• 한국CDE학회논문집
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• 제2권4호
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• pp.253-266
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• 1997

Pencil-curve machining, which is a single-pass ball-end milling along a concave edge on adie surface, is widely employed in die-surface machining. The cutter-path used for pencil-curve machining, which is the trajectory of the “ball-center point” of a ball-endmill sliding along a concave-edge region on the die surface, is called pencil-curve. Presented in the paper is a pencil-curve tracing algorithm in which “concave-type” sharp edges are computed from a “virtually digitized” model of the tool-envelope surface. The resulting “initial” pencil-cures are then refuted by applying a series of fairing operations. illustrative examples and methods for enhancing accuracy are also presented. The proposed pencil-curve tracing algorithm has been successfully implemented in a commercial CAM system specialized in die-machining and in the CAD/CAM system CATIA.

• 한국CDE학회논문집
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• 제11권1호
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• pp.20-26
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• 2006

This paper presents a procedure to compute pencil curves from a triangular mesh which is offset with the radius of a given ball-end mill. An offset triangular mesh has numerous self-intersections caused by an abundance of invalid triangles, which do not contribute to the valid CL-surface. Conceptually, we can obtain valid pencil curves by combining all intersections tying on the outer skin of the offset triangular mesh, i.e., the valid CL-surface. The underlying concept of the proposed algorithm is that visible intersections are always valid for pencil curves, because visible intersections lie on the outer skin of the offset model. To obtain the visibility of intersections efficiently, the proposed algorithm uses a graphics board, which performs hidden surface removal on up to a million polygons per second.

• 대한수학회지
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• 제36권3호
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• pp.567-580
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• 1999

We prove two variants of a base-point-free pencil trick, which are similar in the spirit of the proof, and apply them to the study of special divisors on a smooth plane curve involving a theorem of Max Noether.

• 한국CDE학회논문집
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• 제9권3호
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• pp.246-252
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• 2004

Presented in this Paper is a Micro Machining Service .(MIMS) based on the World Wide Web technologies. In order to ensure easy access to the service, the web browsers are used as the user interface. The pan geometry as an STL file is uploaded with process parameter for 3-axis CNC milling. Depending on the predefined user level, novice or expert, the user interface requires different parameters for process planning. An STL-based CAM resides in the server and automatically provides NC codes upon user's request. Tool-paths for scanning and pencil-cut, which are interference-free and precise, are created by the curve-based polyhedral machining method. A couple of sample parts were fabricated by a micro endmill with 127 fm diameter. From the tests, the parts fabricated by scanning followed by pencil-cut resulted in less error(within 2%) than the parts machined only by scanning tool-path.

• 대한수학회지
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• 제55권3호
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• pp.705-717
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• 2018

We construct some infinite series of free and nearly free curves using pencils of conics with a base locus of cardinality at most two. These curves have an interesting topology, e.g. a high degree Alexander polynomial that can be explicitly determined, a Milnor fiber homotopy equivalent to a bouquet of circles, or an irreducible translated component in the characteristic variety of their complement. Monodromy eigenspaces in the first cohomology group of the corresponding Milnor fibers are also described in terms of explicit differential forms.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제24권1호
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• pp.177-193
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• 2010

본 연구는 고등학교 통계 영역의 확률분포에 제시되어 있는 정규분포를 이항분포에서 정규분포로의 근사, 정규분포곡선의 탐구, Monte Carlo 방법에 의한 정규분포곡선의 넓이 탐구, 정규분포곡선의 선형변환, 그리고 여러 형태의 정규분포곡선 탐구 등의 내용을 중심으로 CAS 계산기를 활용하여 탐구해보고자 한다. CAS 계산기의 도구적 기능인 사소화, 실험, 시각화, 집중의 측면에서 볼 때 지필로서는 교육과정에 제시된 확률분포의 목표를 달성하기 불가능하다고 판단된다. 따라서 본 연구에서는 CAS 계산기를 활용하여 정규분포곡선의 다양한 성질을 탐구하고 이러한 과정과 결과로부터 정규분포곡선에 대한 교수학적 시사점을 도출하고자 한다.

