• Korean Journal of Computational Design and Engineering
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• v.7 no.4
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• pp.269-279
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• 2002

Geometric shape morphing is an interesting geometric operation that interpolates two geometric shapes to generate in-betweens. It is well known that Minkowski operations can be used to test and build collision-free motion paths and to modify shapes in digital image processing. In this paper, we present a new geometric modeling technique to control the morphing on geometric shapes based on Minkowski sum. The basic idea develops from the linear interpolation on two geometric shapes where the traditional algebraic sum is replaced by Minkowski sum. We extend this scheme into a Bezier-like control structure with multiple control shapes, which enables the interactive control over the intermediate shapes during the morphing sequence as in the traditional CAGD curve/surface editing. Moreover, we apply the theory of blossoming to our control structure, whereby our control structure becomes even more flexible and general. In this paper, we present mathematical models of control structure, their properties, and computational issues with examples.

• Journal of the Korea Fashion and Costume Design Association
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• v.26 no.1
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• pp.61-76
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• 2024

The purpose of this study is the development of an experimental design that aims to implement three-dimensional fashion design by observing the human body, extracting and combining geometric shapes and forms, and focusing on attempts to decompose the geometry of the human body in art history. Considering the characteristics of fashion design, which inevitably reflect human images visually, this study considered works by deriving geometric shapes and forms of the human body and focusing on decomposition and combination to apply them to fashion design. The results obtained through the development of fashion design through decomposition and combination based on geometric human body analysis are as follows. First, geometric analysis of the human body as an object of expression continues from the history of Cubism to modern fashion design. Second, the geometric shapes of the human body that appear in contemporary fashion design maximize visual effects through three-dimensional composition, emphasizing simplicity while showing originality through various expressions. Third, when exploring the geometric shapes of a moving human body, it was possible to extract a wide variety of shapes and forms through drawing and simplifying the human body's movements. Fourth, the formative method of fashion design was introduced and used for the aesthetic combination of objects for fashion design through decomposition and combination. This study was able to show unique and diverse combinations of visually concise and ordered geometric shapes in the expression of fashion design by decomposing and combining them. The significance of these geometric forms is that they can diversify formative informativeness in the expression of fashion design with modern compositional beauty.

• Journal of the Korean Society of Clothing and Textiles
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• v.45 no.1
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• pp.155-167
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• 2021

The latest innovation in the field of fashion comes in the form of 3D-printed clothing. This study explores the composition and characteristics of the shapes in the architecture of Zaha Hadid, a representative architectural designer who expresses space in three dimensions. Hadid applies his aesthetic to fashion design using these distinctive geometric shapes to create design motifs as well as develop new clothing material with 3D printing technology. The research was conducted as follows. First, the lines and arrangement of the geometric shapes in Zaha Hadid's architecture were analyzed so that his design principles could be used as a theoretical basis for this study. The study also reviewed geometric fashion designs using 3D printing technology over the last ten years. Second, we developed triangular modules with rods and tongs that could be fashioned into clothing using fused deposition modeling (FDM) 3D printers. Lastly, the 3D printing fashion design was developed to explore new silhouettes, textures, and a novel way of producing clothing. This study hopes to serve as a stepping-stone for further research on innovations that combine fashion with technology.

• Journal of the Korea Fashion and Costume Design Association
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• v.16 no.1
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• pp.53-64
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• 2014

The main objective of this research was to understand the characteristics of printed geometric patterns through the statistical & qualitative analysis of fashion appeared in contemporary female collections 2011 S/S to 2013 A/W. Data collection of 294 was done through review of 'pr$\hat{e}$t-$\grave{a}$-porter Collections' of three major fashion cities; Paris, Milan and NY. Statistical analysis of frequency was conducted. Also qualitative interpretation of natural print design' characteristics were completed. The main findings were as followed; 1,636 of the total 15,852 designs were printed patterns in 12 Collections and the occurrence rate of printed geometric patterns in three collections were 8.6% in Milan, 9.2% in Paris and 12.9% in N.Y. Most geometric patterns were the types of compact or medium density in a front patterns with a variety of sizes and mainly applied to the one piece dress or two piece clothing item combination styles. Formative Characteristics of printed geometric patterns were classified into four types. First, a variety of thicknesses and shapes, such as a line or a rectangle shape to take advantage of the types of the typical geometric pattern. Second types were using the motifs which inspired by geometric shapes such as point, circle star and other special geometric shapes and arranging them regularly with various sizes and density. The third was repeated particular motifs which based on complex and sophisticated mathematical formulas. Fourth were the specific diagram types of bold and free shapes or dividing the flat and arranging them without rules, or the combination type of various geometric motifs.

