Goel Vineet Kumar et al. / International Journal of Engineering Science and Technology (IJEST) GEOMETRICAL MODELING OF 3D PATTERNS FOR TRADITIONAL INDIAN KUNDAN JEWELRY GOEL VINEET KUMAR1 Research Scholar, National Institute of Technology Kurukshetra, Haryana-136119(India) Associate Professor, Department of Mechanical Engineering, JCDM College of Engineering, Sirsa, Haryana-125 055(India) [email protected] GARG T.K.2 Professor, National Institute of Technology Kurukshetra, Haryana-136 119(India) [email protected] TANDON PUNEET3 Professor, PDPM Indian Institute of Information Technology, Design & Manufacturing Jabalpur-482 005(India) [email protected] Abstract: India is famous for its art and culture, which can be found in traditional handicrafts, carvings, potteries, as well as in Jewelry. The traditional Jewelry of India is what makes the Indian Jewelry so rich and unique in their manner. India has a rich tradition of gold ornamental designs and there are a number of styles of ornament making in practice, each with its uniqueness, special forms and style. Our work is based on semantics; 3D patterns are created on the bases of parametric representation. This work aims to associate advantages unfolded by Computer Aided Design (CAD) technology in developing traditional design patterns for Jewelry design and manufacturing. The work also presents three dimensional (3D) semantics used in Traditional Indian Kundan Jewelry with the help of mathematical modeling; to generate the traditional patterns. The goal will be achieved by devising mathematical models for various 3D semantics, for the modeling of Traditional Indian Kundan jewelry (TIKJ). Jewelry Add-In is developed for inventor using c++. Aim of this Jewelry add-in is to develop pattern of 3D geometrical shapes on 3D surface and for communication between Jewelry Add-In and Inventor. Keywords: Semantics; Cluster; Traditional Kundan Jewelry Design; Geometric Modeling; CAD. 1. Introduction: India is famous for its art and culture, which can be found in traditional handicrafts, carvings, potteries, as well as in Jewelry. The traditional Jewelry of India is what makes the Indian Jewelry so rich and unique in their manner. India has a rich tradition of gold ornamental designs and there are a number of styles of ornament making in practice, each with its uniqueness, special forms and style. Elements of ornamental design can be divided into three categories. First is based on geometrical elements (both analytical and synthetic) such as lines, circle, ovals, rectangle, and polygon and curves etc. Second is based on nature, like plants, animals, mountains, star, sun, moon, and the last is based on artificial objects like shields, ribbons, torches, etc. Our work is based on semantics; 3D patterns are created on the bases of parametric representation. In a 3D pattern, designers have various tools to assist them in designing a piece of Jewelry, including transformations, primitive solids, embedded libraries of jewelry part. Finally, an imperative gain of CAD is that models are passed directly to 3D printer or rapid prototyping machines for the manufacturing of three dimensional prototypes for Jewelry. Despite the effectiveness of current CAD systems for Jewelry design, manual design of Jewelry is still in wide use. An example of such a type of jewelry design is Traditional Indian Kundan Jewelry (TIKJ). This work aims to associate advantages unfolded by Computer Aided Design (CAD) technology in developing traditional semantics and patterns for traditional Indian kundan jewelry (TIKJ) design. The work focuses on ISSN : 0975-5462 Vol. 3 No. 7 July 2011 5666 Goel Vineet Kumar et al. / International Journal of Engineering Science and Technology (IJEST) parametrically defined semantics and shape grammar of traditional patterns to generate 3D forms. The goal will be achieved by devising geometrical parameterization of various 3D semantics for the design of Traditional Indian Kundan Jewelry (TIKJ). Jewelry Add-In is developed for inventor using c++. Aim of this Jewelry add-in is to develop pattern of 3D semantics on 3D surfaces and for communication between Jewelry Add-In and Inventor. This paper is organized in the four sections. In Section 2 summarized literature review is given. Section 3 unfolds the algorithms for Geometric Parameterization and generating 3D semantics used in Traditional Indian Kundan Jewelry, and presents the formation of cluster and patterns. Implementation of the proposed methodology and result presented in Section 4. 