• 대한방사선치료학회지
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• 제14권1호
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• pp.175-186
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• 2002

The purpose of this study is directly measure and evaluate about absorbed dose change according to nominal energy and electron cone or medical accelerator on isodose curve, percentage depth dose, contaminated X-ray, inhomogeneous tissue, oblique surface and irradiation on intracavitary that electron beam with high energy distributed in tissue, and it settled standard data of hish energy electron beam treatment, and offer to exactly data for new dote distribution modeling study based on experimental resuls and theory. Electron beam with hish energy of $6{\sim}20$ MeV is used that generated from medical linear accelerator (Clinac 2100C/D, Varian) for the experiment, andwater phantom and Farmer chamber md Markus chamber und for absorbe d dose measurement of electron beam, and standard absorbed dose is calculated by standard measurements of International Atomic Energy Agency(IAEA) TRS 277. Dose analyzer (700i dose distribution analyzer, Wellhofer), film (X-OmatV, Kodak), external cone, intracavitary cone, cork, animal compact bone and air were used for don distribution measurement. As the results of absorbed dose ratio increased while irradiation field was increased, it appeared maximum at some irradiation field size and decreased though irradiation field size was more increased, and it decreased greatly while energy of electron beam was increased, and scattered dose on wall of electron cone was the cause. In percentage depth dose curve of electron beam, Effective depth dose(R80) for nominal energy of 6, 9, 12, 16 and 20 MeV are 1.85, 2.93, 4.07, 5.37 and 6.53 cm respectively, which seems to be one third of electron beam energy (MeV). Contaminated X-ray was generated from interaction between electron beam with high energy and material, and it was about $0.3{\sim}2.3\%$ of maximum dose and increased with increasing energy. Change of depth dose ratio of electron beam was compared with theory by Monte Carlo simulation, and calculation and measured value by Pencil beam model reciprocally, and percentage depth dose and measured value by Pencil beam were agreed almost, however, there were a little lack on build up area and error increased in pendulum and multi treatment since there was no contaminated X-ray part. Percentage depth dose calculated by Monte Carlo simulation appeared to be less from all part except maximum dose area from the curve. The change of percentage depth dose by inhomogeneous tissue, maximum range after penetration the 1 cm bone was moved 1 cm toward to surface then polystyrene phantom. In case of 1 cm and 2 cm cork, it was moved 0.5 cm and 1 cm toward to depth, respectively. In case of air, practical range was extended toward depth without energy loss. Irradiation on intracavitary is using straight and beveled type cones of 2.5, 3.0, 3.5 $cm{\phi}$, and maximum and effective $80\%$ dose depth increases while electron beam energy and size of electron cone increase. In case of contaminated X-ray, as the energy increase, straight type cones were more highly appeared then beveled type. The output factor of intracavitary small field electron cone was $15{\sim}86\%$ of standard external electron cone($15{\times}15cm^2$) and straight type was slightly higher then beveled type.

• 대한디지털의료영상학회논문지
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• 제12권1호
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• pp.65-69
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• 2010

High energy electron beams were to concentrically dose inside a tumor and more energy is a shape decreased of dose. Therefore, it is useful to radiation therapy of a tumor. Also high energy electron beams ionized into collision with a atom in structure material of tissue and it has big changes to dose distribution by multiple scattering. The study had to establish characteristic of electron beams from interaction of electron beams and materials. Experiment method was to measure dependence of electron beam central axis for depth dose curve, field flatness and symmetry and field size dependence. The results were able to evaluate data for a datum pint of electron beam. Also radiotherapy has to be considered for not only energy pencil of lines but characteristic, electron guide and isodose curves distribution.

• 대한방사선치료학회지
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• 제24권2호
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• pp.137-147
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• 2012

