• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.272-276
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• 2000

Reverse engineering refers to the process that creates a physical part from acquiring the surface data of an existing part using a scanning device. In recent years, as the non-contact type scanning devices become more popular, the huge amount of point data can be obtained with high speed. The point data handling process, therefore, becomes more important since the scan data need to be refined for the efficiency of subsequent tasks such as mesh generation and surface fitting. As one of point handling functions, the cross-sectioning function is still frequently used for extracting the necessary data from the point cloud. The commercial reverse engineering software supports cross-sectioning functions, however, these are only for cross-sectioning the point cloud with the constant spacing and direction. In this paper, adaptive cross-sectioning point cloud which allow the changes of the spacing and directions of cross-sections according to the constant spacing and direction. In this paper, adaptive cross-sectioning algorithms which allow the changes of the spacing and directions of cross-sections according to the curvature difference of the point cloud data are proposed.

• Journal of Information Processing Systems
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• v.10 no.1
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• pp.23-35
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• 2014

Recently, novel application areas in digital geometry processing, such as simulation, dynamics, and medical surgery simulations, have necessitated the representation of not only the surface data but also the interior volume data of a given 3D object. In this paper, we present an efficient framework for the shape approximations of spherical solid objects based on trivariate B-splines. To do this, we first constructed a smooth correspondence between a given object and a unit solid cube by computing their harmonic mapping. We set the unit solid cube as a rectilinear parametric domain for trivariate B-splines and utilized the mapping to approximate the given object with B-splines in a coarse-to-fine manner. Specifically, our framework provides user-controllability of shape approximations, based on the control of the boundary condition of the harmonic parameterization and the level of B-spline fitting. Experimental results showed that our method is efficient enough to compute trivariate B-splines for several models, each of whose topology is identical to a solid sphere.

• Journal of Conservation Science
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• v.35 no.1
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• pp.71-80
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• 2019

This study examined the applicability of digital technologies based on three-dimensional(3D) scanning, modeling, and printing to the restoration of damaged artifacts. First, 3D close-range scanning was utilized to make a high-resolution polygon mesh model of a roof-end tile with a missing part, and a 3D virtual restoration of the missing part was conducted using a haptic interface. Furthermore, the virtual restoration model was printed out with a 3D printer using the material extrusion method and a PLA filament. Then, the additive structure of the printed output with a scanning electron microscope was observed and its shape accuracy was analyzed through 3D deviation analysis. It was discovered that the 3D printing output of the missing part has high dimensional accuracy and layer thickness, thus fitting extremely well with the fracture surface of the original roof-end tile. The convergence of digital virtual restoration based on 3D scanning and 3D printing technology has helped in minimizing contact with the artifact and broadening the choice of restoration materials significantly. In the future, if the efficiency of the virtual restoration modeling process is improved and the material stability of the printed output for the purpose of restoration is sufficiently verified, the usability of 3D digital technologies in cultural heritage restoration will increase.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.2
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• pp.65-92
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• 2019

We survey a recently developed immersed finite element method (IFEM) for the interface problems. The IFEM uses structured grids such as uniform grids, even if the interface is a smooth curve. Instead of fitting the curved interface, the bases are modified so that they satisfy the jump conditions along the interface. The early versions of IFEM [1, 2] were suboptimal in convergence order [3]. Later, the consistency terms were added to the bilinear forms [4, 5], thus the scheme became optimal and the error estimates were proven. For elasticity problems with interfaces, we modify the Crouzeix-Raviart based element to satisfy the traction conditions along the interface [6], but the consistency terms are not needed. To satisfy the Korn's inequality, we add the stabilizing terms to the bilinear form. The optimal error estimate was shown for a triangular grid. Lastly, we describe the multigrid algorithms for the discretized system arising from IFEM. The prolongation operators are designed so that the prolongated function satisfy the flux continuity condition along the interface. The W-cycle convergence was proved, and the number of V-cycle is independent of the mesh size.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.419-435
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• 2021

This paper deals with numerical treatment of singularly perturbed differential equations involving small delays. The highest order derivative in the equation is multiplied by a perturbation parameter 𝜀 taking arbitrary values in the interval (0, 1]. For small 𝜀, the problem involves a boundary layer of width O(𝜀), where the solution changes by a finite value, while its derivative grows unboundedly as 𝜀 tends to zero. The considered problem contains delay on the convection and reaction terms. The terms with the delays are approximated using Taylor series approximations resulting to asymptotically equivalent singularly perturbed BVPs. Inducing exponential fitting factor for the term containing the singular perturbation parameter and using central finite difference for the derivative terms, numerical scheme is developed. The stability and uniform convergence of difference schemes are studied. Using a priori estimates we show the convergence of the scheme in maximum norm. The scheme converges with second order of convergence for the case 𝜀 = O(N^-1) and for the case 𝜀 ≪ N^-1, the scheme converge uniformly with first order of convergence, where N is number of mesh intervals in the domain discretization. We compare the accuracy of the developed scheme with the results in the literature. It is found that the proposed scheme gives accurate result than the one in the literatures.

• Korean Journal of Computational Design and Engineering
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• v.15 no.4
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• pp.297-305
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• 2010

Medical image acquisition techniques such as CT and MRI have disadvantages in that the numerous time and efforts are needed. Furthermore, a great amount of radiation exposure is an inherent proberty of the CT imaging technique, a number of side-effects are expected from such method. To improve such conventional methods, a number of novel methods that can obtain 3D medical images from a few X-ray images, such as algebraic reconstruction technique (ART), have been developed. Such methods deform a generic model of the internal body part and fit them into the X-ray images to obtain the 3D model; the initial shape, therefore, affects the entire fitting process in a great deal. From this fact, we propose a novel method that can generate a 3D vertebraic generic model based on the statistical database of CT scans in this study. Moreover, we also discuss a method to generate patient-tailored generic model using the facts obtained from the statistical analysis. To do so, the mesh topologies of CT-scanned 3D vertebra models are modified to be identical to each other, and the database is constructed based on them. Furthermore, from the results of a statistical analysis on the database, the tendency of shape distribution is characterized, and the modeling parameters are extracted. By using these modeling parameters for generating the patient-tailored generic model, the computational speed and accuracy of ART can greatly be improved. Furthermore, although this study only includes an application to the C1 (Atlas) vertebra, the entire framework of our method can be applied to other body parts generally. Therefore, it is expected that the proposed method can benefit the various medical imaging applications.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.37 no.3
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• pp.17-30
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• 2000

In this paper, we propose an efficient algorithm to produce 3-D surface model from a set of range data, based on NURBS (Non-Uniform Rational B-Splines) surface fitting technique. It is assumed that the range data is initially unorganized and scattered 3-D points, while their connectivity is also unknown. The proposed algorithm consists of three steps: initial model approximation, hierarchical representation, and construction of the NURBS patch network. The mitral model is approximated by polyhedral and triangular model using K-means clustering technique Then, the initial model is represented by hierarchically decomposed tree structure. Based on this, $G^1$ continuous NURBS patch network is constructed efficiently. The computational complexity as well as the modeling error is much reduced by means of hierarchical decomposition and precise approximation of the NURBS control mesh Experimental results show that the initial model as well as the NURBS patch network are constructed automatically, while the modeling error is observed to be negligible.