• Title, Summary, Keyword: intersection

### A Study on Intersection Computation in Interval Arithmetic (인터벌 연산 기반의 곡면간 교차선 계산에 관한 연구)

• Ko, Kwang-Hee
• Korean Journal of Computational Design and Engineering
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• v.15 no.3
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• pp.178-188
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• 2010
• This paper addresses the problem of determining if two surfaces intersect tangentially or transversally in a mathematically consistent manner and approximating an intersection curve. When floating point arithmetic is used in the computation, due to the limited precision, it often happens that the decision for tangential and transversal intersection is not clear cut. To handle this problem, in this paper, interval arithmetic is proposed to use, which provides a mathematically consistent way for such decision. After the decision, the intersection is traced using the validated ODE solver, which runs in interval arithmetic. Then an iterative method is used for computing the accurate intersection point at a given arc-length of the intersection curve. The computed intersection points are then approximated by using a B-spline curve, which is provided as one instance of intersection curve for further geometric processing. Examples are provided to demonstrate the proposed method.

### An Improved Tracing algorithm for surface/surface intersection (곡면간의 교차곡선 계산을 위한 개선된 Tracing 알고리즘)

• 조두연;이규열;임중현
• Korean Journal of Computational Design and Engineering
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• v.4 no.3
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• pp.269-283
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• 1999
• Surface/surface intersection is a common and important problem in geometric modeling and CAD/CAM. Several methods have been used to approach this problem. All possible intersection curves can be obtained by using the subdivision algorithm, while it requires a great deal of memory and is somewhat inefficient. The tracing algorithm is much faster than the subdivision algorithm, and can find points on the intersection curve sequentially. But, the tracing algorithm has some problems in the intersection curves on surface boundaries. In this paper, an Improved tracing algorithm that includes some ideas such as a new trace-terminating condition for the intersection curves on surface boundaries, detecting closed intersections and extension for composite surfaces is suggested. This algorithm consists of three step: generating state points for curve tracing, tracing intersection curves and sorting pieces of the intersection curves. The results of this algorithm and comparisons to the 'DESIGNBASE' and 'ACIS' system are presented.

### THE GENERATORS OF COMPLETE INTERSECTION

• Kang, Oh-Jin;Ko, Hyuong-J.
• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.829-841
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• 2000
• We classify complete intersections I of grade 3 in a regular local ring (R, M) by the number of minimal generators of a minimal prime ideal P over I. Here P is either a complete intersection or a Gorenstein ideal which is not a compete intersection.

### Position of Intersection Recognition and Tum Signal Operation Approaching at Target Intersection (교차로 인지와 방향지시등 조작 지점에 관한 검토)

• Jeon, Yong-Wook;Tatsmu, Daimon
• Journal of the Korean Society of Safety
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• v.24 no.3
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• pp.65-70
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• 2009
• In-vehicle route guidance information(RGI) systems have been developed with the advancement of the information and communication technologies. However, the RGI is provided by a pre-determined option, drivers occasionally pass the target intersection owing to non- or late- recognizing it. The purpose of this experiment is to examine the position of driver's tum signal operation and intersection recognition approaching at the target intersection which is difficult to identify as a preliminary research on developing the additional RGI connecting with the tum signal control. The field experiment was conducted to measure distances of the turn signal operation and intersection recognition from the target intersection according to driving lanes and landmarks at adjacent intersection. And, glance behavior to the car navigation display was evaluated by using an eye camera. The results indicate that drivers operate the turn signal after confirming a landmark in the case of the intersection with it. However, most case of driving, drivers operate the tum signal at 40 to 50m before coming to the target. To provide the additional RGI, when drivers do not operate the tum signal approaching at the target intersection based on the results, is expected to improve the traffic safety and the comfort for drivers.

### Analysis of the Tasks to Find Intersection Points of a Function and Its Inverse Function (역함수와의 교점을 구하는 과제에 대한 분석)

• Heo, Nam Gu
• The Mathematical Education
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• v.55 no.3
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• pp.335-355
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• 2016
• The purpose of this study is to analyze tasks to find intersection points of a function and its inverse function. To do this, we produced a task and 64 people solved the task. As a result, most people had a cognitive conflict related to inverse function. Because of over-generalization, most people regarded intersection points of a function and y=x as intersection points of a function and its inverse. To find why they used the method to find intersection points, we investigated 10 mathematics textbooks. As a result, 23 tasks were related a linear function, quadratic function, or irrational function. 21 tasks were solved by using an equation f(x)=x. 3 textbooks presented that a set of intersection points of a function and its inverse was not equal to a set of intersection points of a function and y=x. And there was no textbook to present that a set of intersection points of a function and its inverse was equal to a set of intersection points of $y=(f{\circ}f)(x)$ and y=x.

