aided Design, 38(5): 485-506.
[9] Sederberg T.W., Parry S.R. (1986) “Free-form Deformation of Solid Geometric Models”, In: Proceedings of SIGGRAPH ’86, ACM Computer Graphics, 20(4): 151–160.
[10] Coquillart S. (1990) “Extended Freeform Deformation: a Sculpturing Tool for 3D Geometric Modeling”, In: Proceedings of SIGGRAPH ’90, ACM Computer Graphics, 24(4): 187–196.
[11] Hsu W., Hughes J., Kaufman H. (1992) “Direct Manipulation on Freeform Deformation”, In: Proceedings of SIGGRAPH’92, ACM Computer Graphics, 26(2): 177–184.
[12] MacCracken R., Joy K.I. (1996) “Free-form Deformations with Lattices of Arbitrary Topology”, In: Proceedings of SIGGRAPH ’96, ACM Computer Graphics: 181–190.
[13] Kobayashi K.G., Ootsubo K. (2003) “Deformations and Shaping: t-FFD: Free-form Deformation by Using Triangular Mesh”, In: Proceedings of the Eighth ACM Symposium on Solid Modeling and Applications: 226–234.
[14] Shao J., Zhao Y., Feng J., Jin X., Peng Q. (2003) “Free-form Deformation by Using Arbitrary Topological Mesh”, In: Proceedings of CAD and Computer Graphics: 277–282
[15] Ono Y., Chen B.Y., Nishita T., Feng J. (2002) “Free-form Deformation with Automatically Generated Multiresolution Lattices”, In: Proceedings of IEEE 2002 International Conference on Cyber Worlds: 472–490.
[16] Xu, C.F., Liu, Y., Jiang, Y,L., Pan, Y.H. (2004) “Design and Realization of Customized Shoe Last CAD System”, Computers and Graphics, 16(10): 456-464.
[17] Wang C.C.L., Wang Y., Yuen M.M.F. (2005) “Design Automation for Customized Apparel Products”, Computer-Aided Design, 37(7): 675-691.
[18] Hyunpung P., Kwan H. L. (2005) “A new parametric control method for freeform mesh models”, International Journal of Advanced Manufacturing Technology, 27: 313-320.
[19] Guillet S., Léon J.C. (1998) “Parametrically Deformed Freeform Surfaces as Part of a Variational Model”, Computer Aided Design, 30(8): 621–630.
[20] Pernot J.P., Falcidieno B., Giannini F., Guillet S., Léon J.C. (2003) “Modeling Free-form Surfaces Using a Feature-based Approach”, In: Proceedings of the Eighth ACM Symposium on Solid Modeling and Applications: 270–273.
[21] Vosniakos G. (1999) “Investigation of Feature-based Shape Modeling for Mechanical Parts with Freeform Surfaces”, International Journal of Advanced Manufacturing Technology, 15(3): 553–556.
[22] Wyvill G., McRobie D., Gigante M. (1997) “Modeling with features”, IEEE Computer Graphics and Applications, 17(5): 40–46.
[23] Berg E.V.D., Bronsvoort W.F., Vergeest J.S.M. (2002) “Freeform feature modeling: concepts and Prospects”, Computers in Industry, 49(2): 217–233.
[24] Berg E.V.D., Meiden H.A.V.D., Bronsvoort F. (2003) “Specification of Freeform Features”, In: Proceedings of the Eighth ACM Symposium on Solid Modeling and Applications: 56–64.
[25] Liu H.Z., Chen L., Ye X.Z., Pan X., Xu Q. (2007) “Parameterized Freeform Shape Design and Deformation”, International Conference on Multimedia and Ubiquitous Engineering: 626-632.
[26] Allen B., Curless B., Popović Z. (2003) “The Space of Human Body Shapes: Reconstruction and Parameterization from Range Scans”, ACM SIGGRAPH: 27-31.
