• 통합자연과학논문집
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• 제10권1호
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• pp.27-32
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• 2017

In this paper we consider the two tangent lines of isogonal and isotomic conjugates of the line at both vertices of a given triangle. We find the necessary and sufficient condition for the two tangent lines of isogonal or isotomic conjugates of the line at both vertices and the median line to be concurrent. We also prove that every line whose isogonal conjugate tangent lines at both vertices are concurrent with the median line intersects at a unique point. Moreover, we show that the three intersection points correspond to the vertices of triangle are collinear.

• East Asian mathematical journal
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• 제29권4호
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• pp.425-447
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• 2013

Since the center of mass of mathematics curriculum in middle school is dealt with only on triangle and it is defined as just an intersection point of median lines without any physical experiments, students sometimes have misconception of the centroid as well as it is difficult to promote divergent thinking that enables students to think the centroids of various figures. To overcome these problems and to instruct effectively the centroid unit in middle school mathematics classroom, this study suggests a teaching and learning method for the unit which uses physical experiments, drawing, and calculation methods sequentially based on the investigation of students' understanding on the centroid of triangle and the analysis of the mathematics textbooks.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2007년도 추계학술대회 논문집
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• pp.539-540
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• 2007

• 대한수학회보
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• 제52권3호
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• pp.925-933
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• 2015

It is well-known that the area of parabolic region between a parabola and any chord $P_1P_2$ on the parabola is four thirds of the area of triangle ${\Delta}P_1P_2P$. Here we denote by P the point on the parabola where the tangent is parallel to the chord $P_1P_2$. In the previous works, the first and third authors of the present paper proved that this property is a characteristic one of parabolas. In this paper, with respect to triangles ${\Delta}P_1P_2PQ$ where Q is the intersection point of two tangents to X at $P_1$ and $P_2$ we establish some characterization theorems for parabolas.

• 산업경영시스템학회지
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• 제27권4호
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• pp.94-104
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• 2004

This paper proposed a new method to evaluate service quality attribute of perceived service quality in public sectors, using triangle fuzzy numbers and hamming distance. Our method measured the ratio of the expected and perceived service for the customers' perceived service quality. By using fuzzy numbers, This method not only overcomes linguistic variable problems but also provides more objective and direct information for service quality attributes. The discrepancy rate between expected service and perceived service that is perceived service quality is evaluated by hamming distance. To evaluate the discrepancy rate from hamming distance, we induced general solutions to compute the intersection area between two triangle fuzzy numbers and the weak or strong attributes in public sectors are clarified.

• 한국수학사학회지
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• 제34권4호
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• pp.137-149
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• 2021

The center of gravity of a triangle is the center of a physical shape. This is the content in the second grade of middle school, 'The Use of Similarity'. Unlike the cases of circumcenter and incenter, which are easily recognized visually, it is not easy for teachers to guide students with the visual meaning of center of gravity. According to the survey results, students, regardless of academic achievement, grade, and major, perceived the center of gravity of various plane figure as the center of their shape within a limited area through visual judgment. With reference to the results and contents of this process, it is hoped that the point of the three medians is meaningful not only in argumentative definition that the intersection of the triple line is the center of gravity of the triangle, but also in the center of a figure.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 1995년도 춘계공동학술대회논문집; 전남대학교; 28-29 Apr. 1995
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• pp.603-616
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• 1995

Presented in this paper is an algorithm to obtain the intersections of a polyhedral surface composed of triangle facets with a series of parallel planes for extracting machining information from the surface. The change of the topology of the intersection curves is caused by characteristic points of the surface when sectioning the surface with parallel planes. The characteristic points are internal maximum, internal minimum, internal saddle, boundary maximum, boundary minimum, boundary max-saddle, and boundary min-saddle points. The starting points of the intersects are found efficiently and robustly using the characteristic points. The characteristic points as well as the intersection contours can be used to evaluate the machining information for process planning, and to generate NC tool path in CAD/CAM system.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 1998년도 춘계학술대회 논문집
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• pp.129-134
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• 1998

STL which is used in Rapid Prototyping is composed of a lot of triangular facets. The number of triangles and the shapes of these triangles determine the quality of STL. Therefore, proper algorithm is necessary to enhance the quality of triangular patch. In this paper we used the Delaunay triangulation method to apply to following processes. 1) On processing for reducing sharp triangles which cause errors on intersection. 2) On processing for connecting two or more collinear edges. 3) On processing for deleting unnecessarily inserted points in coplanar polygon.

• 대한산업공학회지
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• 제21권4호
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• pp.493-506
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• 1995

Presented in this paper is an algorithm to obtain the intersections of a polyhedral surface composed of triangle facets with a series of parallel planes for extracting machining information from the surface. The change of the topology of the intersection curves is caused by characteristic points of the surface when sectioning the surface with parallel planes. The characteristic points are internal maximum, internal minimum, internal saddle, boundary maximum, boundary minimum, boundary max-saddle, and boundary min-saddle points. The starting points of the intersects are found efficiently and robustly using the characteristic points. The characteristic points as well as the intersection contours can be used to evaluate the machining information for process planning, and to generate NC tool path in CAD/CAM system.

• 한국컴퓨터정보학회논문지
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• 제29권8호
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• pp.59-65
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• 2024

본 논문에서는 삼각형 메쉬 기반 옷감 시뮬레이션에서 계산이 큰 자기충돌(Self-collision) 처리를 GPU 기반으로 가속화하는 방법을 소개한다. CUDA(Compute Unified Device Architecture) 기반 병렬 최적화를 위해, 본 논문에서는 1) GPU에서 BVH(Bounding Volume Hierarchy) 트리를 효율적으로 구축, 업데이트 및 순회하는 방법을 제안하고, 2) 삼각형 메쉬 기반에서는 R-Triangle(Representative-Triangle) 기법을 GPU에서 최적화하여 프리미티브 충돌 검사를 최소화한다. 결과적으로, 제안된 방법은 GPU 환경에서 옷감 시뮬레이션의 자기충돌과 객체 충돌을 CPU기반 알고리즘에 비해 빠르고 효율적으로 처리할 수 있으며, 다양한 장면에서 실험한 결과 5배~10배정도 빠른 시뮬레이션 결과를 얻을 수 있다. 본 논문에서 제안하는 방법은 BVH를 GPU에서 최적화했기 때문에 BVH를 기반으로 활용하는 다양한 알고리즘과 분야에 쉽게 통합이 가능하다.