• 충청수학회지
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• 제27권2호
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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.

• 대한전자공학회논문지
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• 제23권4호
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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.

• 한국산업경영시스템학회:학술대회논문집
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• 한국산업경영시스템학회 2002년도 춘계학술대회
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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.

• 대한수학회보
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• 제48권5호
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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.

• 한국CDE학회논문집
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• 제13권6호
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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.

• 한국통신학회논문지
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• 제13권4호
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• pp.309-321
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• 1988

본 논문에서는 단면(cross section)이 원(circle)인 곡면물체를 처리하는 방법인 G.C표현에 있어서 필요한 축방정식과 반경함수를 구하는 방법을 제안한다. 우선 입력으로 들어온 깊이 데이터에서 clustering을 통해 선형축을 가지고 있는 부분과 비선형축을 가지는 부분을 분리하였으며 각 표면마스크조각(surface mask patch)들의 법선 벡터를 통하여 축상의 점들을 추출하였다. 또한 추출된 축상의 점들이 비선형인 경우 Hermite 곡선으로 축방정식을 표현하였으며 본 논문의 유용성을 실험에 의하여 입증하였다.

• International Journal of Precision Engineering and Manufacturing
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• 제3권1호
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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.

• 한국수자원학회논문집
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• 제33권S1호
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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.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2000년도 학술발표회 논문집
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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.

• 한국정밀공학회지
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• 제15권11호
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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.