• Journal of the Korea Furniture Society
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• v.18 no.2
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• pp.152-160
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• 2007

The purpose of this study was to suggest a new approach to geometric abstraction for furniture design. For this study, Geometric abstraction that was done during 1917 through 1939 was investigated. Geometric abstraction is one form of pure abstraction and is mainly concerned with geometric elements and primary colors. De stijl and Bauhaus, which were emphasized groups during this period were influenced by geometric abstract arts. The purpose of this body of work has been to create furniture pieces that would express and embody my exploration and interpretation of geometric abstraction. The various compositions of geometric shapes, pure proportion, and primary color have been a focal point.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.9
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• pp.84-93
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• 1996

This paper describes the development of new feature positioning method which embedded into the top-down assembly modeling system supporting conceptual design. In this work, the user provides the geometric constraints representing the position and size of features, then the system calculates their proper solution. The use of geometric constraints which are easy to understand intuitively enables the user to represent his design intents about geometric shapes, and enables the system to propagate the changes automatically when some editing occurs. To find the proper solution of given constraints, the Selective Solving Method in which the redundant or conflict equations are detected and discarded is devised. The validity of feature shapes satisfying the constraints can be maintained by this technique, and under or over constrained user-defined constraints can also be estimated. The problems such as getting the initial guess, controlling the multiple solutions, and dealing with objects of rotational symmetry are also resolved. Through this work, the feature based modeling system can support more general and convenient modeling method, and keeps the model being valid during modifying models.

• Korean Journal of Computational Design and Engineering
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• v.8 no.4
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• pp.243-253
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• 2003

This paper presents a new geometric morphing algorithm for polygons based on a simple geometric structure called direction map, which is mainly composed of a circular list of direction vectors defined by two neighboring vertices of a polygon. To generate a sequence of intermediate morphing shapes, first we merge direction maps of given control shapes based on a certain ordering rule of direction vectors, and scale the length of each direction vectors using Bezier or blossom controls. We show that the proposed algorithm is an improvement of the previous methods based on Minkowski sum (or convolution) in th aspects of computational efficiency and geometric properties.

• Korean Journal of Computational Design and Engineering
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• v.6 no.4
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• pp.271-276
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• 2001

A geometric kernel is the library of core mathematical functions that defines and stores 3D shapes in response to users'commands. We developed a light geometric kernel suitable to develop CAD/CAM application systems. The kernel contains geometric objects, such as points, curves and surfaces and a minimal set of functions for each type but does not contain lots of modeling and handling functions that are useful to create and maintain complex shapes from an idea sketch. The kernel was developed on MS-Windows NT using C++ with STL(Standard Template Library) but it is compatible with UNIX environments. This paper describes the structure of the kernel including several components: base, math, point sequence curve, geometry, translators. The base kernel gives portability to applications and the math kernel contains basic arithmetic and their classes, such as vector and matrix. The geometry kernel contains points, parametric curves, and parametric surfaces. A neutral fie format and programming and document styles are also presented in this paper.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.1
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• pp.54-60
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• 2001

In this paper, a shape-based block layout (SBL) approach is presented to solve the facility layout problem with unequal-area and fixed shapes. The SBL approach employs hybrid genetic algorithm (Hybrid-GA) to find a good solution and the concept of bay structure is used. In the typical facility layout problem with unequal area and fixed shapes, the given geometric constraints of unequal-area and fixed shapes are mostly approximated to original shape by aspect ratio. Thus, the layout results require extensive manual revision to create practical layouts and it produces irregular building shapes and too much unusable spaces. Experimental results show that a SBL model is able to produce better solution and to create more practical layouts than those of existing approaches.

• Research in Mathematical Education
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• v.16 no.1
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• pp.31-50
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• 2012

The present study explored whether the implementation of focused activities (intervention programme) can enhance 22 pre-service mathematics teachers' proficiency in solid geometry thinking level as well as change for the better their feelings in this discipline. Over a period of 6 weeks the pre-service teachers participated in activities and diversified experiences with 3D shapes, using illustration aids and actual experience of building 3D shapes in relation to the various spatial thinking levels. The research objectives were to investigate whether the intervention programme, comprising task-oriented activities of solid geometry, enhance mathematics pre-service teachers' mastery of their geometric thinking levels as well as examine their feelings towards this discipline before and after the intervention programme. The findings illustrate that learners' levels of geometric thinking can be promoted, entailing control on higher thinking levels as well as a more positive attitude towards this field.