• Journal of the Korea Computer Graphics Society
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• v.3 no.2
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• pp.77-84
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• 1997

Solid modeling refers to techniques for unambiguous representations of three- dimensional objects. The most widely used techniques for solid modeling have been Constructive Solid Geometry (CSG) and Boundary Representation (BRep). Contemporary solid modeling systems typically support both representations, and bilateral conversions between CSG and BRep are essential. However, computing a CSG from a BRep is largely an open problem. This paper presents 3D geometric reasoning algorithms for converting a BRep into a special CSG, called Destructive Solid Geometry (DSG) whose Boolean operations are all subtractions. The major application area of BRep-to-DSG conversion is feature recognition, which is essential for integrating CAD and CAM.

• Research in Mathematical Education
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• v.14 no.3
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• pp.195-209
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• 2010

Utilizing a structure of operations known as Dissection-Motion-Operations (DMO), a set of mathematics propositions or area-formulas in school mathematics will be introduced through shape-to-shape transforms. The underlying theme for DMO is problem-solving through visual reasoning and proving manipulatively or electronically vs. rote learning and memorization. Visual reasoning is the focus here where two operations that constitute DMO are utilized. One operation is known as Dissection (or Decomposition) operation that operates on a given region in 2D or 3D and dissects it into a number of subregions. The second operation is known as Motion (or Composition) operation applied on the resultant sub-regions to form a distinct area (or volume)-equivalent region. In 2D for example, DMO can transform a given polygon into a variety of new and distinct polygons each of which is area-equivalent to the original polygon (cf [Rahim, M. H. & Sawada, D. (1986). Revitalizing school geometry through Dissection-Motion Operations. Sch. Sci. Math. 86(3), 235-246] and [Rahim, M. H. & Sawada, D. (1990). The duality of qualitative and quantitative knowing in school geometry, International Journal of Mathematical Education in Science and Technology 21(2), 303-308]).

• Journal of Korea Technical Association of The Pulp and Paper Industry
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• v.47 no.4
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• pp.177-186
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• 2015

Until Mandelbrot introduced the concept of fractal geometry and fractal dimension in early 1970s, it has been generally considered that the geometry of nature should be too complex and irregular to describe analytically or mathematically. Here fractal dimension indicates a non-integer number such as 0.5, 1.5, or 2.5 instead of only integers used in the traditional Euclidean geometry, i.e., 0 for point, 1 for line, 2 for area, and 3 for volume. Since his pioneering work on fractal geometry, the geometry of nature has been found fractal. Mandelbrot introduced the concept of fractal geometry. For example, fractal geometry has been found in mountains, coastlines, clouds, lightning, earthquakes, turbulence, trees and plants. Even human organs are found to be fractal. This suggests that the fractal geometry should be the law for Nature rather than the exception. Fractal geometry has a hierarchical structure consisting of the elements having the same shape, but the different sizes from the largest to the smallest. Thus, fractal geometry can be characterized by the similarity and hierarchical structure. A process requires driving energy to proceed. Otherwise, the process would stop. A hierarchical structure is considered ideal to generate such driving force. This explains why natural process or phenomena such as lightning, thunderstorm, earth quakes, and turbulence has fractal geometry. It would not be surprising to find that even the human organs such as the brain, the lung, and the circulatory system have fractal geometry. Until now, a normal frequency distribution (or Gaussian frequency distribution) has been commonly used to describe frequencies of an object. However, a log-normal frequency distribution has been most frequently found in natural phenomena and chemical processes such as corrosion and coagulation. It can be mathematically shown that if an object has a log-normal frequency distribution, it has fractal geometry. In other words, these two go hand in hand. Lastly, applying fractal principles is discussed, focusing on pulp and paper industry. The principles should be applicable to characterizing surface roughness, particle size distributions, and formation. They should be also applicable to wet-end chemistry for ideal mixing, felt and fabric design for papermaking process, dewatering, drying, creping, and post-converting such as laminating, embossing, and printing.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2004.10a
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• pp.225-232
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• 2004

Recently, there has been a rapid development in computer technology, which has in turn led to develop the automated welding system using Artificial Intelligence (AI). However, the automated welding system has not been achieved duo to difficulties of the control and sensor technologies. In this paper, the classification of the optimized bead geometry such as bead width, height penetration and bead area in the Gas Metal Arc (GMA) welding with fuzzy logic is presented. The fuzzy C-Means algorithm (FCM), which is best known an unsupervised fuzzy clustering algorithm is employed here to analysis the specimen of the bead geometry. Then the quality of the GMA welding can be classified by this fuzzy clustering technique and the choice for obtaining the optimal bead geometry can also be determined.