### Effect of Intersection Angle of the Flow-focusing Type Droplet Generation Device Channel on Droplet Diameter by using Numerical Simulation Modeling (수치해석 모델링을 이용한 교차 흐름 미세유체 액적 생성 디바이스 채널 교차각이 액적 직경에 미치는 영향)

• Kim, Shang-Jin;Kang, Hyung-Sub;Yang, Yeong-Seok;Kim, Gi-Beum
• Journal of Biomedical Engineering Research
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• v.36 no.3
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• pp.61-68
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• 2015
• In this paper, we studied the effects of intersection angles of the flow-foucusing type droplet generation device inlet channel on droplet diameter using numerical simulation modeling. We modeled different intersection angles with a fixed continuous channel width, dispersed channels width, orifices width, and expansion channels width. Numerical simulations were performed using COMSOL Multiphysics$^{(R)}$ to solve the incompressible Navier-Stokes equations for a two-phase flow in various flow-focusing geometries. Modeling results showed that an increase of the intersection angle causes an increase in the modification of the dispersed flow rate ($v^{\prime}{_d}$), and the increase of the modification of the continuous flow rate ($v^{\prime}{_c}$) obstructs the dispersed phase fluid flow, thereby reducing the droplet diameter. However, the droplet diameter did not decrease, even when the intersection angle increased. The droplet diameter decreased when the intersection angle was less than $90^{\circ}$, increased at an intersection angle of $90^{\circ}$, and decreased when the intersection angle was more than $90^{\circ}$. Furthermore, when the intermediate energy deceased, there was a decrease in the droplet diameter when the intersection angle increased. Therefore, variations in the droplet diameter can be used to change the intersection angle and fluid flow rate.

### A Comparative Study on the Mean Control Delay by Signalized Intersections by the Analysis Model (분석모형별 신호교차로 평균제어지체 비교·분석 연구)

• Lee, kyu soon;Park, Jin Woo;Sung, Sam Hyun;Lee, Tak Soo
• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.19 no.1
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• pp.83-93
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• 2020
• The time delay is used as a major indicator of the level of traffic congestion on traffic crossroads. For this purpose, the Daechi Station intersection where traffic congestion occurs and the Yeongdong 5 Bridge intersection where the traffic condition is relatively good, and the average lag time based on the field survey with the lag time calculated various simulation programs. comparison of the average control delay of the field survey data the signal intersection analysis model the KHCS Dechi intersection 7.7 second / vehicle Young dong 5 bridge intersection 7.9 second / vehiclehe VISSIM showed a difference Dechi intersection 21.1 second / vehicle and Young dong 5 bridge intersection 8.1 second / vehiclehe T7F showed a difference Dechi intersection 3.3 second / vehicle and Young dong 5 bridge intersection 9.3 second / vehicle. Analyzing the same intersection proved that the results differed from one simulation model to another.

### Multi-Sensor Multi-Target Passive Locating and Tracking

• Liu, Mei;Xu, Nuo;Li, Haihao
• International Journal of Control, Automation, and Systems
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• v.5 no.2
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• pp.200-207
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• 2007
• The passive direction finding cross localization method is widely adopted in passive tracking, therefore there will exist masses of false intersection points. Eliminating these false intersection points correctly and quickly is a key technique in passive localization. A new method is proposed for passive locating and tracking multi-jammer target in this paper. It not only solves the difficulty of determining the number of targets when masses of false intersection points existing, but also solves the initialization problem of elastic network. Thus this method solves the problem of multi-jammer target correlation and the elimination of static false intersection points. The method which dynamically establishes multiple hypothesis trajectory trees solves the problem of eliminating the remaining false intersection points. Simulation results show that computational burden of the method is lower, the elastic network can more quickly find all or most of the targets and have a more probability of locking the real targets. This method can eliminate more false intersection points.

### A Study on Unifying Topology and Numerical Accuracy in Geometric Modeling: Surface to Surface Intersections (토폴로지와 수치적 정확도를 통합한 기하모델링에 관한 연구: 곡면간 교차선)

• Ko, Kwang-Hee
• Korean Journal of Computational Design and Engineering
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• v.12 no.5
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• pp.344-353
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• 2007
• In this paper, we address the problem of robust geometric modeling with emphasis on surface to surface intersections. We consider the topology and the numerical accuracy of an intersection curve to find the best approximation to the exact one. First, we perform the topological configuration of intersection curves, from which we determine the starting and ending points of each monotonic intersection curve segment along with its topological structure. Next, we trace each monotonic intersection curve segment using a validated ODE solver, which provides the error bounds containing the topological structure of the intersection curve and enclosing the exact root without a numerical instance. Then, we choose one approximation curve and adjust it within the bounds by minimizing an objective function measuring the errors from the exact one. Using this process, we can obtain an approximate intersection curve which considers the topology and the numerical accuracy for robust geometric modeling.

### INTERSECTION-SOFT IDEALS IN CI-ALGEBRAS

• Ko, Jung Mi;Kim, Yong Chan;Song, Seok Zun
• The Pure and Applied Mathematics
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• v.21 no.2
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• pp.105-112
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• 2014
• The notion of intersection-soft ideal of CI-algebras is introduced, and related properties are investigated. A characterization of an intersection-soft ideal is provided, and a new intersection-soft ideal from the old one is established.