• International Journal of Internet, Broadcasting and Communication
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• v.15 no.2
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• pp.175-180
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• 2023

Fractal geometry, a relatively new branch of mathematics, was first introduced by Benoit Mandelbrot in 1975. Since then, its applications have expanded into various fields of natural science. In fact, it has been recognized as one of the three significant scientific discoveries of the mid-20th century, along with the Dissipative System and Chaos Theory. With the help of fractal geometry, designers can create intricate and expressive artistic patterns, using the concept of self-similarity found in nature. The impact of fractal geometry on the digital art world is significant and its exploration could lead to new avenues for creativity and expression. This paper aims to explore and analyze the development and applications of fractal geometry in digital art design. It also aims to showcase the benefits of applying fractal geometry in art creation and paves the way for future research on sacred geometry.

• Korean Institute of Interior Design Journal
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• v.23 no.4
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• pp.129-139
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• 2014

The objective of this research is to suggest new geometric possibilities in digital architecture by investigating the characteristics of hybridization in digital geometry. The research begins with theoretical background research such as defining hybridization, investigating hybrid thinking, and studying the theory of digital geometry, along with the four conceptual characteristics of hybridization that could be drawn, such as temporality, liquidity, complexity, and connectivity. Based on these characteristics, the generative method of hybrid digital geometric languages such as Blob, Particle, Morph, Loft, and Boolean was analyzed with case research in contemporary digital architecture. As a result, diverse hybrid geometric keywords were extracted; these keywords suggest potential meanings of hybridization such as accidentality, mobility, diversity, and identity. Different elements represent the "mobility" in time by the force and wave, and they are "accidentally" combined in gradual change. The united species in "diverse" characters are seamlessly connected and emerge as a new "identity." The research maximizes the generative possibilities in digital geometry and provides a theoretical basis to apply the digital hybrid methods to architectural design by suggesting the potential meanings and possibilities in hybridization.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.207-217
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• 2008

Digital geometry has strongly contributed to the study of a discrete topological space $X{\subset}{\mathbf{Z}}^n$ with k-adjacency of ${\mathbf{Z}}^n$. As a survey-type article, we review various utilities of digital geometry.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.10 no.2
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• pp.25-30
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• 1992

Most algorithms in computer vision and digital photogrammetry assume that digital stereo pairs are registered in epipolar geometry. But, an aerial stereo pair is not likely to be in epiplar geometry since the attitude of the camera at the instant of exposure is different at every exposure station. In this paper, stereo digital imagery is obtained from aerial stereo pair by scanner. Then procesure to resample the digital imagery to epipolar geometry using exterior orientation elements after absolute orientation is described. As a result, a stereo imagery in epipolar geometry is produced from stereo digital imagery. Epipolar imagery in this paper is applied to the image matching method by digital image correlation technique. Then, a digital elevation model is produced from the result of image matching. The digital elevation model in this paper is compared to the other digital elevation model produced by analytical plotter. As a result, an economical method to generate digital elevation model is presented.

• Journal of The Korean Digital Architecture Interior Association
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• v.9 no.3
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• pp.15-23
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• 2009

Chaos theory, qualitative study of unstable aperiodic behavior in deterministic nonlinear dynamical systems, is dominant paradigm in the twenty first century. Fractal geometry, as an expressed form of chaos, now influences many areas such as architecture, art, music, economics, literature, etc. The purpose of this study is to analyze fractal geometry and fractal formative elements in architectural design. There are scaling, superimposition, distortion, deformation and repetition in the fractal form generator that can be applied to design concept and process in architecture. This study shows fractal geometry can be the architectural form creation method. Fractal geometry similar to nature's patterned order can be provided endless possibilities for design analysis and methodology in architecture. Therefore the further study of fractal geometry should progress synthetically through the basis of the study.

• Journal of the Korean School Mathematics Society
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• v.6 no.2
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• pp.39-53
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• 2003

We study the dynamic geometry software suitable for the Internet Environment. First, we look into the necessity of dynamic geometry software and compare the functions and the features of commercial softwares, GSP, Cabri and Cinderella. Secondly, we introduce the process of development and the structure of the new software DRC(Digital Ruler and Compass) designed by authors and discuss the learning program with DRC and Internet, and view the upgrade of the software in the future.

• Journal of KIBIM
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• v.12 no.1
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• pp.10-22
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• 2022

Prefabricated bridges require strict management of tolerance during fabrication and assembly. In this paper, digital engineering models for prefabricated bridge components such as deck, girder, pier, abutment are suggested to support information delivery through the life-cycle of the bridge. Rule-based modeling is used to define geometry of the members considering variable dimensions due to fabrication and assembly error. DfMA(design for manufacturing and assembly) provides the rules for ease of fabrication and assembly. The digital engineering model consists of geometry, constraints and corresponding parameters for each phase. Alignment and control points are defined to manage tolerances of the prefabricated bridge during fabrication and assembly. Quality control by digital measurement of dimensions was also considered in the model definition. A pilot bridge was defined virtually to validate the suggested digital engineering models. The digital engineering models for DfMA showed excellent potential to realize prefabricated bridges.

• Honam Mathematical Journal
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• v.34 no.3
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• pp.451-465
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• 2012

Since there are several kinds of continuities of maps between digital spaces, the paper compares them, which can play an important role in digital topology and discrete geometry.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.1634-1637
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• 2003

Any given object on the motor-driven turntable is pictured from 8 to 72 different views with a digital camera. 3D shape reconstruction is performed with the integrated software called by Scanware from these multiple digital photographs. There are several steps such as configuration, calibration, capturing, segmentation, shape creation, texturing and merging process during the shape reconstruction process. 3D geometry data can be exported to cad data such as Autocad input file. Also 3D image model is generated from 3D geometry and texture data, and is used to advertise the model in the internet environment. Consumers can see the object realistically from wanted views by rotating or zooming in the internet browsers with Scanbull spx plug-in. The spx format allows a compact saving of 3D objects to handle or download. There are many types of scan equipments such as laser scanners and photogrammetric scanners. Line or point scan methods by laser can generate precise 3D geometry but cannot obtain color textures in general. Reversely, 3D image modeling with photogrammetry can generate not only geometries but also textures from associated polygons. We got various 3D image models and introduced the process of getting 3D image model of an internet-connected watchdog robot.

• The Journal of the Korea Contents Association
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• v.16 no.5
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• pp.306-317
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• 2016

Both the formal type of architecture and free-form architecture have basic factors and methods for basic expression. Because the use of digital design tools for creation of free-form design mostly depends on the character and ability of designer, this study aims to propose establishment of free-form design creation method as a prototype, including the method to create free-form design, through setting up rules that can be used in common. This study is carried out on the basis of the application of digital design tools used for creation of conceptual free-form styles at the phase of conceptualization and development, which is different from the general theory of free-from design. The free-from style in the modern architecture has begun with the changes in digital design tools and design concepts. In the case study based on the free-form designs in precedent studies, the morphological characteristics have been analyzed and interpreted by using the language of digital design tools, so that this study will suggest the techniques to realize the free-form style on the basis of geometric transformation by using the digital design tools, as well.