• Journal of Industrial Technology
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• v.27 no.B
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• pp.91-96
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• 2007

Electrical impedance tomography (EIT) is a technique for determining the electrical conductivity and permittivity distribution within the interior of a body from measurements made on its surface. One recent application area of the EIT is the detection of breast cancer by imaging the conductivity and permittivity distribution inside the breast. The present standard for breast cancer detection is X-ray mammography, and it is desirable that EIT and X-ray mammography use the same geometry. A forward model of a simplified mammography geometry for EIT imaging was proposed earlier. In this paper, we propose an iterative algorithm for computing the current pattern that will be applied to the electrodes. The current pattern applied to the electrodes influences the voltages measured on the electrodes. Since the measured voltage data is going to be used in the impedance imaging computation, it is desirable to apply currents that result in the largest possible voltage signal. We compute the eigenfunctions for a homogenous medium that will be applied as current patterns to the electrodes. The algorithm for the computation of the eigenfunctions is presented. The convergence of the algorithm is shown by computing the eigencurrent of the simplified mammography geometry.

• School Mathematics
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• v.4 no.1
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• pp.15-27
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• 2002

The purpose of this thesis is, through analysing the characteristics of the definitions in Korean school mathematics textbooks, to explore the levels of them. Definitions use din academic mathematics are rigorous. But they should be transformed into various types, which are presented in school mathematics textbooks, with didactical purposes. In this thesis we investigated such types of transformation. With the result of this investigation we tried to identify the levels of the definitions in school mathematics textbooks. We tried to construct, with consideration about methods of definition, frame for analysing the types of the definitions in school mathematics. Methods of definition are classified as connotative method, denotative method, and synonymous method. Especially we identified that connotative method contains logical definition, genetic definition, relational definition, operational definition, and axiomatic definition. With these analyses we made a frame for investigating the characteristics of the definitions in school mathematics textbooks. With this frame we identified concrete types of transformations of methods of definition. We tried to analyse this result with van Hieles' theory about let·els of geometry learning and the mathematical language levels described by Freudenthal, and identify the levels of definitions in school mathematics. We showed the levels of definitions in the geometry area of the Korean school mathematics.

• Journal of Korean Association for Spatial Structures
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• v.17 no.1
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• pp.49-58
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• 2017

The result of the previous work leads to the idea that the inner area of the hyperbolic shell generator should be minimized for the cooling tower with higher first natural frequency. In this study the inner area of the hyperbolic shell generator was graphically established under varying height of the throat and angle of the base lintel. From the graph, several shell geometries were selected and analysed in the aspect of the natural frequency. Three representative towers reinforced differently due to different first natural frequencies were analysed non-linearly and evaluated using a damage indicator based on the change of natural frequencies. The results demonstrated that the damage behaviour of the tower reinforced higher due to a lower first natural frequency was not necessarily advantageous than the others.

• Journal of ILASS-Korea
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• v.26 no.2
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• pp.57-66
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• 2021

The reactivity controlled compression ignition (RCCI) is the technology that provides two different types of fuel to the combustion chamber with the advantage of significantly reducing particulate matter and nitrogen oxides emissions. However, due to the characteristics of lean combustion, combustion efficiency is worsened. The conventional type of pistons for conventional diesel combustion (CDC) has mostly been used in the researches on RCCI. Because the pistons for CDC are optimized to enhance flow and target spray, the pistons are unsuitable for RCCI. In this study, a piston that is suitable for RCCI is designed to improve combustion efficiency. The new piston was designed by considering the factors such as squish geometry, bowl depth, and surface area. The experiment was carried out by fixing the energy supply to 0.9kJ/cycle and 1.5kJ/cycle respectively. The two pistons were quantitatively compared in terms of thermal efficiency and combustion efficiency.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.985-998
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• 1997

For n random strips chosen so as to meet a fixed bounded convex set K of the plane we let $\nu$ be the number of intersection regions that meet K. We develop the integral formula for the mean value of $\nu$ and $\nu^2$ involving the area and the perimeter of K and the breadths of the strips. We get some geometric inequalities in way of studying integral geometry.

• Education of Primary School Mathematics
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• v.5 no.2
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• pp.111-119
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• 2001

Over the years, the benefits of instructional manipulatives in mathematics education have been verified by classroom practice and educational research. The purpose of this paper is to introduce how the instructional material, specifically, geoboard could be used and integrated in elementary mathematics classroom in order to develop student's mathematical concepts and process in terms of the following areas: (1) Number '||'&'||' Operation : counting, fraction '||'&'||' additio $n_traction/multiplication (2) Geometry : geometric concepts (3) Geometry : symmetry '||'&'||' motion (4) Measurement : area '||'&'||' perimeter (5) Probability '||'&'||' Statistics : table '||'&'||' graph (6) Pattern : finding patterns Further, future study will continue to foster how manipulatives will enhance children's mathematics knowledge and influence on their mathematics performance.