• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.27-60
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• 1996

We compute low order terms of automorphisms of a quadric CR manifold defined by $v^a$ =< $A^az$, z > where there is a real vector ${\kappa}{\in}R^m$ such that $det({\kappa}{\cdot}A){\neq}0$.

• The KIPS Transactions:PartA
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• v.11A no.5
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• pp.365-372
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• 2004

Recently, the studies for mesh simplification have been increased according to the application area of the complicate 3D mesh models has been expanded. This paper introduces a novel method for mesh simplification which uses the properties of the mesh model in addition to the geometric locations of the model. The information of the 3D mesh model Includes surface properties such as color, texture, and curvature information as well as geometic information of the model. The most of current simplification methods adopt such geometric information and surface properties individually for mesh simplification. However, the proposed simplification method combines the geometric information and solace properties and applies them to the simplification process simultaneously. In this paper, we exploit the extended geometry based quadric error metric(QEM) which relatively allows fast and accurate geometric simplification of mesh. Thus, the proposed mesh simplification utilizes the quadric error metric based on geometric information and the surface properties such as color, normal, and texture. The proposed mesh simplification method can be expressed as a simple quadric equation which expands the quadric error metric based on geometric information by adding surface properties such as color, normal, and texture. From the experimental results, the simplification of the mesh model based on the proposed method shows the high fidelity to original model in some respects such as global appearance rather than using current geometry based simplification.

• East Asian mathematical journal
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• v.33 no.5
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• pp.571-585
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• 2017

Let M be a connected n-dimensional submanifold of a Euclidean space $E^{n+k}$ equipped with the induced metric and ${\Delta}$ its Laplacian. If the position vector x of M is decomposed as a sum of three vectors $x=x_1+x_2+x_0$ where two vectors $x_1$ and $x_2$ are non-constant eigen vectors of the Laplacian, i.e., ${\Delta}x_i={\lambda}_ix_i$, i = 1, 2 (${\lambda}_i{\in}R$) and $x_0$ is a constant vector, then, M is called a 2-type submanifold. In this paper we showed that a 2-type surface M in $E^3$ satisfies ${\langle}{\Delta}x,x-x_0{\rangle}=c$ for a constant c, where ${\langle},{\rangle}$ is the usual inner product in $E^3$, then M is an open part of a circular cylinder. Also we showed that if a quadric hypersurface M in a Euclidean space satisfies ${\langle}{\Delta}x,x{\rangle}=c$ for a constant c, then it is one of a minimal quadric hypersurface, a genaralized cone, a hypersphere, and a spherical cylinder.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.3C
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• pp.264-270
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• 2010

Non-planar screens such as cylinder and sphere shaped screens are widely used for high-resolution immersive visualization environments. An existing method employs quadric matrix that maps an image onto a curved screen. However if the shape of the screen changes or moves, the quadric matrix will not be valid. In this paper, we assume that the screen is a quadric shape and the screen movement or change are relatively small. Then we propose to use a piecewise planar approximations for the screen to compensate for the geometric distortion on a non-planar screen. We demonstrate the effectiveness and efficiency of the proposed method through experiments.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.683-699
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• 2017

We introduce the notion of Killing shape operator for real hypersurfaces in the complex hyperbolic quadric $Q^{m*}=SO_{m,2}/SO_mSO_2$. The Killing shape operator implies that the unit normal vector field N becomes A-principal or A-isotropic. Then according to each case, we give a complete classification of real hypersurfaces in $Q^{m*}=SO_{m,2}/SO_mSO_2$ with Killing shape operator.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.551-570
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• 2020

We introduce the notion of Lie invariant normal Jacobi operators for real hypersurfaces in the complex hyperbolic quadric Q^m∗ = SO^o_m,2/SO_mSO₂. The invariant normal Jacobi operator implies that the unit normal vector field N becomes 𝕬-principal or 𝕬-isotropic. Then in each case, we give a complete classification of real hypersurfaces in Q^m∗ = SO^o_m,2/SO_mSO₂ with Lie invariant normal Jacobi operators.

• Journal of the Korean Mathematical Society
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• v.60 no.6
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• pp.1137-1169
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• 2023

Let C be a curve and V → C an orthogonal vector bundle of rank r. For r ≤ 6, the structure of V can be described using tensor, symmetric and exterior products of bundles of lower rank, essentially due to the existence of exceptional isomorphisms between Spin(r, ℂ) and other groups for these r. We analyze these structures in detail, and in particular use them to describe moduli spaces of orthogonal bundles. Furthermore, the locus of isotropic vectors in V defines a quadric subfibration Q_V ⊂ ℙV . Using familiar results on quadrics of low dimension, we exhibit isomorphisms between isotropic Quot schemes of V and certain ordinary Quot schemes of line subbundles. In particular, for r ≤ 6 this gives a method for enumerating the isotropic subbundles of maximal degree of a general V , when there are finitely many.

• Proceedings of the IEEK Conference
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• 2000.11c
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• pp.109-112
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• 2000

Many applications in computer graphics require highly detailed complex models. However, the level of detail may vary considerably according to applications. It is often desirable to use approximations in place of excessively detailed models. We have developed a surface simplification algorithm which uses iterative contractions of edges to simplify models and maintains surface error approximations using a quadric metric. In this paper, we present an improved quadric error metric for simplifying meshes. The new metric, based on subdivided edge classification, results in more accurate simplified meshes. We show that a subdivided edge classification captures discontinuities efficiently. The new scheme is demonstrated on a variety of meshes.

• Proceedings of the Korea Information Processing Society Conference
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• 2010.11a
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• pp.779-782
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• 2010

Self-calibration에서 3차원 좌표의 복원은 호모그래피 행렬 H를 계산하면 얻을 수 있다. 이 호모그래피 행렬을 얻는 방법은 dual absolute quadric, Kruppa Equation(dual conic), plane at infinity(modulus constraint)를 사용하는 방법과 같이 세 가지 방법이 일반적으로 사용된다. 제안하는 방식은 dual absolute quadric을 사용한다. 카메라 내부 속성이 모든 뷰에서 동일하고 비틀림이나 영상의 원점이 중심이라는 가정을 두고 호모그래피 행렬 H를 계산한다. 실험을 통해서 주어진 가정으로 정밀한 복원이 가능함을 보였다.

• Korean Journal of Computational Design and Engineering
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• v.4 no.3
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• pp.173-179
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• 1999

In reverse engineering, when a shape containing multi-patched surfaces is digitized, the boundaries of these surfaces should be detected. The objective of this paper is to introduce a computationally efficient segmentation technique for extracting edges, ad partitioning the 3D measuring point data based on the location of the boundaries. The procedure begins with the identification of the edge points. An automatic edge-based approach is developed on the basis of local geometry. A parametric quadric surface approximation method is used to estimate the local surface curvature properties. the least-square approximation scheme minimizes the sum of the squares of the actual euclidean distance between the neighborhood data points and the parametric quadric surface. The surface curvatures and the principal directions are computed from the locally approximated surfaces. Edge points are identified as the curvature extremes, and zero-crossing, which are found from the estimated surface curvatures. After edge points are identified, edge-neighborhood chain-coding algorithm is used for forming boundary curves. The original point set is then broke down into subsets, which meet along the boundaries, by scan line algorithm. All point data are applied to each boundary loops to partition the points to different regions. Experimental results are presented to verify the developed method.