• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집C
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• pp.235-239
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• 2001

Finding intersection point between a surface and a line is one of major problem in CAD/CAM. The intersection point could be found in an exact form or with numerical method. In this paper, the exact solution of the intersection point between a ruled surface which is generated by the movement of an endmill and the z-direction vector is presented. The cutter swept surface which is a ruled surface and the Z-direction vector are represented with parametric equations. With the nature of parametric equations, the geometric properties at the intersection point are easily acquired.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권3호
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• pp.309-317
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• 2016

As a generalization of an inflection point, we consider a point P on a smooth plane curve C of degree m at which another curve C' of degree n meets C with high intersection multiplicity. Especially, we deal with the existence of two curves of degree m and n meeting at the unique point.

• 한국CDE학회논문집
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• 제15권3호
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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.

• 한국정보처리학회논문지
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• 제4권8호
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• pp.2163-2172
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• 1997

곡면간의 교차계산은 부울연산(Boolean operations)과 조각된 곡면들을 지원하기위한 기하 모델링과 솔리드에서 사용되는 기본적인 기하학 연산이다. 본 논문에서는 두 정규화된 곡면의 교차곡선을 따라 추적하기 위한 새로운 알고리즘을 제안한다. 그러므로 본 논문에서는 계산상의 간소화와 2차 연속성을 나타낸다. 따라서, 교차 곡선의 한 점이 주어지면 이 점을 초기점으로 하여 교차 곡선의 전체 곡선을 추적한다. 그리고 각각의 교선들의 초기점들은 쿼드트리에서 DFS(Depth First Search) 기법으로 검색되고 교선은 연속적인 형태로 자연스럽게 표현된다.

• 호남수학학술지
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• 제45권4호
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• pp.648-654
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• 2023

Schwarz lemma at the non-smooth boundary point for holomorphic self-map on the intersection of two balls in ℂ² is obtained. At the complex tangent point in the corner of the boundary of the domain, the tangential eigenvalue of the complex Jacobian of the holomorphic map is estimated if the map is transversal.

• 한국정밀공학회지
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• 제9권4호
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• pp.65-71
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• 1992

This paper develops an algorithm for efficiently computing the intersection points between rays and an object in a simulated radiograph. This algorithm allows interactive calculation of simulated radiographs for very complex parts. It needs a geometric model of a part which is approximated by a bounding surface made up of flat triangular polygons. Since rays have a point source, a perspective transformation is applied to convert the point source problem to one that has parallel rays. This permits to use a scan-line algorithm which utilizes the coherence of the grid of rays for the intersection calculations. The efficiency of the algorithm is shown by comparing compute time of the intersection calculations to a commercial software that computes each ray intersection independently.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제7권1호
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• pp.1-5
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• 2003

We suggest Bisection method, Fixed point method and Newton's method for finding the intersection point of a nonparametric surface and a line in $R^3$ and apply ray-tracing in Color Picture Tube or Color Display Tube.

• 호남수학학술지
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• 제39권1호
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• pp.127-136
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• 2017

For a quadrangle P, we consider the centroid $G_0$ of the vertices of P, the perimeter centroid $G_1$ of the edges of P and the centroid $G_2$ of the interior of P, respectively. If $G_0$ is equal to $G_1$ or $G_2$, then the quadrangle P is a parallelogram. We denote by M the intersection point of two diagonals of P. In this note, first of all, we show that if M is equal to $G_0$ or $G_2$, then the quadrangle P is a parallelogram. Next, we investigate various quadrangles whose perimeter centroid coincides with the intersection point M of diagonals. As a result, for an example, we show that among circumscribed quadrangles rhombi are the only ones whose perimeter centroid coincides with the intersection point M of diagonals.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 1997년도 제8회 학술강연회논문집
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• pp.43-51
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• 1997

Steady and unsteady numerical simulations are conducted for the experiments performed to investigate the ram accelerator flow field by using the expansion tube facility in Stanford University. Navier-Stokes equations for chemically reacting flows are analyzed by fully implicit and time accurate numerical methods with Jachimowski's detailed chemistry model for hydrogen-air combustion involving 9 species and 19 reaction steps. Although the steady state assumption shows a good agreement with the experimental schlieren and OH PLIF images for the case of $2H_2$+$O_2$+$17N_2$, it fails in reproducing the combustion region behind the shock intersection point shown in the case of $2H_2$+$O_2$+$12N_2$, mixture. Therefore, an unsteady numerical simulation is conducted for this case and the result shows all the detailed flow stabilization process. The experimental result is revealed to be an instantaneous result during the flow stabilization process. The combustion behind the shock intersection point is the result of a normal detonation formed by the intersection of strong oblique shocks that exist at early stage of the stabilization process. At final stage, the combustion region behind the shock intersection point disappears and the steady state result is retained. The time required for stabilization of the reacting flow in the model ram accelerator is found to be very long in comparison with the experimental test time.

• 한국수학교육학회지시리즈A:수학교육
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• 제55권3호
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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.