• KSII Transactions on Internet and Information Systems (TIIS)
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• 제11권6호
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• pp.2926-2945
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• 2017

In geo-location database oriented spectrum sharing system, the entire geographic area is divided into meshes to classify, store and delivery the cognitive information. In this paper, we propose a flexible polygon mesh division scheme to reduce the number of meshes. Hence the cognitive information can be reduced correspondingly. Besides, polygon mesh can approximate the real environment and reduce the error of cognitive information because the edges of polygon are selected along the boundaries of the networks. We have designed the polygon approximation algorithm and have analyzed the relation between the error and the number of polygon's edges. Finally, the simulation results are provided to verify the algorithm and analysis. The polygon mesh division scheme in this paper provides an efficient approach for cognitive information organization in database oriented spectrum sharing system.

• 한국생산제조학회지
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• 제9권1호
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• pp.68-74
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• 2000

The STL file format is an approximation of 3-D model with triangular facets. STL is a standard input file format of Rapid Prototyping(RP) equipment In computer graphics a circle has been approximated with an inscribed polygon which causes an error between the real and approximated circles. In this study an intersecting polygon has been used to approximate the circle and applied to produce more accurate RP part. The newly proposed method shows it's excellence in part accuracy.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 1999년도 춘계학술대회 논문집
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• pp.81-86
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• 1999

The STL file format is an approximation of 3-D model with triangular facets. STL is a standard input file format of Rapid Prototyping(RP) equipment. In computer graphics, a circle has been approximated with an inscribed polygon, which causes an error between the real and approximated circles. In this study, an intersecting polygon has been used to approximate the circle and applied to produce more accurate RP part. The newly proposed method shows it's excellence in part accuracy.

• International Journal of Ocean System Engineering
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• 제3권1호
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• pp.22-32
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• 2013

A heuristic physical theory of diffraction (PTD) for an acoustic impedance wedge is proposed. This method is based on Ufimtsev's three-dimensional PTD, which is derived for an acoustic soft or hard wedge. We modify the original PTD according to the process of physical optics (or the Kirchhoff approximation) to obtain a 3D heuristic diffraction model for an impedance wedge. In principle, our result is equivalent to Luebbers' model presented in electromagnetism. Moreover, our approach provides a useful insight into the theoretical basis of the existing heuristic diffraction methods. The derived heuristic PTD is applied to an arbitrary impedance polygon, and a simple PTD formula is derived as a supplement to the physical optics formula.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.575-584
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• 2006

In this paper we introduce a discrete tangent vector of a polygon defined on each vertex by a linear combination of forward difference and backward difference, and show that if the polygon is originated from a smooth curve then direction of the discrete tangent vector is a second order approximation of the direction of the tangent vector of the original curve. Using this discrete tangent vector, we also introduced the geometric cubic Hermite interpolation of a polygon with controlled initial and terminal speed of the curve segments proportional to the edge length. In this case the whole interpolation is $C^1$. Experiments suggest that about $90\%$ of the edge length is the best fit for the initial and terminal speeds.

• 융합신호처리학회 학술대회논문집
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• 한국신호처리시스템학회 2000년도 추계종합학술대회논문집
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• pp.93-96
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• 2000

본 논문에서는 2D 자연영상을 MPEG-4의 메쉬 구조로 압축/저장하기 위한 메쉬 구성(meshgeneration)의 전처리에 사용될 수 있도록, 특징점들을 블록기반의 웨터쉐드 영역분할과 다각형 근사화를 통해 추출하는 방법을 제안한다. 우선 2D 자연영상을 8$\times$8 또는 4$\times$4 블록 패턴분류를 이용한 웨터쉐드 분할을 이용하여 영역별로 분리해 낸다 이렇게 분할된 영역의 구분선을 이루는 화소들은 영상의 특징을 나타내며, 이들은 폐곡선을 이루게 된다. 이들 폐곡선 위의 연속적인 화소들을 다각형 근사화와 중복 정점을 제거하는 후처리를 이용해 특징점으로 얻어낸다.

• 대한수학회논문집
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• 제22권4호
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• pp.641-648
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• 2007

In this paper, we present the exact Hausdorff distance between the offset curve of quadratic $B\'{e}zier$ curve and its quadratic $GC^1$ approximation. To illustrate the formula for the Hausdorff distance, we give an example of the quadratic $GC^1$ approximation of the offset curve of a quadratic $B\'{e}zier$ curve.

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.245-250
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• 2002

Consider the Convex Polygon Pm={Al , A2, ‥‥, Am} With Vertex points A$\_$i/ = (a$\_$i/, b$\_$i/),i : 1,‥‥, m, interior P$\^$0/$\_$m/, and length of perimeter denoted by L(P$\_$m/). Let R$\_$n/ = {B$_1$,B$_2$,‥‥,B$\_$n/), where B$\_$i/=(x$\_$i/,y$\_$I/), i =1,‥‥, n, denote a regular polygon with n sides of equal length and equal interior angle. Kaiser[4] used the regular polygon R$\_$n/ to approximate P$\_$m/, and the problem examined in his work is to position R$\_$n/ with respect to P$\_$m/ to minimize the area of the symmetric difference between the two figures. In this paper we give the quality of a approximating regular polygon R$\_$n/ to approximate P$\_$m/.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제27권1호
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• pp.37-55
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• 2023

In this paper we propose a new algorithm for detecting and counting flowers in a complex background based on digital images. The algorithm mainly includes the following parts: edge contour extraction of flowers, edge contour determination of overlapped flowers and flower counting. We use a contour detection technique in Computer Vision (CV) to extract the edge contours of flowers and propose an improved algorithm with a concave point detection technique to find accurate segmentation for overlapped flowers. In this process, we first use the polygon approximation to smooth edge contours and then adopt the second-order central moments to fit ellipse contours to determine whether edge contours overlap. To obtain accurate segmentation points, we calculate the curvature of each pixel point on the edge contours with an improved Curvature Scale Space (CSS) corner detector. Finally, we successively give three adaptive judgment criteria to detect and count flowers accurately and automatically. Both experimental results and the proposed evaluation indicators reveal that the proposed algorithm is more efficient for flower counting.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.513-518
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• 2007

A polygon-wise constant curvature natural element approximation is presented in this paper for the numerical implementation of the abstract Kirchhoff plate model. The strict continuity requirement in the displacement field is relaxed by converting the area integral of the curvatures into the boundary integral along the Voronoi boundary. Curvatures and bending moments are assumed to be constant within each Voronoi polygon, and the Voronoi-polygon-wise constant curvatures are derived in a selective manner for the sake of the imposition of essential boundary conditions. The numerical results illustrating the proposed method are also given.