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
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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.
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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.
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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
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