• Proceedings of the KSME Conference
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• 2001.06c
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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.

• The Pure and Applied Mathematics
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• v.23 no.3
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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.

• 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.

• The Transactions of the Korea Information Processing Society
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• v.4 no.8
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• pp.2163-2172
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• 1997

SSI(Surface/Surface Intersection)is a fundamental geometric operation which is used in solid and geometric modeling to support trimmed surface and Boolean operations. In this paper, we suggest a new algorithm for tracing along the intersection curve of two regular surfaces. Thus, in this paper, we present a simplicity of computing and second degree continunity. Given a point of intersection curve, it is traced to entire curve of a intersection curve as the initial point of its and the initial point of each of a intersection curve is detected to DFS(Depth First Search) method in the Quadtree and is naturally presented a continuous form.

• Honam Mathematical Journal
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• v.45 no.4
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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.

• Journal of the Korean Society for Precision Engineering
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• v.9 no.4
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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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• v.7 no.1
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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.

• Honam Mathematical Journal
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• v.39 no.1
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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.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 1997.04a
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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.

• 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.