• 한국수학사학회지
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• 제33권3호
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• pp.155-165
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• 2020

Pythagorean theorem is a proposition on the relationship between the lengths of three sides of a right triangle. It is well known that Pythagorean theorem for Euclidean geometry deforms into an interesting form in non-Euclidean geometry. In this paper, we investigate a new perspective that replaces right triangles with 'proper triangles' so that Pythagorean theorem extends to non-Euclidean geometries without any modification. This is seen from the perspective that a rectangle is an equiangular quadrilateral, and a right triangle is a half of a rectangle. Surprisingly, a proper triangle (defined by Paolo Maraner), which is a half of an equiangular quadrilateral, satisfies Pythagorean theorem in many geometries, including hyperbolic geometry and spherical geometry.

• 호남수학학술지
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• 제34권1호
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• pp.103-111
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• 2012

Wetzel[5] proved if ${\Gamma}$ is a closed curve of length L in $E^n$, then ${\Gamma}$ lies in some ball of radius [L/4]. In this paper, we generalize Wetzel's result to the non-Euclidean plane with much stronger version. That is to develop a lower bound of length of a triangle inscribed in a circle in non-Euclidean plane in terms of a chord of the circle.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1998년도 가을 학술발표회 논문집
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• pp.251-257
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• 1998

Spherical space frame structure with triangular network pattern, which has the various characteristics for the mechanic property, a funtional property, an aesthetic property and so on, has often been used as one of the most efficient space structures. It is expected that this type will be used widely in large-span structural roofs. But because this structure is made of network by combination of line elements there me many nodes therefore, the structure behavior is very complicated and there can be an overall collapse of structure by buckling phenomenon if the external force reaches a limitation. This kind of buckling is due to geometric shape, network pattern, the number of layer and so on, of structure. Therefore spherical space frame with triangle network pattern have attracted many designers and researchers attention all over the world. The number of layer of space frame is divided in to the simgle, double, multi layer. That is important element which is considered deeply in the beginning of structural design. The buckling characteristics of single-layer model and double-layer model for the spherical space frame structure with triangular network pattern are evaluated and the buckling loads of these types are compared with investigation their structural efficiency in this study.

• 대한전자공학회논문지SP
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• 제40권6호
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• pp.41-50
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• 2003

디지털 워터마킹 기술은 디지털 콘텐츠의 불법 복제를 방지하기 위해 디지털 데이터에 사람이 감지할 수 없는 정보를 은닉한다. 본 논문에서는 3차원 메쉬 모델(mesh model)에 대한 적응형 워터마킹 방법을 제안한다 본 논문에서 제안한 방법에서는 서로 이웃하는 꼭지점 좌표들 사이의 공간적 상관성에 따라 워터마크를 삽입하며, 이는 사람의 눈에 잘 감지되지 않는 지역에 워터마크를 강하게 삽입하고 그렇지 않은 지역에는 약하게 삽입하는 적응형 워터마킹 기술이다., 우선, 3차원 메쉬 모델을 운행(traversing)하여 삼각형 스트립(triangle strip)을 생성하고, 모든 꼭지점 좌표를 구 좌표계(spherical coordinate system)로 변환시킨다. 그리고, 3차원 모델의 지역적 외관을 결정하는 꼭지점 좌표 값들의 변화량을 계산한 후, 워터마크 신호를 계산한 변화량의 크기에 따라 유연하게 꼭지점 좌표 값에 삽입시킨다. 본 논문에서 제안한 워터마크 방법이 워터마크 신호의 비지각성(imperceptibility)을 크게 개선시킬 수 있음을 실험을 통해 검증했으며, 제안한 방법의 강인성 (robustness)에 대한 BER (bit error rate) 결과를 제시하였다.

• 한국정밀공학회지
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• 제24권11호
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• pp.134-143
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• 2007

A new approach based on mean value coordinate combined with Laplacian coordinate is proposed for shape deformation of a large polygon model composed of triangular net. In the method, the spherical mean value coordinates for closed control meshes is introduced to describe a vertex in the triangle meshes to be deformed. Furthermore, the well known quardratic least square method for the Laplacian coordinates is employed in order to deform the control meshes. Because the mean value coordinates are continuous and smooth on the interior of control meshes, deforming operation of control meshes change the shape of polygon model while preserving the intrinsic surface detail. The effectiveness and validity of this novel approach was demonstrated by using it to deform large and complex polygon models with arbitrary topologies.

