• The Pure and Applied Mathematics
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• v.22 no.1
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• pp.91-99
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• 2015

A normal surface is determined by how the surface under consideration meets each tetrahedron in a given triangulation. We call such a nice embedded disk, which is a component of the intersection of the surface with a tetrahedron, an elementary disk. We classify all elementary disk types in a truncated ideal triangulation.

• Korean Journal of Computational Design and Engineering
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• v.5 no.4
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• pp.336-346
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• 2000

This paper presents a geometric method that can detect and compute all conic sections in the intersection of two tori. Conic sections contained in a torus must be circles. Thus, when two tori intersect in a conic section, the intersection curve must be a circle as well. Circles in a torus are classified into profile circles, cross-sectional circlet, and Yvone-Villarceau circles. Based on a geometric classification of these circles, we present a procedural method that can detect and construct all intersection circles between two tori. All computations can be carried out using simple geometric operations only: e.g., circle-circle intersections, circle-line intersections, vector additions, and inner products. Consequently, this simple structure makes our algorithm robust and efficient, which is an important advantage of our geometric approach over other conventional methods of surface intersection.

• Geomechanics and Engineering
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• v.15 no.2
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• pp.769-774
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• 2018

The growth of cities requires the construction of new tunnels close to the existing ones. Prediction and control of ground movement around the tunnel are important especially in urban area. The ground respond due to EPB (Earth Pressure Balance) pressure are investigated using the finite element method by ABAQUS in intersection of the triplet tunnels (Line 2, 3 and 4) of Mashhad Urban Railway in Iran. Special attention is paid to the effect of EPB pressure on the tunnel face displacement. The results of the analysis show that in EPB tunneling, surface settlement and face displacement is related to EPB pressure. Moreover, it is found that tunnel construction sequence is a great effect in face displacement value. For this study, this value in Line 4 where is excavated after line 3, is smaller than that line. In addition, the trend of the displacement curves are changed with the depth for all lines where is located in above and below, close to and above the centerline tunnel face for Line 2, 3 and 4, respectively. It is concluded that: (i) the surface settlement decreases with increasing EPB pressure on the tunnel face; (ii) at a constant EPB pressure, the tunnel face displacement values increase with depth. In addition, this is depended on the tunneling sequence; (iii) the trend of the displacement curves change with the depth.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.711-719
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• 2000

We generalize Gieseker\`s lemma and use it to compute Picard number of a complete intersection surface.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.11
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• pp.144-153
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• 2007

In order to generate the input data for rapid prototyping, a new approach which is based on the implicit surface interpolation method is presented. In the method a surface is reconstructed by creating smooth implicit surface from unorganized cloud of points through which the surface should pass. In the method an implicit surface is defined by the adaptive local shape functions including quadratic polynomial function, cubic polynomial function and RBF(Radial Basis Function). By the reconstruction of a surface, various types of error in raw STL file including degenerated triangles, undesirable holes with complex shapes and overlaps between triangles can be eliminated automatically. In order to get the slicing data for rapid prototyping an efficient intersection algorithm between implicit surface and plane is developed. For the direct usage for rapid prototyping, a robust transformation algorithm for the generation of complete STL data of solid type is also suggested.

• Journal of the Society of Naval Architects of Korea
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• v.58 no.2
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• pp.90-96
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• 2021

In this study, the method of determining the state of grid points in the adaptable surface particle method based on grid system developed as a free-surface tracing method was improved. The adaptable surface particle method is a method of determining the state of the grid point according to the shape of the free-surface and obtaining the intersection of the given free-surface and grid line where the state of the grid point changes. It is difficult to determine the state of grid points in the event of rapid flow, such as collision or separation of free-surfaces, and this study suggests a method for determining the state of current grid points using the state of surrounding grid points where the state of grid point are known. A grid layer value was assigned sequentially to a grid away from the free-surface, centering on the boundary cell where the free-surface exists, to identify the connection information that the grid was separated from the free-surface, and to determine the state of the grid point sequentially from a grid away from the free-surface to a grid close to the free-surface. To verify the improved method, a numerical analysis was made on the problem of dam break in which a sudden collision of free-surface occurred and the results were compared, and the results were relatively reasonable.

• 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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.8
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• pp.1536-1544
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• 1992

A relatively simple prediction method is proposed for initially semicircular surface crack growth under axial loading. The method takes into account the difference in surface crack closure behavior at the depth point and at the surface intersection point, and also the relationship of crack closure for surface crack and through-thickness crack. The prediction method provides conservative estimation for fatigue life within factor of two, and the predicted crack geometry variations agree well with the observed results. As a result, the prediction method proposed here is considered to be useful for engineering application.

• Korean Journal of Computational Design and Engineering
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• v.7 no.4
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• pp.219-232
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• 2002

In numerically controlled(NC) machining simulation, a Z-map has been used frequently for representing a workpiece. Since the Z-map is usually represented by a set of Z-axis aligned vectors, the machining process can be simulated through calculating the intersection points between the vectors and the surface swept by a machining tool. In this paper, we present an efficient method to calculate those intersection points when an APT-type tool moves along a linear tool path. Each of the intersection points can be expressed as the solution of a system of non-linear equations. We transform this system of equations into a single-variable equation, and calculate the candidate interval in which the unique solution exists. We prove the existence of a solution and its uniqueness in this candidate interval. Based on these characteristics, we can effectively apply numerical methods to finally calculate the solution of the non-linear equations within a given precision. The whole process of NC simulation can be achieved by updating the Z-map properly. Our method can provide more accurate results with a little more processing time, in comparison with the previous closed-form solution.

• Journal of the Korean Institute of Gas
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• v.2 no.1
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• pp.74-82
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• 1998

The grain boundary etching method as a technique for assessing degradation of structural materials used at elevated temperature has received much attention since it is simple, inexpensive and easy to apply to real plant components. In this study, the technique is applied to some aged petroleum and chemical plant components such as reactors and drums. As a degradation parameter, intersection number ratio ($N_i/N_o$), is employed. The intersection number ratio ($N_i/N_o$) is defined as the ratio of intersection number ($N_i$) obtained from 5-minute picric acid etched surface to the number ($N_o$) obtained from Nital etched surface. In order to study degradation level, several relationships were measured such as the correlation between shift in ductile brittle transition temperature, $({\Delta}DBTT)_{sp}$ and intersection number ratio, ($N_i/N_o$) and the correlation between the measured ($N_i/N_o$) values and Larson-Miller Parameter values.