• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.287-295
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• 2014

In this paper, we prove that the image of the representation of the automorphism group of a supersingular K3 surface of Artin-invariant 1 over odd characteristic p on the global two forms is a finite cyclic group of order p + 1. Using this result, we deduce, for such a K3 surface, there exists an automorphism which cannot be lifted over a field of characteristic 0.

• Journal of the Korean Institute of Telematics and Electronics
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• v.23 no.4
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• pp.535-542
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• 1986

In this paper, a hidden surface removal algorithm that generates a perspective view of three space plane-faced objects using scan line coherence is proposed. In particular, the proposed algorithm deals with hidden surface elimination of penetrating objects by using the optimum span division method with minimum test for priority test of segments. Also, a hidden surface redmoval method for representing sectional view of solids by using boolean difference is described.

• Proceedings of the Society of Korea Industrial and System Engineering Conference
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• 2002.05a
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• pp.461-466
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• 2002

In many applications of computer aided geometric design and computer graphics, B-spline is one of the most popular representation for curves and surfaces, and the evaluation of B-spline curves and surfaces is the most frequently used operation. For the evaluation and others, the power form representation of the curves and surfaces is preferred because it is possible to speed-up the operation using Horner's rule. In this paper, we present a new algorithm for the above-mentioned conversion focusing on a dynamic case. Experiment shows that the proposed algorithm significantly outperforms the conventional approach when one or more control points of a B-spline curve and surface are dynamically moving.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1015-1021
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• 2011

A point of a Riemann surface X is said to be its fixed point if it is a fixed point of one of its nontrivial holomorphic automorphisms. We start this note by proving that the set Fix(X) of fixed points of Riemann surface X of genus g${\geq}$2 has at most 82(g-1) elements and this bound is attained just for X having a Hurwitz group of automorphisms, i.e., a group of order 84(g-1). The set of such points is invariant under the group of holomorphic automorphisms of X and we study the corresponding symmetric representation. We show that its algebraic type is an essential invariant of the topological type of the holomorphic action and we study its kernel, to find in particular some sufficient condition for its faithfulness.

• Korean Journal of Computational Design and Engineering
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• v.13 no.6
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• pp.469-477
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• 2008

Physically-based rendering is an image synthesis technique based on simulation of physical interactions between light and surface materials. Since generated images are highly photorealistic, physically-based rendering has become an indispensable tool in advanced design visualization for manufacturing and architecture as well as in film VFX and animations. Especially, BRDF (bidirectional reflectance distribution function) is critical in realistic visualization of materials since it models how an incoming light is reflected on the surface in terms of intensity and outgoing angles. In this paper, we introduce techniques to represent BRDF as B-spline volumes and to utilize them in physically-based rendering. We show that B-spline volume BRDF (BVB) representation is suitable for measured BRDFs due to its compact size without quality loss in rendering. Moreover, various CAGD techniques can be applied to B-spline volume BRDFs for further controls such as refinement and blending.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.13 no.4
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• pp.309-321
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• 1988

This paper proposes on the algorithm of axis equation & radius function for the G.C representation which describes the curved objects with circular cross section. Object combined with linear and nonlinear parts is detached by clustering from depth data & axis points is extracted by normal vecter of the surface mask patches. In ths case of nonlinear axis point, axis equation is described by Hermite curve & the effectiveness of this paper is demonstrated by serveral experiments.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.1
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• pp.49-56
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• 2002

The Z-map is a special farm of discrete non-parametric representation in which the height values at grid points on the xy-plane are stored as a 2D array z[ij]. While the z-map is the simplest farm of representing sculptured surfaces and is the most versatile scheme for modeling non-parametric objects, its practical application in industry (eg, tool-path generation) has aroused much controversy over its weaknesses, namely its inaccuracy, singularity (eg, vertical wall), and some excessive storage needs. Much research or the application of the z-map can be found in various articles, however, research on the systematic analysis of sculptured surface shape representation via the z-map model is rather rare. Presented in this paper are the following: shape modeling power of the simple z-map model, exact (within tolerance) z-map representation of sculptured surfaces which have some feature-shapes such as vertical-walls and real sharp-edges by adopting some complementary z-map models, and some application examples.

• Journal of Korea Water Resources Association
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• v.33 no.S1
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• pp.28-36
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• 2000

A TIN, Triagulated Irregular Network, based topographic modeling method and a distributed rainfall-runoff model using the topographic representation is presented. In the TIN based topographic representation, a watershed basin is modeled as a set of contiguous non-overlapping triagular facets : the watershed basin is subdivided according to streamlines to deal with water movement one-dimensionally ; and each partitioned catchment is approximated to a slope element having a quasi-three-dimensional shape by using cubic spline functions. On an approximated slope element, water movement is represented by combined surface-subsurface kinematic wave equations considering a change of slope gradient and slope width. By using the distributed rainfall-runoff model, the effects of spatial variability of soil properties on runoff response are examined.

• Proceedings of the Korea Water Resources Association Conference
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• 2000.05a
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• pp.28-36
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• 2000

A TIN, Triangulated Irregular Network, based topographic modeling method and a distributed rainfall-runoff model using the topographic representation is presented. In the TIN based topographic representation, a watershed basin is modeled as a set of contiguous non-overlapping triangular facets: the watershed basin is subdivided according to streamlines to deal with water movement one-dimensionally; and each partitioned catchment is approximated to a slope element having a quasi-three-dimensional shape by using cubic spline functions. On an approximated slope element, water movement is represented by combined surface-subsurface kinematic wave equations considering a change of slope gradient and slope width. By using the distributed rainfall-runoff model, the effects of spatial variability of soil properties on runoff response are examined.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.11
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• pp.180-188
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• 1998

Z-map is a special form of discrete nonparametric representation in which the height values at grid points on the xy-plane are stored as a 2D array z[i.j]. While z-map is the simplest form of representing sculptured surfaces and it is the most versatile scheme for modeling nonparametric objects, its practical application in industry (eg, tool-path generation) aroused much controversy over its weaknesses ; accuracy, singularity (eg, vertical wall), and some excessive storage needs. Although z-map has such limitations, much research on the application of z-map can be found in various articles. However, research on the systematic analysis of sculptured surface shape representation via z-map model is rather rare. Presented in this paper are the following: shape modeling power of the simple z-map model, exact (within tolerance) B-map representation of sculptured surfaces which have some feature-shapes such as vertical-walls and real sharp-edges by adopting some complementary B-map models, and some application examples.