• 대한수학회지
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• 제38권5호
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• pp.1069-1105
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• 2001

Regular maps and hypermaps are cellular decompositions of closed surfaces exhibiting the highest possible number of symmetries. The five Platonic solids present the most familar examples of regular maps. The gret dodecahedron, a 5-valent pentagonal regular map on the surface of genus 5 discovered by Kepler, is probably the first known non-spherical regular map. Modern history of regular maps goes back at least to Klein (1878) who described in [59] a regular map of type (3, 7) on the orientable surface of genus 3. In its early times, the study of regular maps was closely connected with group theory as one can see in Burnside’s famous monograph [19], and more recently in Coxeter’s and Moser’s book [25] (Chapter 8). The present-time interest in regular maps extends to their connection to Dyck\`s triangle groups, Riemann surfaces, algebraic curves, Galois groups and other areas, Many of these links are nicely surveyed in the recent papers of Jones [55] and Jones and Singerman [54]. The presented survey paper is based on the talk given by the author at the conference “Mathematics in the New Millenium”held in Seoul, October 2000. The idea was, on one hand side, to show the relationship of (regular) maps and hypermaps to the above mentioned fields of mathematics. On the other hand, we wanted to stress some ideas and results that are important for understanding of the nature of these interesting mathematical objects.

• 한국게임학회 논문지
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• 제8권3호
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• pp.69-76
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• 2008

본 논문에서는 보다 효율적인 렌더링을 위해 물체를 구좌표계(sperical coordinate system) 상에서 표현하는 새로운 렌더링 알고리즘이 제안된다. 먼저 직교 좌표로 표현되어 있는 물체의 정점을 구좌표로 변환하고, 카메라의 가시 절두체(frustum) 영역 내의 정점을 판단하기 위해 삼각형의 무게중심, 색인(index), 메모리 접근(access) 맵 등의 자료구조를 구성한다. 제안된 방법은 카메라에 의해 보여지는 영역, 즉 렌더링되는 물체의 가시 영역에 해당하는 정점만으로 렌더링한다. 따라서 렌더링 파이프라인에서 고려되는 정점의 개수를 크게 줄여 전체적인 시스템 성능이 크게 향상되었음을 실험을 통해서 확인하였다.

• 한국정보통신학회논문지
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• 제22권4호
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• pp.691-699
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• 2018

천문을 이용한 측위는 과거로부터 육분의(Sextant)를 이용하여 시행하여 왔다. 주로 천측력과 천측계산표를 이용하여 St. Hilaire 방식을 사용하였는데, 현대에는 IT 기술과의 접목으로 LOP(Line of Position) 방식을 원활히 사용할 수 있게 되었다. 그러나 과거의 방식 대비 LOP 방식은 항상 위치가 진위(True Position)와 허위(False Position) 두 가지로 나타나게 되는데, 이를 항해사가 반드시 판별하지 않으면 안 된다. 따라서 본 논문에서는 LOP 방식에서 발생하는 허위의 제거를 위해 방위를 이용하는 알고리즘을 제안한다. 특히 방위를 이용하게 되는 이론적 고찰을 여러 방법으로 제시하여 그 타당성을 확보하였으며, 시뮬레이션을 통하여 본 논문의 이론적 근거가 타당성을 가지고 있음을 평가하였다.

• Journal of Biosystems Engineering
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• 제12권3호
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• pp.30-41
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• 1987

The geometrical shape of a plow bottom may be the most important factor affecting the performance of a plow for a given soil and operating conditions. There are various designs of the Jaenggi (Korean plow) available commercially, which may be different from each other and from the plow (Western plow) in respect to the shape and performance. This study was intended to investigate the geometrical characteristics of Jaenggi. The coordinate digitizer equipped with 3 potentiometers was designed and manufactured for measurement of the shape of curved plane of moldboard and share. The digitizer was connected to a microcomputer having the data acquisition system. This device was used to analyze the plow bottoms of 5 differently-made Jaenggis and one cylindrical plow. The results of the study are summarized as follows: 1. It was possible to measure easily and quickly the curved plane of plow bottom and to plot the view on three major plans using the coordinate digitizer electrically connected to a microcomputer system. 2. The shape of five Jaenggi bottoms analyzed could be characterized by the cutting angle having the range of $33-42^{\circ}$, the maximum share-lift angle of $41-50^{\circ}$, and the setting angle of moldboard wing of $46-70^{\circ}$. The most critical difference of the shape factors between the Jaenggi and the plow was found in the maximum share-lift angle, the former was more than twice as much as the latter. 3. The analysis of the shape of Jaenggi bottoms showed that the share projections on 3 major plans had a varied triangle, which was quite different from that of plow bottom. Especially, it was analyzed that the shape of furrow slice for the Jaenggi had a skewed rectangle, leaving a considerable height of the ridge at the furrow bottom. 4. The dihedral angle was similar range of $30-85^{\circ}$ for the all bodies investigated, but the directional angle was somewhat different from each other. The difference in directional angle was $5^{\circ}$ for the plow, $20^{\circ}$ for the Jaenggi A and $30^{\circ}$ for the Jaenggi B. 5. Area of the spherical representation region was 0.0328 for the plow, 0.1194 for the Jaenggi A and 0.1716 for the Jaenggi B. This may indicate that the plow came close to a working surface and the Jaenggi A and the Jaenggi B departed from a working surface to a somewhat greater extent.