• 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.

• Journal of the Korea Computer Graphics Society
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• v.6 no.4
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• pp.29-34
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• 2000

This paper classifies the structure of the intersection curve between a surface of extrusion and a free-form surface. Our algorithm computes the silhouette curve of the free-form surface with respect to the unique ruling direction of the surface of extrusion. By intersecting the silhouette curve and the base curve of the surface of extrusion, we can classify the topological structure of the intersection curve, and compute all singularities in the intersection curve. Moreover, we can determine which ruling lines of the surface of extrusion intersect the other free-form surface and how many times. This classification provides a robust and efficient method for computing the intersection curve.

• 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.

• 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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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• pp.1832-1843
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• 1995

Tool interference is one of the most critical problems in sculptured surface machining. When machining cavities and concaves, the tool frequently overcuts the portions of the surface, which cause inaccuracy in machining. So tool interference-free paths must be generated for rough cutting more efficiently. In this paper a software using SSI(Surface/Surface intersection) algorithm is developed for eliminating tool interference which occurs in an offset surface in 3-dimensional free form surface modeling. this work consists of two stages : using the offset data, the intersection curves are rapidly checked by this algorithm at the first stage. CL(cutter location) data are obtained by deleting the loop section of intersected offset patches at the second stage. This algorithm can reduce the amount of memory required to store machining data and also easily check region which have the possibility of intersection. Also, This software is verified to be useful in machining a curved object on a DNC milling machine.

• Korean Journal of Computational Design and Engineering
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• v.3 no.2
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• pp.127-134
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• 1998

This paper presents d new algorithm to compute the offlet curve of a given planar parametric curve. We reduce the problem of computing an offset curve to that of intersecting a surface to a paraboloid. Given an input curve C(t)=(x(t), y(t))∈R², the corresponding surface D/sub c(t)/ is constructed symbolically as the envelope surface of a one-parameter family of tangent planes of the paraboloid Q:z=x²+y²along a lifted curve C(t)=(x(t), y(t), x(t)²+y(t)²∈Q. Given an offset distance d∈R, the offset curve C/sub d/(t) is obtained by the projection of the intersection curve of D/sub c(t)/ and a paraboloid Q:z=x²+y²-d² into the xy-plane.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.9
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• pp.1814-1821
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• 2002

NC cutting simulation is an important factor in the development of products. The geometric modelling of cutter swept surface should be done in NC cutting simulation. A part of cutter swept surface is a ruled surface blended with silhouette curve and cutter path. Finding an intersection point between cutter swept surface and a line is one of major problems in Z-map based cutting simulation. In this paper, cutter swept surface is defined parametrically and it's intersection point with Z-map is found in an exact form. Triangular grid Z-map based 3-axis NC cutting simulation is performed.

• Journal of the Society of Naval Architects of Korea
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• v.54 no.1
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• pp.26-33
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• 2017

In this study, the surface marker method, one of the particle tracking methods, used to track the free surface is extended to cover the more general cases easily including the collision and separation of the free surface. In surface particle method to redistribute particles effectively using the grid system, the free surface is composed of the sum of quadrilaterals having four curves where fixed markers are placed at ends of each curve. Fixed markers are used to know how curves are connected to each other. The position of fixed markers can move as the free surface deforms but all fixed markers cannot be deleted during all time of simulation to keep informations of curve connection. In the case of the collision or separtion of the free surface where several curves can be intersected disorderly, severe difficulties can occur to define newly states of curve connection. In this study, the adaptable surface parTicle method without fixed markers is introduced. Intersection markers instead of the fixed markers are used to define quadrilaterals. The position of the intersection markers is defined to be the intersection point between the free surface and the edge of the grid and it can be added or deleted during the time of simulation to allow more flexibilities. To verify numerical schemes, two flow cases are simulated and the numerical results are compared with other's one and shown to be valid.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.3
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• pp.123-137
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• 1993

In this paper, an integrated approach is proposed to generate gouging-free Cartesian tool paths for machining sculptured surfaces from 3D measurement data. The integrated CAD/CAM system consists of two modules : offset surface module an Carteian tool path module. The offset surface module generates an offset surface of an object from its 3D measurement data, using an offsetting method and a surface fitting method. The offsetting is based on the idea that the envelope of an inversed tool generates an offset surface without self-intersection as the center of the inversed tool moves along on the surface of an object. The surface-fitting is the process of constructing a compact representation to model the surface of an object based on a fairly large number of data points. The resulting offset surtace is a composite Bezier surface without self-intersection. When an appropriate tool-approach direction is selected, the tool path module generates the Cartesian tool paths while the deviation of the tool paths from the surface stays within the user-specified tolerance. The tool path module is a two-step process. The first step adaptively subdivides the offset surface into subpatches until the thickness of each subpatch is small enough to satisfy the user-defined tolerance. The second step generates the Cartesian tool paths by calculating the intersection of the slicing planes and the adaptively subdivided subpatches. This tool path generation approach generates the gouging-free Cartesian CL tool paths, and optimizes the cutter movements by minimizing the number of interpolated points.