• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.3
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• pp.217-224
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• 2009

In this paper we present an approximation method of quadric surface using quartic spline. Our method is based on the approximation of quadratic rational B$\acute{e}$zier patch using quartic B$\acute{e}$zier patch. We show that our approximation method yields $G^1$ (tangent plane) continuous quartic spline surface. We illustrate our results by the approximation of helicoid-like surface.

• East Asian mathematical journal
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• v.32 no.1
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• pp.93-100
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• 2016

The generalized Gaussian image of a spacelike surface in $L^n$ lies in the indefinite positive quadric ${\mathbb{Q}}_+^{n-2}$ in the open submanifold ${\mathbb{C}}P_+^{n-1}$ of the complex projective space ${\mathbb{C}}P^{n-1}$. The purpose of this paper is to find out detailed information about ${\mathbb{Q}}_+^{n-2}{\subset}{\mathbb{C}}P_+^{n-1}$.

• 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.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.547-557
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• 1998

In this paper, we study submanifolds in the Euclidean space with parallel normal mean curvature vectorand special quadric representation. Especially we give a complete classification result relative to surfaces satisfying these conditions.

• 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.

• 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.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.637-644
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• 2008

In this paper, we study some properties about the parallel surfaces of ruled surfaces in a Euclidean 3-space. Furthermore, we classify the parallel surfaces of ruled surfaces in a Euclidean 3-space satisfying a linear type and a quadric type with respect to the Gaussian curvature and the mean curvature.

• Proceedings of the IEEK Conference
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• 1999.11a
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• pp.448-451
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• 1999

In this paper, we propose a new object representation method and matching algorithm for object recognition using a 3-fingered robot hand. Each finger tip can measure normal vector and shapes of a contacting surface. Object is represented by the inter-surface description table where the features of a surface are described in the diagonal and the relations between two surfaces are in the upper diagonal. Based on this table, a fast and the efficient matching algorithm has been proposed. This algorithm can be applied to natural quadric objects.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.157.6-157
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• 2001

We estimated various neuron functions to construct of engineering neurons, which are the combination of sigmoid, linear, sine, quadric, double/single bended, soft max/minimum functions. These combinations are estimated by the property on the potential surface between the learning points, calculation speed, and learning convergence; because the surface depends on the inference ability of a neuron system; and speed and convergence are depend on the efficiency on the points of engineering applications. After the evaluating discussions, we can select more appropriate combination than original sigmoid function´s, which is single bended function and linear one. The combination ...