목 적: 알고리즘에 따른 치료계획의 영향을 분석하고 실제 치료계획을 수립할 때 고려사항을 적용하고, 나아가 최선의 치료계획을 수립하는 프로토콜을 제시하고자 한다. 대상 및 방법: 치료계획 시스템은 이클립스 10.0 (Eclipse 10.0, Varian, USA)이다. 선량계산의 알고리즘은 PBC (Pencil Beam Convolution)와 AAA (Anisotropic Analytical Algorithm)을 각각 적용하였고, 세기 조절 방사선 치료(IMRT)를 위한 최적화(Optimization) 알고리즘은 DVO (Dose Volume Optimizer 10.0.28), VMAT을 위한 최적화 알고리즘은 PRO II (Progressive Resolution Optimizer V 8.9.17)와 PRO III (Progressive Resolution Optimizer V 10.0.28)을 사용하였다. 실험을 위한 팬텀은 치료계획시스템에서 가상으로 만들었으며, $30{\times}30{\times}30$ cm의 규격에 밀도가 균일한 것(HU: 0)과 중간에 공기(HU: -1,000)로 가정되는 물질이 삽입한 된 비균질 팬텀으로 설정하였다. 실험은 먼저 팬텀(Phantom) 계획을 실시하여 일반적인 치료계획의 특징을 분석하고 그 내용을 토대로 실제 임상적용 할 치료계획을 수립하였다. 결 과: 균일한 밀도 팬텀에서 6 MV, 10 cm PDD (Percentage Depth Dose)는 PBC와 AAA는 모두 65.2%로 유사한 값을 나타냈지만, 비균질 팬텀에서 PDD는 저밀도 물질을 만나기 전까진 유사한 PDD 값을 보이다가 공기 영역에서 다른 선량곡선을 보여주고, 투과한 후에는 PDD 10 cm은 각각 75%, 73%이었다. 동일한 MU의 3차원 치료계획에서 보면, AAA 치료계획이 폐가 포함된 영역에서 저 선량으로 나타났다. 기관지와 폐의 영역이 포함된 경추 치료 환자의 2차원 대향 2문조사 치료계획을 15 MV을 이용하여 설계하였을 때, Conformity Index (ICRU 62)는 PBC 계산에서 0.95, AAA에서 0.93이었다. IMRT 치료계획은 DVO에서 보여지는 DVH가 선량계산 DVH와 동일하게 나타났다. 하지만 AAA으로 선량계산을 하였을 때는 DVO에서 조건을 만족하는 결과가 선량계산에서는 선량부족으로 나타났다. PRO II을 이용한 VMAT 치료계획은 최적화 할 때는 만족스런 결과를 얻었지만, 선량계산을 실시하였을 때는 저밀도 영역이 선량 부족으로 나타났다. 하지만 PRO III에서 같은 조건을 1회 더 최적화함으로써 최적화 결과와 선량계산 결과가 유사하였다. 결 론: 본 연구에서는 선량계산 알고리즘의 옳고 그름을 판단하지 않는다. 알고리즘이 나타내는 선량 분포의 특성을 분석하고, 특히 최적화가 필요한 IMRT나 VMAT 치료계획에서 최적화 알고리즘의 요인도 치료계획을 수립할 때 고려함으로써 최적의 치료계획을 위한 방법을 제시하고자 한다.

• 한국의학물리학회지:의학물리
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• 제23권1호
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• pp.48-53
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• 2012

방사선치료계획장치에서 선량계산을 위해 PBC 알고리즘(pencil beam convolution)은 가장 널리 사용되고 있다. Varian (Varian Medical System, Palo Alto, CA)사는 광자의 선량 계산을 위해서 AAA 알고리즘을 새롭게 선량계산모델로 탑재하였다. 본 연구는 폐와 같은 저밀도 영역에 종양부위가 있는 환자를 대상으로 세기조절방사선치료를 시행할 경우에 PBC 알고리즘과 AAA 알고리즘으로 계산했을 때 차이를 정량적으로 알고자 하는데 목적이 있다. 두 알고리즘의 정량적 분석을 위해서 Eclipse planning system과 I'mRT matrixx (IBA, Schwarzenbruck, Germany)를 사용하였다. 또한 두 알고리즘으로 계산된 선량과 실제 측정된 선량의 차이를 확인하기 위해서 인체모형펜텀(Alderson Rando phantom)속에 TLD-100 (LiF)을 위치 시켰다. 종양부위 주위의 중요장기인 trachea, esophagus, lung, PRV spinal cord의최대선량, 평균선량, 최소선량은 알고리즘의 변화에 따라서 거의 변화가 없었으나, PTV의 V95는 PBC와 비교하여 AAA가 약 6% 감소하는 결과를 얻었다. 이러한 결과는 I'mRT matrixx를 이용하여 저밀도를 가지는 폐의 위치에서 확연하게 나타남을 확인할 수 있었다. 또한 인체모형펜텀(Alderson Rando phantom)과 TLD-100 (LiF)을 이용한 계산선량과 실제 측정치의 결과는 PBC 알고리즘은 평균 4.6%의 차이를 보였으며, AAA 알고리즘은 평균 2.7%의 차이를 보였다. 이 결과로 저밀도를 가지는 폐암에서의 세기조절방사선치료를 시행할 경우에 PBC 알고리즘보다 AAA 알고리즘이 더 유효함을 알 수 있다.