[27] Hasler N., Stoll C., Sunkel M., Rosenhahn B., Seidel H.-P. (2009) “A Statistical Model of Human Pose and Body Shape”, Computer Graphics Forum, 28(2): 337-346.
[28] Blanz V., Vetter T. (1999) “A Morphable Model for the Synthesis of 3d Faces”, ACM SIGGRAPH, ACM Press: 187–194.
[29] Praune E., Sweldens W., Schroder P. (2001) “Consistent Mesh Parameterizations”, In Proc. ACM SIGGRAPH, ACM Press, Computer Graphics Proceedings, Annual Conferences: 179-184.
[30] Turk M.A., Pentland A.P. (1991) “Face Recognition Using Eigenfaces”, IEEE Conf. on Computer Vision and Pattern Recognition: 586-591.
[31] Boardman J. (1993) “Automating Spectral Unmixing of AVIRIS Data Using Convex Geometry Concepts”, In the 4th JPL Airborne Geoscience Workshop, Pasadena.
[32] Weeks J. (1991) “Convex Hulls and Isometrics of Cusped Hyperbolic 3-manifolds”, Tech. Rep. TR GCG32, The Geometry Center, Univ. of Minnesota, Minneapolis, Minn.
[33] Golub G. H., Van Loan C. F. (1996) Matrix Computations (Johns Hopkins Studies in Mathematical Sciences). The Johns Hopkins University Press.
[34] Barber C. B., Dobkin D. P., and Huhdanpaa H. (1993) “The Quickhull Algorithm for Convex Hull”, Tech. Rep. GCG53, The Geometry Center, Univ. of Minnesota, Minneapolis, Minn.
[35] Barber C. B., Dobkin D. P., and Huhdanpaa H. (1996) “The Quickhull Algorithm for Convex Hulls”, ACM Transactions on Mathematical Software, 22(4): 469-483.
[36] Wang C.C.L. (2005) “Parameterization and Parametric Design of Mannequins”, Computer-Aided Design, 37: 83–98.
[37] Wang C.C.L., Cheng T.K.K., Yuen M.M.F. (2003) “From Laser-scanned Data to Feature Human Model: a System Based on Fuzzy Logic Concept”, Computer-Aided Design, 35(3): 241-253.
[38] Mortenson M.E. (1997) Geometric Modeling (2nd Edition). Wiley: New York.
[39] Jindo T., Hirasago K. (1997) “Application studies to car interior of kansei engineering”, International Journal of Industrial Ergonomics, 19: 105–114.
[40] Chuang, M.C., Chang, C.C., Hsu, S.H. (2001) “Perceptual Factors Underlying User Preferences toward Product Form of Mobile Phones”, International Journal of Industrial Ergonomics, 27(4): 247-258.
[41] Nakada K. (1997) “Kansei Engineering Research on the Design of Construction Machinery”, International Journal of Industrial Ergonomics, 19: 129-146.
[42] Helander M., Po T.M. (2003) “Hedonomics - Affective Human Factors Design”, Ergonomics, 46: 1269–1272.
[43] Hsiao K.A., Chen L.L. (2006) “Fundamental Dimensions of Affective Responses to Product Shapes”, International Journal of Industrial Ergonomics, 36: 553-564.
[44] Osgood C. E., Suci G. J., Tannenbaum P. H. (1957) The measurement of meaning. University of Illinois Press.
[45] Scupin R. (1997) “The KJ Method: A technique for Analyzing Data Derived from Japanese Ethnology”, Human Organization, 56(3): 233–237.
[46] Montgomery D. C. (2004) Design and Analysis of Experiments, 6th ed. Wiley
[47] MAYA: 3D modeling and rendering software packages. Alias Wavefront, http://www.alias.com.eng/productsservices/maya/, 2004.
[48] Hair J. F., Tatham R. L., Anderson R. E., Black W. (1998) Multivariate Data Analysis, 5th ed. Prentice Hall.
[49] Field A. (2005) Discovering Statistics Using SPSS, 2nd ed. Sage Publications Ltd.