2. Literature Review: In Traditional Indian Kundan Jewelry (TIKJ) designs cognitive processes of design is still a growing area. Kundan Jewelry with the help of mathematical modeling to generate the traditional patterns. Parametrically defined shape grammar of traditional Kundan jewelry to generate 3D forms patterns in computer aided design. Many attempts have been made to reinvent the design process using geometric patterns, resulting in a variety of successful analyses and constructions. Bastanfard et al. [1] presents a novel algorithm to generate patterns based on the novel parametric methods. They include aesthetic ornaments, architecture and tilling. Adding semantics can ease specification and modification of an object model, help to guarantee its validity, and be useful for applications which use the model. About the use of semantics in modeling approaches is briefly discussed by Bronsvoort [2]. Catalano [3] described that semantics represents certain invariant properties of the object is discussed and it can be very helpful in building object models in traditional object modeling. Hoffmannt [4] proposed the Feature-based design in which the basic unit is a feature and parts are constructed by a sequence of feature attachment operations. Parag et al. [7] focused at identification of smallest semantic units that are used in Kundan Jewelry. These were classified into five categories based on geometry. These semantic units alone or in combination with other units in meticulous manner create Kundan Jewelry. Stamati et al. [8-10] introduce ByzantineCAD, a parametric CAD system for the design of pierced medieval jewelry, which is Jewelry created by piercing, a traditional Byzantine technique. Byzantine CAD is an automated parametric system where the design of a piece of Jewelry is expressed by a collection of parameters and constraints and the user’s participation in the design process is through the definition of the parameter values. A feature based CAD approach to re-engineering Jewelry has also been presented. Sheena [11] propose a novel approach called the solid deflation method. In which a solid model is assumed to be created by using air to inflate a shell that comprises the surface of the 3D solid model. Vyzantiadoua et al. [12] proposes an approach where structural systems can be developed according to the mathematical theory of fractals. Architecture can take advantage of the complexity, by the use of present day computer technology, where algorithms of mathematical and geometric functions can produce new motifs of design. Wannarumon et al. [13] proposes a computer-based design tool to automate art form generation used in Jewelry design. Expert system and evolutionary algorithm are integrated into the prototype design tool named JAFG (Jewelry Art Form Generator). Wannarumon et al. [14] proposes the framework of the automatic computer-based design system supporting the design of jewelry. Jewel Space [5] proposes an approach where structural systems can be developed according to the mathematical theory of fractals. The Koch curve, for example, is exactly self-similar. JewelCAD [6] offers good rendering techniques. The user can define its own libraries for different designs of jewelry. These approaches are aimed to produce an accurate pattern in 3D models that can be manufactured. Designers can take advantage of CAD, where mathematical and geometrical algorithms produce new patterns design. 3. Modeling of 3d Kundan Jewelry Geometrical Patterns: Geometric modeling of 3D Kundan Jewelry patterns is determined using. Profile of Semantics will define using Geometry Parameterization and constrains on those geometry Semantics can be modified using scale, rotate, and transform operators. Semantics are the building block for most features. Semantics consists of entities (lines, circles, arc, etc.) whose behavior is controlled by geometric and dimension constraints. The combination of semantics create cluster. Cluster type depends upon Semantics arrangements and then clusters are used to generate the 3D patterns. ISSN : 0975-5462 Vol. 3 No. 7 July 2011 5667 Goel Vineet Kumar et al. / International Journal of Engineering Science and Technology (IJEST) 3.1 Geometric parameterization of semantics used in Traditional Indian Kundan Jewelry (TIKJ): Different types of semantics are used in cluster creation i.e. Jau, Chand, Heart etc. Semantics are created using geometric parameterization. The parametric equations