• Honam Mathematical Journal
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• v.28 no.1
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• pp.83-111
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• 2006

After introducing Tropical Algebraic Varieties, we give a polyhedral description of tropical hypersurfaces. Using TOPCOM and GAP, we show that there exist 59 types of two dimensional tropical quadric surfaces. We also show a criterion for a quadric hypersurface to be non-degenerate in terms of a tropical rank.

• Honam Mathematical Journal
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• v.38 no.3
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• pp.593-611
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• 2016

This paper is concerned with the classifications of quadric surfaces of first and second kinds in Euclidean 3-space satisfying the Jacobi condition with respect to their curvatures, the Gaussian curvature K, the mean curvature H, second mean curvature $H_{II}$ and second Gaussian curvature $K_{II}$. Also, we study the zero and non-zero constant curvatures of these surfaces. Furthermore, we investigated the (A, B)-Weingarten, (A, B)-linear Weingarten as well as some special ($C^2$, K) and $(C^2,\;K{\sqrt{K}})$-nonlinear Weingarten quadric surfaces in $E^3$, where $A{\neq}B$, A, $B{\in}{K,H,H_{II},K_{II}}$ and $C{\in}{H,H_{II},K_{II}}$. Finally, some important new lemmas are presented.

• 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.

• 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.

• 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.

• 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.

• 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.

• Journal of KIISE:Computer Systems and Theory
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• v.27 no.6
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• pp.541-548
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• 2000

An area light source in the three dimensional space shines past a scene polygon, to generate two types of shadow volumes for each scene polygon, i.e., one with partial occlusion and the other with the complete occlusion. These are called, penumbra and umbra, respectively. In this paper, consider the problem for computing the umbra of a convex polygon from convex quadric light sources such as circles, ellipses, spheres, ellipsoids and cylinders. First, we give characteristics of the boundary surfaces of the umbra and then propose an algorithm for generating the umbra using them.

• 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.

• Proceedings of the Korean Information Science Society Conference
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• 2001.04b
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• pp.610-612
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• 2001

본 논문은 이산 곡률을 확장된 QEM(Quadric Error Metrics)으로 변환한 새로운 메쉬 간략화 알고리즘을 제안한다. 이산 곡률이란 이산적인 표면으로 구성된 메쉬 표면의 곡률이며, 기하학 정보만을 이용하여 계산 가능하다. QEM은 간략화 오차를 평면과 한 점과의 거리 제곱의 합인 이차식으로 표현함으로써 빠른 간략화를 수행한다. 본 논문은 모서리 간략화 수행 시의 새로운 점과 주변 평면과의 거리 뿐만 아니라, 그 점에서의 이산 곡률을 계산한다. 즉, 간략화 오차에 거리와 곡률을 함께 고려하여 이차식으로 표현함으로써 빠르고 높은 품질의 간략화가 수행 가능하다.