• Journal of KIISE:Computer Systems and Theory
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• v.31 no.3_4
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• pp.239-246
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• 2004

Image snapping for an image moves the cursor location to nearby features in the image, such as edges. In this paper, we propose geometric snapping for 3D triangular meshes, which is extended from image snapping. Similar to image snapping, geometric snapping also moves the cursor location naturally to a location which represents main geometric features in the 3D triangular meshes. Movement of cursor is based on the approximate curvatures which appear geometric features on the 3D triangular meshes. The proposed geometric snapping can be applied to extract main geometric features on 3D triangular meshes. Moreover, it can be applied to extract the geometric features of a tooth which are necessary for generating the occlusal surfaces in dental prostheses.

• Structural Engineering and Mechanics
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• v.18 no.3
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• pp.363-376
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• 2004

The present study provides a relatively simple and accurate analytical model for the prediction of time-dependent stresses and curvatures of cracked R.C. sections under working loads. A more simplified solution is also provided. The proposed models are demonstrated by considering a numerical example and conducting a parametric study on the effects of relevant R.C. design parameters. In contrary to tension reinforcement, the compression reinforcement is found to contribute significantly in reducing tensile stresses in tension steel and in reducing the total section curvatures. The good accuracy of the proposed approximate solution opens a new vision towards a simple yet accurate model for the prediction of time-dependent effects in R.C. structures.

• The KIPS Transactions:PartA
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• v.10A no.2
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• pp.149-156
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• 2003

In the latest medical world, the attempt of reconstructing anatomical human body system using computer graphics technology awakes people's interests. Actually, this trial has been made in dentistry too. There are a lot of practicable technology fields using computer graphics in dentistry For example, 3D visualization and measurement of dental data, detection of implant location, surface reconstruction for restoring artificial teeth in prostheses and relocation of teeth in orthodontics can be applied. In this paper, we propose methods for definitely detecting the geometric features of teeth such as cusp, ridge, fissure and pit, which have been used as most important characteristics in dental applications. The proposed methods are based on the approximate curvatures that are measured on a 3D tooth model made by scanning an impression. We also give examples of the geometric features detected by using the proposed methods. Comparing to other traditional methods visually, the methods are very useful in detecting more accurate geometric features.

• Journal of Korea Game Society
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• v.2 no.2
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• pp.28-36
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• 2002

In general, triangular meshes have been used for modeling geometric objects such as virtual game characters. The dense meshes give us considerable advantages in representing complex, highly detailed objects, while they are more expensive for storing, transmitting and rendering the objects. Therefore, several researches have been performed for producing a high quality approximation in place of detailed objects, that is, a simplification of triangular meshes. In this paper, we propose a new measure with respect to edges and vertices, which is called an approximate mean curvature and is used as criteria to simplify an original mesh. An edge mean curvature is computed by considering its neighboring edges, and a vertex mean curvature is defined as an average of its incident edges' mean curvatures. And we apply the proposed measure to simplify the models such as a bunny, dragon and teeth. As a result, we can see that the mean curvatures can be used as good criteria for providing much better approximation of models.

• Bulletin of the Society of Naval Architects of Korea
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• v.12 no.1
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• pp.77-82
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• 1975

An analytical formulation of obtaining propeller sections for a given vortex system of radial and chordwise distribution is given as an indirect problem of tracing the propeller surface. The formulation satisfies the boundary condition of potential flow exactly rather than previous approximate use of induced streamline curvatures at the zero camber line.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.10a
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• pp.462-467
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• 1998

A rational method for prediction of long-term deflections of reinforced concrete beams under sustained loads was proposed. Strain and stress distributions of uncracked and fully cracked sections after creep and shrinkage were determined from the requirements of strain compatibility and force equilibrium of a section, and then long-term deflections were calculated from the section analysis results. In fully cracked section analysis, noncoincidence of the neutral axis of strain and the neutral axis of stress after creep and shrinkage was taken into account. The accuracy of the proposed method was verified by comparison with several experimental measurements of beam deflections. The proposed approximate procedure gave the better predictions than the existing approximate methods. At the same time, the proposed method also retained simplicity of the calculation, since maximum long-term deflection could be obtained without tedious integration of the curvatures.

• Steel and Composite Structures
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• v.9 no.3
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• pp.275-301
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• 2009

The long-term behaviour of simply supported composite steel-concrete beams with deformable connectors subjected to skew bending and torsion is presented. The problem is dealt with by recurring to the displacement method, assuming the bending and torsional curvatures and the longitudinal deformations of each sectional part as unknowns and obtaining a system of differential and integro-differential equations. Some solving methods are presented, in order to obtain exact and approximate solutions and evaluate the precision of the approximate ones. A case study is then presented. For the sake of clearness, the responses of the composite beam under loads applied in different directions are studied separately, in order to correctly evaluate the effects of each load condition.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.310-324
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• 2022

In this paper, we define timelike curves in R⁴₂ and characterize such curves in terms of Frenet frame. Also, we examine the timelike helices of R⁴₂, taking into account their curvatures. In addition, we study timelike slant helices, timelike B₁-slant helices, timelike B₂-slant helices in four dimensional semi-Euclidean space, R⁴₂. And then we obtain an approximate solution for the timelike B₁ slant helix with Taylor matrix collocation method.

• Journal of the Korea Computer Graphics Society
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• v.9 no.2
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• pp.11-18
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• 2003

For extracting geometric features in 3D meshes according to user-steering with effective interactions. this paper generalizes the 2D algorithms of snapping and wrapping that. respectively. moves a cursor to a nearby feature and constructs feature boundaries. First. we define approximate curvatures and move cost functions that are the numerical values measuring the geometric characteristics of the meshes, By exploiting the measuring values. the algorithms of geometric snapping and geometric wrapping are developed and implemented. We also visualize the results from applying the algorithms to extracting geometric features of general 3D mesh models such as a face model and a tooth model.

• The KIPS Transactions:PartA
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• v.12A no.1 s.91
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• pp.13-22
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• 2005

Similarly to the edges defined in a 2D image, we can define the geometric features representing the boundary of the distinctive parts appearing on 3D meshes. The geometric features have been used as basic primitives in several applications such as mesh simplification, mesh deformation, and mesh editing. In this paper, we propose geometric livewire and geometric livelane for extracting geometric features in a 3D mesh, which are the extentions of livewire and livelane methods in images. In these methods, approximate curvatures are adopted to represent the geometric features in a 3D mesh and the 3D mesh itself is represented as a weighted directed graph in which cost functions are defined for the weights of edges. Using a well-known shortest path finding algorithm in the weighted directed graph, we extracted geometric features in the 3D mesh among points selected by a user. In this paper, we also visualize the results obtained from applying the techniques to extracting geometric features in the general meshes modeled after human faces, cows, shoes, and single teeth.