• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.22 no.6
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• pp.1018-1024
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• 2013

In the process of draw die design for stamping automotive press panels, the addendum surfaces generated in metal forming simulation software cannot be used in downstream processes such as machining and making draw dies because simulation tools use simple discrete models for the surface geometry. The downstream processes require more precise and continuous geometric models such as NURBS surfaces. Generally, automotive die engineers manually regenerate the addendum surface geometry using the discrete model. This paper presents an automated geometric modeling process for generating addendum surfaces using draft surface models. The design parameters of the section curve for the addendum surfaces are extracted automatically from the draft geometry. Using the extracted design parameters, smooth addendum surfaces are generated automatically as NURBS surfaces. The generated surfaces are $G^1$ continuous with the part surface and the binder surface, and can be used in downstream processes.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.1 s.256
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• pp.105-112
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• 2007

The linkage framework of geometric modeling based on NURBS(Non-Uniform Rational B-Spline) surface and shell finite analysis is developed in the present study. For this purpose, geometrically exact shell finite element is implemented. NURBS technology is employed to obtain the exact geometric quantities for the analysis. Especially, because NURBS is the most powerful and wide-spread method to represent general surfaces in the field of computer graphics and CAD(Computer Aided Design) industry, the direct computation of surface geometric quantities from the NURBS surface equation without approximation shows great potential for the integration between geometrically exact shell finite element and geometric modeling in the CAD systems. Some numerical examples are given to verify the performance and accuracy of the developed linkage framework. In additions, trimmed surfaces with some cutouts are considered for more practical applications.

• Korean Journal of Computational Design and Engineering
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• v.6 no.4
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• pp.271-276
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• 2001

A geometric kernel is the library of core mathematical functions that defines and stores 3D shapes in response to users'commands. We developed a light geometric kernel suitable to develop CAD/CAM application systems. The kernel contains geometric objects, such as points, curves and surfaces and a minimal set of functions for each type but does not contain lots of modeling and handling functions that are useful to create and maintain complex shapes from an idea sketch. The kernel was developed on MS-Windows NT using C++ with STL(Standard Template Library) but it is compatible with UNIX environments. This paper describes the structure of the kernel including several components: base, math, point sequence curve, geometry, translators. The base kernel gives portability to applications and the math kernel contains basic arithmetic and their classes, such as vector and matrix. The geometry kernel contains points, parametric curves, and parametric surfaces. A neutral fie format and programming and document styles are also presented in this paper.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.10
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• pp.172-181
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• 1999

The objective of this research is to develop a measurement error model for sculptured surfaces in On-Machine Measurement (OMM) process based on a closed-loop configuration. The geometric error model of each axis of a vertical CNC Machining center is derived using a 4${\times}$4 homogeneous transformation matrix. The ideal locations of a touch-type probe for the scupltured surface measurement are calculated from the parametric surface representation and X-, Y- directional geometric errors of the machine. Also, the actual coordinates of the probe are calculated by considering the pre-travel variation of a probe and Z-directional geometric errors. Then, the step-by-step measurement error analysis method is suggested based on a closed-loop configuration of the machining center including workpiece and probe errors. The simulation study shows the simplicity and effectiveness of the proposed error modeling strategy.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.147-163
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• 2017

We define de Sitter focal surfaces and hyperbolic focal surfaces of hyperbolic space curves. As an application of the theory of unfoldings of function germs, we investigate the singularities of these surfaces. For characterizing the singularities of these surfaces, we discover a new hyperbolic invariants and investigate the geometric meanings.

• Korean Journal of Mathematics
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• v.32 no.2
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• pp.259-284
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• 2024

In present study, we introduce ruled surfaces whose base curve is the Salkowski curve in Euclidean 3-space and whose generating lines consist of the Frenet vectors of this curve (tangent, principal normal and binormal vectors). Then, we produce regular surfaces from a vector with real coefficients, which is a linear combination of these vectors, and we examine some special cases for these surfaces. Moreover, we present some geometric properties and graphics of all these surfaces.

• Journal of the Korea Computer Graphics Society
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• v.25 no.3
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• pp.93-103
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• 2019

We introduce a geometric processing method for freeform surfaces based on high-precision torus patch approximation, a new spatial data structure for efficient geometric operations on freeform surfaces. A torus patch fits the freeform surface with flexibility: it can handle not only positive and negative curvature but also a zero curvature. It is possible to precisely approximate the surface regardless of the convexity/concavity of the surface. Unlike the traditional method, a torus patch easily bounds the surface normal, and the offset of the torus becomes a torus again, thus helps the acceleration of various geometric operations. We have shown that the torus patch's approximation accuracy of the freeform surface is high by measuring the upper bound of the two-sided Hausdorff distance between the freeform surface and set of torus patches. Using the method, it can be easily processed to detect an intersection curve between two freeform surfaces and find the offset surface of the freeform surface.

• International Journal of Precision Engineering and Manufacturing
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• v.6 no.2
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• pp.12-18
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• 2005

A geometric compensation of thin-walled molded parts in reverse engineering is presented. Researches in reverse engineering have focused on the fitting of points to curves and surfaces. However, the reconstructed model is not the geometric model because the molded parts have some dimensional errors in measurements and deformation during molding. Geometric information can give an improved accuracy in reverse engineering. Thus, measurement data must be compensated with geometric information to reconstruct the mathematical model. The functional and geometric concepts of the part can be derived from geometric information. LSM (Least square method) is adopted to determine the geometric information. Also, an example of geometric compensation is given to improve the accuracy of geometric model and to inspect the reconstructed model.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.139-148
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• 2006

Catmull-Clark subdivision scheme provides a powerful method for building smooth and complex surfaces. But the number of faces in the uniformly refined meshes increases exponentially with respect to subdivision depth. Adaptive tessellation reduces the number of faces needed to yield a smooth approximation to the limit surface and, consequently, makes the rendering process more efficient. In this paper, we present a new adaptive tessellation method for general Catmull-Clark subdivision surfaces. Different from previous control mesh refinement based approaches, which generate approximate meshes that usually do not interpolate the limit surface, the new method is based on direct evaluation of the limit surface to generate an inscribed polyhedron of the limit surface. With explicit evaluation of general Catmull-Clark subdivision surfaces becoming available, the new adaptive tessellation method can precisely measure error for every point of the limit surface. Hence, it has complete control of the accuracy of the tessellation result. Cracks are avoided by using a recursive color marking process to ensure that adjacent patches or subpatches use the same limit surface points in the construction of the shared boundary. The new method performs limit surface evaluation only at points that are needed for the final rendering process. Therefore it is very fast and memory efficient. The new method is presented for the general Catmull-Clark subdivision scheme. But it can be used for any subdivision scheme that has an explicit evaluation method for its limit surface.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.329-342
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• 2019

In this paper, we give a geometric approach to Killing magnetic flux surfaces in Euclidean 3-space and solve the differential equations which expressed the mentioned surfaces. Furthermore we give some examples and draw their pictures by using the programme Mathematica.