of different 3D Semantics in jewelry design are: θ [0,2 ] px(θ,t) = xc + rcos(θ) py(θ,t) = yc + rsin(θ) t [0,1] pz(θ,t) = zc + t*H Here (xc, yc, zc) is the center of the Gole. r is radius of Gole. H is thickness. Gole/ Circle Nim Gole/ Oval Jau Chand px(θ,t) = xc + acos(θ)cos(α)‐ bsin(θ)sin(α) θ [0,2 ] py(θ,t) = yc + acos(θ)sin(α)‐ bsin(θ)cos(α) t [0,1] pz(θ,t) = zc + t*H ‘a’ major radius of Nim Gole. ‘b’ minor radius of Nim Gole. ‘α’ is the angle between the X‐axis and the major axis of the ellipse. For Nim Gole in canonical position (center at origin, major axis along the X‐axis), the equation simplifies to px(θ,t) = xc + acos(θ) py(θ,t) = yc + cos(θ) pz(θ,t) = zc + t*H Jau made up of two arcs: Arc1 : Arc2: θ [0, ] px(θ,t) = x2c + rcos(θ) θ [0,2 ] px(θ,t) = x1c + rcos(θ) py(θ,t) = y2c +rsin(θ) py(θ,t) = y1c + rsin(θ) t [0,1] pz(θ,t) = zc + t*H t [0,1] pz(θ,t) = zc + t*H Chand made up of two arcs: Arc1 : Arc2: θ [0, ] px(θ,t) = x2c + r2cos(θ) θ [ ,2 ] px(θ,t) = x1c + r1cos(θ) py(θ,t) = y2c +r2sin(θ) py(θ,t) = y1c +r1sin(θ) t [0,1] pz(θ,t) = zc + t*H t [0,1] pz(θ,t) = zc + t*H (xc, yc, zc) is the center of arc. ‘r1‘is large radius of Chand. ‘r2‘is small radius of Chand. px(θ,t) = xc +16a* sin3(θ) py(θ,t) = yc +a(13cos(θ)‐5cos(2t)‐2cos(3θ)‐cos(4θ)) pz(θ,t) = zc + t*H Heart θ [0, /2] t [0,1] Gole Trikon 3.2 Gole Trikon made up of three arcs: Arc1 : θ [0,2 /3] px(θ,t) =x1c + rcos(θ) py(θ,t) =y1c +rsin(θ) t [0,1] pz(θ,t) =zc + t*H Arc2: Arc3 : θ [2 /3, 4 /3] px(θ,t) =x3c + rcos(θ) px(θ,t) =x2c + rcos(θ) py(θ,t) =y2c +rsin(θ) py(θ,t) =y3c +rsin(θ) t [0,1] pz(θ,t) =zc + t*H pz(θ,t) =zc + t*H θ [4 /3,2 ] t [0,1] Constraint: The geometric and dimensional constraints are applied on the Semantics. Define the behavior of single entities: ground, vertical, and horizontal. Define the relationship between two entities: coincident, collinear, concentric, equal length, equal radius, horizontal align, midpoint, parallel, perpendicular, symmetry, tangent, and vertical align etc. Constraint applied as per the Semantics development requirements. 3.3 Cluster: The combination of semantics create cluster. Cluster type depends upon Semantics arrangements and then cluster used to create the pattern. Different types of clusters are Circular cluster (figure-1), Rectangular cluster (figure-2), Mirror cluster, Pentagon cluster, Hexagon cluster. ISSN : 0975-5462 Vol. 3 No. 7 July 2011 5668 Goel Vineet Kumar et al. / International Journal of Engineering Science and Technology (IJEST) 3.3.1 Circular cluster: A duplicate selected Semantics and arranges it in arc or circular pattern. Select the geometry to cluster and a point or vertex to serve as the axis. Specify the number of copies and the angle in which they fit. The 4x4 homogeneous rotational transformations is performed to create circular cluster Figure 1: Circular Cluster 3.3.2 Rectangle Cluster: A duplicate selected Semantics geometry and arranges it in rows and columns. The 4x4 homogenous transformations is performed to create rectangular cluster. Figure 2: Rectangular Cluster 3.4 Pattern: Cluster combination along a rectangular, circular plane creates the pattern. Patterns are used to create design on the sheets. Figure3 Rectangular Pattern 4 Implementation and Result: This paper has introduced a novel CAD approach to designing handmade objects of complex and sophisticated craftsmanship. This system provides the user with the capability of designing jewelry in an easy-touse and efficient manner. Jewelry Add-In is developed for inventor using c++. Jewelry Add-In for inventor designed to provide rich development capabilities. The CAD system uses the SAT solid modeling format for the internal representation and is capable of Figure 4: 3D Jau Cluster Arranged Parametrically exporting to stereo lithography (STL) format. The system renders the SAT models, whereas the STL model is ready to be submitted to a rapid prototyping machine, for manufacturing. The approach creates design models using the parameterized Kundan Jewelry shapes is shown in Fig. 4. 5 References: [1] [2] [3] [4] [5] [6] Bastanfard, A.; Mansourifar, H.: A Novel Decorative Islamic Star Pattern Generation Algorithm, Inter National Conference on Computational Science and Its Application, 2010 IEEE, 111-117, DOI:10.1109/ICCSA.2010.42. Bronsvoort,W.F.; Bidarra,R.; Meiden,H.; Tutenel,T.: The Increasing Role of Semantics in Object Modeling, Computer-Aided Design & Applications, 7(3), 2010, 431-440. 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